Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B

Percentage Accurate: 94.2% → 98.8%

Time: 11.3s

Alternatives: 21

Speedup: 0.9×

• 68.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (+
 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
 (/
  (+
   (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
   0.083333333333333)
  x)))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.2% accurate, 1.0× speedup

Math

\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (+
 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
 (/
  (+
   (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
   0.083333333333333)
  x)))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.9× speedup

Math

\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\left(\left(z \cdot y + z \cdot 0.0007936500793651\right) - 0.0027777777777778\right) \cdot \frac{z}{x} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  (+
 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
 (+
  (*
   (- (+ (* z y) (* z 0.0007936500793651)) 0.0027777777777778)
   (/ z x))
  (* 0.083333333333333 (/ 1.0 x)))))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((((z * y) + (z * 0.0007936500793651)) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (((((z * y) + (z * 0.0007936500793651d0)) - 0.0027777777777778d0) * (z / x)) + (0.083333333333333d0 * (1.0d0 / x)))
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (((((z * y) + (z * 0.0007936500793651)) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (((((z * y) + (z * 0.0007936500793651)) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(z * y) + Float64(z * 0.0007936500793651)) - 0.0027777777777778) * Float64(z / x)) + Float64(0.083333333333333 * Float64(1.0 / x))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((((z * y) + (z * 0.0007936500793651)) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(z * y), $MachinePrecision] + N[(z * 0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.2%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

2. Taylor expanded in z around 0

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right)} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}}\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000}} \cdot \frac{1}{x}\right) \]

   3. lower--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   5. lower-+.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   7. lower-/.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   8. lower-/.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   10. lower-/.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \color{blue}{\frac{1}{x}}\right) \]

   12. lower-/.f64 94.5%

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{\color{blue}{x}}\right) \]

4. Applied rewrites 94.5%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000}} \cdot \frac{1}{x}\right) \]

   2. lift--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   3. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   4. lift-/.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   5. mult-flip-rev N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{\frac{13888888888889}{5000000000000000}}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

6. Applied rewrites 98.8%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\left(\left(y - -0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot \frac{z}{x} + \color{blue}{0.083333333333333} \cdot \frac{1}{x}\right) \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   2. *-commutative N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   3. lift--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   4. metadata-eval N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   5. add-flip N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(\left(z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   7. *-commutative N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(\left(y \cdot z + z \cdot \frac{7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(\left(y \cdot z + z \cdot \frac{7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   9. lower-+.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(\left(y \cdot z + z \cdot \frac{7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   10. lift-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(\left(y \cdot z + z \cdot \frac{7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   11. *-commutative N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(\left(z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   12. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(\left(\left(z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   13. lower-*.f64 98.8%

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\left(\left(z \cdot y + z \cdot 0.0007936500793651\right) - 0.0027777777777778\right) \cdot \frac{z}{x} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

8. Applied rewrites 98.8%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\left(\left(z \cdot y + z \cdot 0.0007936500793651\right) - 0.0027777777777778\right) \cdot \frac{z}{x} + 0.083333333333333 \cdot \frac{1}{x}\right) \]
9. Add Preprocessing

Alternative 2: 98.8% accurate, 0.9× speedup

Math

\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\left(\left(y - -0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot \frac{z}{x} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  (+
 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
 (+
  (* (- (* (- y -0.0007936500793651) z) 0.0027777777777778) (/ z x))
  (* 0.083333333333333 (/ 1.0 x)))))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((((y - -0.0007936500793651) * z) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (((((y - (-0.0007936500793651d0)) * z) - 0.0027777777777778d0) * (z / x)) + (0.083333333333333d0 * (1.0d0 / x)))
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (((((y - -0.0007936500793651) * z) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (((((y - -0.0007936500793651) * z) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(y - -0.0007936500793651) * z) - 0.0027777777777778) * Float64(z / x)) + Float64(0.083333333333333 * Float64(1.0 / x))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((((y - -0.0007936500793651) * z) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.2%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

2. Taylor expanded in z around 0

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right)} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}}\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000}} \cdot \frac{1}{x}\right) \]

   3. lower--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   5. lower-+.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   7. lower-/.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   8. lower-/.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   10. lower-/.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \color{blue}{\frac{1}{x}}\right) \]

   12. lower-/.f64 94.5%

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{\color{blue}{x}}\right) \]

4. Applied rewrites 94.5%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000}} \cdot \frac{1}{x}\right) \]

   2. lift--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   3. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   4. lift-/.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   5. mult-flip-rev N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{\frac{13888888888889}{5000000000000000}}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

6. Applied rewrites 98.8%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\left(\left(y - -0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot \frac{z}{x} + \color{blue}{0.083333333333333} \cdot \frac{1}{x}\right) \]
7. Add Preprocessing

Alternative 3: 97.8% accurate, 0.9× speedup

Math

\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\frac{0.083333333333333}{x} - \frac{0.0027777777777778 - \left(y - -0.0007936500793651\right) \cdot z}{x} \cdot z\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  (+
 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
 (-
  (/ 0.083333333333333 x)
  (* (/ (- 0.0027777777777778 (* (- y -0.0007936500793651) z)) x) z))))

C

double code(double x, double y, double z) {
	return ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 / x) - (((0.0027777777777778 - ((y - -0.0007936500793651) * z)) / x) * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((0.083333333333333d0 / x) - (((0.0027777777777778d0 - ((y - (-0.0007936500793651d0)) * z)) / x) * z))
end function

Java

public static double code(double x, double y, double z) {
	return ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 / x) - (((0.0027777777777778 - ((y - -0.0007936500793651) * z)) / x) * z));
}

Python

def code(x, y, z):
	return ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((0.083333333333333 / x) - (((0.0027777777777778 - ((y - -0.0007936500793651) * z)) / x) * z))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(0.083333333333333 / x) - Float64(Float64(Float64(0.0027777777777778 - Float64(Float64(y - -0.0007936500793651) * z)) / x) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((0.083333333333333 / x) - (((0.0027777777777778 - ((y - -0.0007936500793651) * z)) / x) * z));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(0.083333333333333 / x), $MachinePrecision] - N[(N[(N[(0.0027777777777778 - N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.2%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

   2. *-commutative N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   3. lift--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   4. sub-flip N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   5. distribute-rgt-in N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   6. fp-cancel-sign-sub-inv N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   7. lower--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   8. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   10. *-commutative N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   12. lift-+.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   13. add-flip N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   14. lower--.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   15. metadata-eval N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   16. remove-double-neg N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   17. lower-*.f64 94.2%

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

3. Applied rewrites 94.2%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

5. Applied rewrites 97.8%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(\frac{0.083333333333333}{x} - \frac{0.0027777777777778 - \left(y - -0.0007936500793651\right) \cdot z}{x} \cdot z\right)} \]
6. Add Preprocessing

Alternative 4: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;t\_0 + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_0 + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(\left(\left(y - -0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot \frac{z}{x} + 0.083333333333333 \cdot \frac{1}{x}\right)\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)))
  (if (<=
       (+
        t_0
        (/
         (+
          (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
          0.083333333333333)
         x))
       2e+307)
    (+
     t_0
     (/
      (+
       (-
        (* (* z (- y -0.0007936500793651)) z)
        (* 0.0027777777777778 z))
       0.083333333333333)
      x))
    (+
     (+ 0.91893853320467 (* -0.5 (log x)))
     (+
      (*
       (- (* (- y -0.0007936500793651) z) 0.0027777777777778)
       (/ z x))
      (* 0.083333333333333 (/ 1.0 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (((x - 0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307) {
		tmp = t_0 + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	} else {
		tmp = (0.91893853320467 + (-0.5 * log(x))) + (((((y - -0.0007936500793651) * z) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0
    if ((t_0 + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)) <= 2d+307) then
        tmp = t_0 + (((((z * (y - (-0.0007936500793651d0))) * z) - (0.0027777777777778d0 * z)) + 0.083333333333333d0) / x)
    else
        tmp = (0.91893853320467d0 + ((-0.5d0) * log(x))) + (((((y - (-0.0007936500793651d0)) * z) - 0.0027777777777778d0) * (z / x)) + (0.083333333333333d0 * (1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((x - 0.5) * Math.log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307) {
		tmp = t_0 + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	} else {
		tmp = (0.91893853320467 + (-0.5 * Math.log(x))) + (((((y - -0.0007936500793651) * z) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x - 0.5) * math.log(x)) - x) + 0.91893853320467
	tmp = 0
	if (t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307:
		tmp = t_0 + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x)
	else:
		tmp = (0.91893853320467 + (-0.5 * math.log(x))) + (((((y - -0.0007936500793651) * z) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if (Float64(t_0 + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307)
		tmp = Float64(t_0 + Float64(Float64(Float64(Float64(Float64(z * Float64(y - -0.0007936500793651)) * z) - Float64(0.0027777777777778 * z)) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(Float64(Float64(Float64(y - -0.0007936500793651) * z) - 0.0027777777777778) * Float64(z / x)) + Float64(0.083333333333333 * Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((x - 0.5) * log(x)) - x) + 0.91893853320467;
	tmp = 0.0;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307)
		tmp = t_0 + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	else
		tmp = (0.91893853320467 + (-0.5 * log(x))) + (((((y - -0.0007936500793651) * z) - 0.0027777777777778) * (z / x)) + (0.083333333333333 * (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[LessEqual[N[(t$95$0 + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], 2e+307], N[(t$95$0 + N[(N[(N[(N[(N[(z * N[(y - -0.0007936500793651), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] - N[(0.0027777777777778 * z), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision] + N[(0.083333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x)) < 2e307

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   if 2e307 < (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x))

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right)} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000}} \cdot \frac{1}{x}\right) \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      8. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      10. lower-/.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \color{blue}{\frac{1}{x}}\right) \]

      12. lower-/.f64 94.5%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{\color{blue}{x}}\right) \]

   4. Applied rewrites 94.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\left(z \cdot \left(z \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) - 0.0027777777777778 \cdot \frac{1}{x}\right) + 0.083333333333333 \cdot \frac{1}{x}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \color{blue}{\frac{83333333333333}{1000000000000000}} \cdot \frac{1}{x}\right) \]

      2. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{13888888888889}{5000000000000000} \cdot \frac{1}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      5. mult-flip-rev N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \left(z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) - \frac{\frac{13888888888889}{5000000000000000}}{x}\right) + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

   6. Applied rewrites 98.8%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\left(\left(y - -0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot \frac{z}{x} + \color{blue}{0.083333333333333} \cdot \frac{1}{x}\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \left(\left(\left(y - -0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot \frac{z}{x} + 0.083333333333333 \cdot \frac{1}{x}\right) \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \color{blue}{\frac{-1}{2} \cdot \log x}\right) + \left(\left(\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \color{blue}{\log x}\right) + \left(\left(\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot \frac{z}{x} + \frac{83333333333333}{1000000000000000} \cdot \frac{1}{x}\right) \]

      3. lower-log.f64 65.4%

         \[\leadsto \left(0.91893853320467 + -0.5 \cdot \log x\right) + \left(\left(\left(y - -0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot \frac{z}{x} + 0.083333333333333 \cdot \frac{1}{x}\right) \]

   9. Applied rewrites 65.4%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \left(\left(\left(y - -0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot \frac{z}{x} + 0.083333333333333 \cdot \frac{1}{x}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;t\_0 + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_0 + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)))
  (if (<=
       (+
        t_0
        (/
         (+
          (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
          0.083333333333333)
         x))
       2e+307)
    (+
     t_0
     (/
      (+
       (-
        (* (* z (- y -0.0007936500793651)) z)
        (* 0.0027777777777778 z))
       0.083333333333333)
      x))
    (* (/ 1.0 (/ x (* (- y -0.0007936500793651) z))) z))))

C

double code(double x, double y, double z) {
	double t_0 = (((x - 0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307) {
		tmp = t_0 + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0
    if ((t_0 + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)) <= 2d+307) then
        tmp = t_0 + (((((z * (y - (-0.0007936500793651d0))) * z) - (0.0027777777777778d0 * z)) + 0.083333333333333d0) / x)
    else
        tmp = (1.0d0 / (x / ((y - (-0.0007936500793651d0)) * z))) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((x - 0.5) * Math.log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307) {
		tmp = t_0 + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x - 0.5) * math.log(x)) - x) + 0.91893853320467
	tmp = 0
	if (t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307:
		tmp = t_0 + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x)
	else:
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if (Float64(t_0 + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307)
		tmp = Float64(t_0 + Float64(Float64(Float64(Float64(Float64(z * Float64(y - -0.0007936500793651)) * z) - Float64(0.0027777777777778 * z)) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(1.0 / Float64(x / Float64(Float64(y - -0.0007936500793651) * z))) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((x - 0.5) * log(x)) - x) + 0.91893853320467;
	tmp = 0.0;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307)
		tmp = t_0 + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	else
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[LessEqual[N[(t$95$0 + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], 2e+307], N[(t$95$0 + N[(N[(N[(N[(N[(z * N[(y - -0.0007936500793651), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] - N[(0.0027777777777778 * z), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(x / N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x)) < 2e307

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   if 2e307 < (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x))

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      7. lower-*.f64 43.5%

         \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      8. lift-+.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      10. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      11. mult-flip-rev N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      13. div-add-rev N/A

          \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      15. add-flip N/A

          \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

      16. metadata-eval N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      17. lift--.f64 N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      18. lower-/.f64 43.5%

          \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

   8. Applied rewrites 43.5%

      \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      5. lift--.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      6. metadata-eval N/A

         \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

      7. add-flip N/A

         \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      8. distribute-lft-out N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      11. lift-+.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      12. div-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      13. lower-unsound-/.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      14. lower-unsound-/.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot 0.0007936500793651}} \cdot z \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      18. distribute-lft-out N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}} \cdot z \]

      19. add-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}} \cdot z \]

      20. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      21. lift--.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      22. *-commutative N/A

          \[\leadsto \frac{1}{\frac{x}{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}} \cdot z \]

      23. lift-*.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]

   10. Applied rewrites 43.6%

       \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;t\_0 + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_0 + \frac{1}{x} \cdot \left(\left(z \cdot \left(y - -0.0007936500793651\right) - 0.0027777777777778\right) \cdot z - -0.083333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)))
  (if (<=
       (+
        t_0
        (/
         (+
          (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
          0.083333333333333)
         x))
       2e+307)
    (+
     t_0
     (*
      (/ 1.0 x)
      (-
       (* (- (* z (- y -0.0007936500793651)) 0.0027777777777778) z)
       -0.083333333333333)))
    (* (/ 1.0 (/ x (* (- y -0.0007936500793651) z))) z))))

C

double code(double x, double y, double z) {
	double t_0 = (((x - 0.5) * log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307) {
		tmp = t_0 + ((1.0 / x) * ((((z * (y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333));
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0
    if ((t_0 + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)) <= 2d+307) then
        tmp = t_0 + ((1.0d0 / x) * ((((z * (y - (-0.0007936500793651d0))) - 0.0027777777777778d0) * z) - (-0.083333333333333d0)))
    else
        tmp = (1.0d0 / (x / ((y - (-0.0007936500793651d0)) * z))) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (((x - 0.5) * Math.log(x)) - x) + 0.91893853320467;
	double tmp;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307) {
		tmp = t_0 + ((1.0 / x) * ((((z * (y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333));
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x - 0.5) * math.log(x)) - x) + 0.91893853320467
	tmp = 0
	if (t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307:
		tmp = t_0 + ((1.0 / x) * ((((z * (y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333))
	else:
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467)
	tmp = 0.0
	if (Float64(t_0 + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307)
		tmp = Float64(t_0 + Float64(Float64(1.0 / x) * Float64(Float64(Float64(Float64(z * Float64(y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333)));
	else
		tmp = Float64(Float64(1.0 / Float64(x / Float64(Float64(y - -0.0007936500793651) * z))) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (((x - 0.5) * log(x)) - x) + 0.91893853320467;
	tmp = 0.0;
	if ((t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307)
		tmp = t_0 + ((1.0 / x) * ((((z * (y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333));
	else
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision]}, If[LessEqual[N[(t$95$0 + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], 2e+307], N[(t$95$0 + N[(N[(1.0 / x), $MachinePrecision] * N[(N[(N[(N[(z * N[(y - -0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] - -0.083333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(x / N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x)) < 2e307

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x}} \]

      2. mult-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}\right) \cdot \frac{1}{x}} \]

      3. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{1}{x} \cdot \left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{1}{x} \cdot \left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}\right)} \]

      5. lower-/.f64 94.1%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{x}} \cdot \left(\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333\right) \]

      6. lift-+.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}\right)} \]

      7. add-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right)} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \left(\left(\color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z} - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \left(\left(\color{blue}{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)} - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \left(\left(\color{blue}{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)} - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right) \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)} - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right) \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)} - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right) \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)} - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{1}{x} \cdot \left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right) - \frac{13888888888889}{5000000000000000}\right) \cdot z - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right)\right) \]

      16. metadata-eval 94.1%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{1}{x} \cdot \left(\left(z \cdot \left(y - -0.0007936500793651\right) - 0.0027777777777778\right) \cdot z - \color{blue}{-0.083333333333333}\right) \]

   3. Applied rewrites 94.1%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \color{blue}{\frac{1}{x} \cdot \left(\left(z \cdot \left(y - -0.0007936500793651\right) - 0.0027777777777778\right) \cdot z - -0.083333333333333\right)} \]

   if 2e307 < (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x))

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      7. lower-*.f64 43.5%

         \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      8. lift-+.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      10. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      11. mult-flip-rev N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      13. div-add-rev N/A

          \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      15. add-flip N/A

          \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

      16. metadata-eval N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      17. lift--.f64 N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      18. lower-/.f64 43.5%

          \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

   8. Applied rewrites 43.5%

      \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      5. lift--.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      6. metadata-eval N/A

         \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

      7. add-flip N/A

         \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      8. distribute-lft-out N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      11. lift-+.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      12. div-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      13. lower-unsound-/.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      14. lower-unsound-/.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot 0.0007936500793651}} \cdot z \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      18. distribute-lft-out N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}} \cdot z \]

      19. add-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}} \cdot z \]

      20. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      21. lift--.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      22. *-commutative N/A

          \[\leadsto \frac{1}{\frac{x}{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}} \cdot z \]

      23. lift-*.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]

   10. Applied rewrites 43.6%

       \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\left(\frac{\left(z \cdot \left(y - -0.0007936500793651\right) - 0.0027777777777778\right) \cdot z - -0.083333333333333}{x} - -0.91893853320467\right) - \left(x - \log x \cdot \left(x - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<=
     (+
      (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
      (/
       (+
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
        0.083333333333333)
       x))
     2e+307)
  (-
   (-
    (/
     (-
      (* (- (* z (- y -0.0007936500793651)) 0.0027777777777778) z)
      -0.083333333333333)
     x)
    -0.91893853320467)
   (- x (* (log x) (- x 0.5))))
  (* (/ 1.0 (/ x (* (- y -0.0007936500793651) z))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307) {
		tmp = ((((((z * (y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333) / x) - -0.91893853320467) - (x - (log(x) * (x - 0.5)));
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)) <= 2d+307) then
        tmp = ((((((z * (y - (-0.0007936500793651d0))) - 0.0027777777777778d0) * z) - (-0.083333333333333d0)) / x) - (-0.91893853320467d0)) - (x - (log(x) * (x - 0.5d0)))
    else
        tmp = (1.0d0 / (x / ((y - (-0.0007936500793651d0)) * z))) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307) {
		tmp = ((((((z * (y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333) / x) - -0.91893853320467) - (x - (Math.log(x) * (x - 0.5)));
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307:
		tmp = ((((((z * (y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333) / x) - -0.91893853320467) - (x - (math.log(x) * (x - 0.5)))
	else:
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * Float64(y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333) / x) - -0.91893853320467) - Float64(x - Float64(log(x) * Float64(x - 0.5))));
	else
		tmp = Float64(Float64(1.0 / Float64(x / Float64(Float64(y - -0.0007936500793651) * z))) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)) <= 2e+307)
		tmp = ((((((z * (y - -0.0007936500793651)) - 0.0027777777777778) * z) - -0.083333333333333) / x) - -0.91893853320467) - (x - (log(x) * (x - 0.5)));
	else
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], 2e+307], N[(N[(N[(N[(N[(N[(N[(z * N[(y - -0.0007936500793651), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] - -0.083333333333333), $MachinePrecision] / x), $MachinePrecision] - -0.91893853320467), $MachinePrecision] - N[(x - N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(x / N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x)) < 2e307

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x}} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right)} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

      3. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \left(\frac{91893853320467}{100000000000000} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x}\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x}\right) + \left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right)} \]

      5. add-flip N/A

         \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x}\right) - \left(\mathsf{neg}\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right)\right)\right)} \]

      6. lift--.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x}\right) - \left(\mathsf{neg}\left(\color{blue}{\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right)}\right)\right) \]

      7. sub-negate-rev N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x}\right) - \color{blue}{\left(x - \left(x - \frac{1}{2}\right) \cdot \log x\right)} \]

      8. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x}\right) - \left(x - \left(x - \frac{1}{2}\right) \cdot \log x\right)} \]

   3. Applied rewrites 94.2%

      \[\leadsto \color{blue}{\left(\frac{\left(z \cdot \left(y - -0.0007936500793651\right) - 0.0027777777777778\right) \cdot z - -0.083333333333333}{x} - -0.91893853320467\right) - \left(x - \log x \cdot \left(x - 0.5\right)\right)} \]

   if 2e307 < (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x))

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      7. lower-*.f64 43.5%

         \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      8. lift-+.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      10. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      11. mult-flip-rev N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      13. div-add-rev N/A

          \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      15. add-flip N/A

          \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

      16. metadata-eval N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      17. lift--.f64 N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      18. lower-/.f64 43.5%

          \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

   8. Applied rewrites 43.5%

      \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      5. lift--.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      6. metadata-eval N/A

         \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

      7. add-flip N/A

         \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      8. distribute-lft-out N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      11. lift-+.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      12. div-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      13. lower-unsound-/.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      14. lower-unsound-/.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot 0.0007936500793651}} \cdot z \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      18. distribute-lft-out N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}} \cdot z \]

      19. add-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}} \cdot z \]

      20. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      21. lift--.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      22. *-commutative N/A

          \[\leadsto \frac{1}{\frac{x}{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}} \cdot z \]

      23. lift-*.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]

   10. Applied rewrites 43.6%

       \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0
        (+
         (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
         (/
          (+
           (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
           0.083333333333333)
          x))))
  (if (<= t_0 2e+307)
    t_0
    (* (/ 1.0 (/ x (* (- y -0.0007936500793651) z))) z))))

C

double code(double x, double y, double z) {
	double t_0 = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	double tmp;
	if (t_0 <= 2e+307) {
		tmp = t_0;
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    if (t_0 <= 2d+307) then
        tmp = t_0
    else
        tmp = (1.0d0 / (x / ((y - (-0.0007936500793651d0)) * z))) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	double tmp;
	if (t_0 <= 2e+307) {
		tmp = t_0;
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	tmp = 0
	if t_0 <= 2e+307:
		tmp = t_0
	else:
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x))
	tmp = 0.0
	if (t_0 <= 2e+307)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / Float64(x / Float64(Float64(y - -0.0007936500793651) * z))) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	tmp = 0.0;
	if (t_0 <= 2e+307)
		tmp = t_0;
	else
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+307], t$95$0, N[(N[(1.0 / N[(x / N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x)) < 2e307

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 2e307 < (+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) (log.f64 x)) x) #s(literal 91893853320467/100000000000000 binary64)) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) z) #s(literal 13888888888889/5000000000000000 binary64)) z) #s(literal 83333333333333/1000000000000000 binary64)) x))

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      7. lower-*.f64 43.5%

         \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      8. lift-+.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      10. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      11. mult-flip-rev N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      13. div-add-rev N/A

          \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      15. add-flip N/A

          \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

      16. metadata-eval N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      17. lift--.f64 N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      18. lower-/.f64 43.5%

          \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

   8. Applied rewrites 43.5%

      \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      5. lift--.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      6. metadata-eval N/A

         \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

      7. add-flip N/A

         \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      8. distribute-lft-out N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      11. lift-+.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      12. div-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      13. lower-unsound-/.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      14. lower-unsound-/.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot 0.0007936500793651}} \cdot z \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      18. distribute-lft-out N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}} \cdot z \]

      19. add-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}} \cdot z \]

      20. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      21. lift--.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      22. *-commutative N/A

          \[\leadsto \frac{1}{\frac{x}{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}} \cdot z \]

      23. lift-*.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]

   10. Applied rewrites 43.6%

       \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 86:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right) + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(y \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x 86.0)
  (+
   (+ 0.91893853320467 (* -0.5 (log x)))
   (/
    (+
     (-
      (* (* z (- y -0.0007936500793651)) z)
      (* 0.0027777777777778 z))
     0.083333333333333)
    x))
  (+
   (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
   (/ (+ (* (- (* y z) 0.0027777777777778) z) 0.083333333333333) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 86.0) {
		tmp = (0.91893853320467 + (-0.5 * log(x))) + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((((y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 86.0d0) then
        tmp = (0.91893853320467d0 + ((-0.5d0) * log(x))) + (((((z * (y - (-0.0007936500793651d0))) * z) - (0.0027777777777778d0 * z)) + 0.083333333333333d0) / x)
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (((((y * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 86.0) {
		tmp = (0.91893853320467 + (-0.5 * Math.log(x))) + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (((((y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 86.0:
		tmp = (0.91893853320467 + (-0.5 * math.log(x))) + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x)
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (((((y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 86.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(Float64(Float64(Float64(z * Float64(y - -0.0007936500793651)) * z) - Float64(0.0027777777777778 * z)) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 86.0)
		tmp = (0.91893853320467 + (-0.5 * log(x))) + (((((z * (y - -0.0007936500793651)) * z) - (0.0027777777777778 * z)) + 0.083333333333333) / x);
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((((y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 86.0], N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(z * N[(y - -0.0007936500793651), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] - N[(0.0027777777777778 * z), $MachinePrecision]), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(y * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 86

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right) + 0.083333333333333}{x} \]
   5. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \color{blue}{\frac{-1}{2} \cdot \log x}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \frac{13888888888889}{5000000000000000} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \color{blue}{\log x}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \frac{13888888888889}{5000000000000000} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lower-log.f64 63.3%

         \[\leadsto \left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right) + 0.083333333333333}{x} \]

   6. Applied rewrites 63.3%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right) + 0.083333333333333}{x} \]

   if 86 < x

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in y around inf

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\color{blue}{y \cdot z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. lower-*.f64 83.7%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(y \cdot \color{blue}{z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   4. Applied rewrites 83.7%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\color{blue}{y \cdot z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 86:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(y \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x 86.0)
  (+
   (+ 0.91893853320467 (* -0.5 (log x)))
   (/
    (+
     (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
     0.083333333333333)
    x))
  (+
   (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
   (/ (+ (* (- (* y z) 0.0027777777777778) z) 0.083333333333333) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 86.0) {
		tmp = (0.91893853320467 + (-0.5 * log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((((y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 86.0d0) then
        tmp = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (((((y * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 86.0) {
		tmp = (0.91893853320467 + (-0.5 * Math.log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (((((y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 86.0:
		tmp = (0.91893853320467 + (-0.5 * math.log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (((((y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 86.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(Float64(Float64(Float64(Float64(y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 86.0)
		tmp = (0.91893853320467 + (-0.5 * log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (((((y * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 86.0], N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(N[(y * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 86

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \color{blue}{\frac{-1}{2} \cdot \log x}\right) + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \color{blue}{\log x}\right) + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lower-log.f64 63.3%

         \[\leadsto \left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   4. Applied rewrites 63.3%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 86 < x

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in y around inf

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\color{blue}{y \cdot z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. lower-*.f64 83.7%

         \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(y \cdot \color{blue}{z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   4. Applied rewrites 83.7%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\color{blue}{y \cdot z} - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 98:\\ \;\;\;\;\left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x 98.0)
  (+
   (+ 0.91893853320467 (* -0.5 (log x)))
   (/
    (+
     (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
     0.083333333333333)
    x))
  (+
   (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
   (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 98.0) {
		tmp = (0.91893853320467 + (-0.5 * log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 98.0d0) then
        tmp = (0.91893853320467d0 + ((-0.5d0) * log(x))) + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 98.0) {
		tmp = (0.91893853320467 + (-0.5 * Math.log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 98.0:
		tmp = (0.91893853320467 + (-0.5 * math.log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 98.0)
		tmp = Float64(Float64(0.91893853320467 + Float64(-0.5 * log(x))) + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 98.0)
		tmp = (0.91893853320467 + (-0.5 * log(x))) + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 98.0], N[(N[(0.91893853320467 + N[(-0.5 * N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y + 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] - 0.0027777777777778), $MachinePrecision] * z), $MachinePrecision] + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 98

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \log x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \color{blue}{\frac{-1}{2} \cdot \log x}\right) + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{91893853320467}{100000000000000} + \frac{-1}{2} \cdot \color{blue}{\log x}\right) + \frac{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lower-log.f64 63.3%

         \[\leadsto \left(0.91893853320467 + -0.5 \cdot \log x\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   4. Applied rewrites 63.3%

      \[\leadsto \color{blue}{\left(0.91893853320467 + -0.5 \cdot \log x\right)} + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   if 98 < x

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\frac{83333333333333}{1000000000000000}}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333}}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 84.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 98:\\ \;\;\;\;\frac{\left(0.083333333333333 + {z}^{2} \cdot \left(0.0007936500793651 + y\right)\right) - 0.0027777777777778 \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x 98.0)
  (/
   (-
    (+ 0.083333333333333 (* (pow z 2.0) (+ 0.0007936500793651 y)))
    (* 0.0027777777777778 z))
   x)
  (+
   (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
   (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 98.0) {
		tmp = ((0.083333333333333 + (pow(z, 2.0) * (0.0007936500793651 + y))) - (0.0027777777777778 * z)) / x;
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 98.0d0) then
        tmp = ((0.083333333333333d0 + ((z ** 2.0d0) * (0.0007936500793651d0 + y))) - (0.0027777777777778d0 * z)) / x
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 98.0) {
		tmp = ((0.083333333333333 + (Math.pow(z, 2.0) * (0.0007936500793651 + y))) - (0.0027777777777778 * z)) / x;
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 98.0:
		tmp = ((0.083333333333333 + (math.pow(z, 2.0) * (0.0007936500793651 + y))) - (0.0027777777777778 * z)) / x
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 98.0)
		tmp = Float64(Float64(Float64(0.083333333333333 + Float64((z ^ 2.0) * Float64(0.0007936500793651 + y))) - Float64(0.0027777777777778 * z)) / x);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 98.0)
		tmp = ((0.083333333333333 + ((z ^ 2.0) * (0.0007936500793651 + y))) - (0.0027777777777778 * z)) / x;
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 98.0], N[(N[(N[(0.083333333333333 + N[(N[Power[z, 2.0], $MachinePrecision] * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(0.0027777777777778 * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 98

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      7. lower-*.f64 43.5%

         \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      8. lift-+.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      10. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      11. mult-flip-rev N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      13. div-add-rev N/A

          \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      15. add-flip N/A

          \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

      16. metadata-eval N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      17. lift--.f64 N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      18. lower-/.f64 43.5%

          \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

   8. Applied rewrites 43.5%

      \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\left(\frac{83333333333333}{1000000000000000} + {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)\right) - \frac{13888888888889}{5000000000000000} \cdot z}{x}} \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{\left(\frac{83333333333333}{1000000000000000} + {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)\right) - \frac{13888888888889}{5000000000000000} \cdot z}{\color{blue}{x}} \]

       2. lower--.f64 N/A

          \[\leadsto \frac{\left(\frac{83333333333333}{1000000000000000} + {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)\right) - \frac{13888888888889}{5000000000000000} \cdot z}{x} \]

       3. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{83333333333333}{1000000000000000} + {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)\right) - \frac{13888888888889}{5000000000000000} \cdot z}{x} \]

       4. lower-*.f64 N/A

          \[\leadsto \frac{\left(\frac{83333333333333}{1000000000000000} + {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)\right) - \frac{13888888888889}{5000000000000000} \cdot z}{x} \]

       5. lower-pow.f64 N/A

          \[\leadsto \frac{\left(\frac{83333333333333}{1000000000000000} + {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)\right) - \frac{13888888888889}{5000000000000000} \cdot z}{x} \]

       6. lower-+.f64 N/A

          \[\leadsto \frac{\left(\frac{83333333333333}{1000000000000000} + {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)\right) - \frac{13888888888889}{5000000000000000} \cdot z}{x} \]

       7. lower-*.f64 63.6%

          \[\leadsto \frac{\left(0.083333333333333 + {z}^{2} \cdot \left(0.0007936500793651 + y\right)\right) - 0.0027777777777778 \cdot z}{x} \]

   11. Applied rewrites 63.6%

       \[\leadsto \color{blue}{\frac{\left(0.083333333333333 + {z}^{2} \cdot \left(0.0007936500793651 + y\right)\right) - 0.0027777777777778 \cdot z}{x}} \]

   if 98 < x

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\frac{83333333333333}{1000000000000000}}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333}}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 84.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 98:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x 98.0)
  (/
   (+
    0.083333333333333
    (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
   x)
  (+
   (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
   (/ 0.083333333333333 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 98.0) {
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 98.0d0) then
        tmp = (0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x
    else
        tmp = ((((x - 0.5d0) * log(x)) - x) + 0.91893853320467d0) + (0.083333333333333d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 98.0) {
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	} else {
		tmp = ((((x - 0.5) * Math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 98.0:
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x
	else:
		tmp = ((((x - 0.5) * math.log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 98.0)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	else
		tmp = Float64(Float64(Float64(Float64(Float64(x - 0.5) * log(x)) - x) + 0.91893853320467) + Float64(0.083333333333333 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 98.0)
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	else
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + (0.083333333333333 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 98.0], N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 98

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\frac{83333333333333}{1000000000000000}}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333}}{x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) \cdot x + \frac{83333333333333}{1000000000000000}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) \cdot x + \frac{83333333333333}{1000000000000000}}{x}} \]

   6. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\frac{\left(\log x \cdot \left(x - 0.5\right) - \left(x - 0.91893853320467\right)\right) \cdot x + 0.083333333333333}{x}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + \color{blue}{z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \color{blue}{\left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \color{blue}{\frac{13888888888889}{5000000000000000}}\right)}{x} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]

      5. lower-+.f64 63.7%

         \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   9. Applied rewrites 63.7%

      \[\leadsto \frac{\color{blue}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}}{x} \]

   if 98 < x

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\frac{83333333333333}{1000000000000000}}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333}}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 84.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.083333333333333}{x} + \left(\log x - 1\right) \cdot x\right) - -0.91893853320467\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x 3.8e+19)
  (/
   (+
    0.083333333333333
    (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
   x)
  (-
   (+ (/ 0.083333333333333 x) (* (- (log x) 1.0) x))
   -0.91893853320467)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.8e+19) {
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	} else {
		tmp = ((0.083333333333333 / x) + ((log(x) - 1.0) * x)) - -0.91893853320467;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 3.8d+19) then
        tmp = (0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x
    else
        tmp = ((0.083333333333333d0 / x) + ((log(x) - 1.0d0) * x)) - (-0.91893853320467d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.8e+19) {
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	} else {
		tmp = ((0.083333333333333 / x) + ((Math.log(x) - 1.0) * x)) - -0.91893853320467;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 3.8e+19:
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x
	else:
		tmp = ((0.083333333333333 / x) + ((math.log(x) - 1.0) * x)) - -0.91893853320467
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.8e+19)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	else
		tmp = Float64(Float64(Float64(0.083333333333333 / x) + Float64(Float64(log(x) - 1.0) * x)) - -0.91893853320467);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 3.8e+19)
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	else
		tmp = ((0.083333333333333 / x) + ((log(x) - 1.0) * x)) - -0.91893853320467;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.8e+19], N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(0.083333333333333 / x), $MachinePrecision] + N[(N[(N[Log[x], $MachinePrecision] - 1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - -0.91893853320467), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.8e19

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\frac{83333333333333}{1000000000000000}}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333}}{x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) \cdot x + \frac{83333333333333}{1000000000000000}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) \cdot x + \frac{83333333333333}{1000000000000000}}{x}} \]

   6. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\frac{\left(\log x \cdot \left(x - 0.5\right) - \left(x - 0.91893853320467\right)\right) \cdot x + 0.083333333333333}{x}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + \color{blue}{z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \color{blue}{\left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \color{blue}{\frac{13888888888889}{5000000000000000}}\right)}{x} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]

      5. lower-+.f64 63.7%

         \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   9. Applied rewrites 63.7%

      \[\leadsto \frac{\color{blue}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}}{x} \]

   if 3.8e19 < x

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\frac{83333333333333}{1000000000000000}}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333}}{x} \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \color{blue}{\left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x} \]

      2. lower--.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - \color{blue}{1}\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x} \]

      4. lower-log.f64 N/A

         \[\leadsto \left(x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x} \]

      5. lower-/.f64 56.5%

         \[\leadsto \left(x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]

   7. Applied rewrites 56.5%

      \[\leadsto \left(\color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + 0.91893853320467\right) + \frac{0.083333333333333}{x} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\frac{83333333333333}{1000000000000000}}{x} + \left(x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) + \frac{91893853320467}{100000000000000}\right)} \]

      3. lift-+.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{x} + \color{blue}{\left(x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) + \frac{91893853320467}{100000000000000}\right)} \]

      4. add-flip N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000}}{x} + \color{blue}{\left(x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) - \left(\mathsf{neg}\left(\frac{91893853320467}{100000000000000}\right)\right)\right)} \]

      5. associate-+r- N/A

         \[\leadsto \color{blue}{\left(\frac{\frac{83333333333333}{1000000000000000}}{x} + x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)\right) - \left(\mathsf{neg}\left(\frac{91893853320467}{100000000000000}\right)\right)} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{\frac{83333333333333}{1000000000000000}}{x} + x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)\right) - \left(\mathsf{neg}\left(\frac{91893853320467}{100000000000000}\right)\right)} \]

   9. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\left(\frac{0.083333333333333}{x} + \left(\log x - 1\right) \cdot x\right) - -0.91893853320467} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 65.5% accurate, 4.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 61000000000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - -0.0007936500793651\right) \cdot z}{x} \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x 61000000000.0)
  (/
   (+
    0.083333333333333
    (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
   x)
  (* (/ (* (- y -0.0007936500793651) z) x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 61000000000.0) {
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	} else {
		tmp = (((y - -0.0007936500793651) * z) / x) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 61000000000.0d0) then
        tmp = (0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x
    else
        tmp = (((y - (-0.0007936500793651d0)) * z) / x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 61000000000.0) {
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	} else {
		tmp = (((y - -0.0007936500793651) * z) / x) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 61000000000.0:
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x
	else:
		tmp = (((y - -0.0007936500793651) * z) / x) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 61000000000.0)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	else
		tmp = Float64(Float64(Float64(Float64(y - -0.0007936500793651) * z) / x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 61000000000.0)
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	else
		tmp = (((y - -0.0007936500793651) * z) / x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 61000000000.0], N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.1e10

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\frac{83333333333333}{1000000000000000}}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333}}{x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) \cdot x + \frac{83333333333333}{1000000000000000}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) \cdot x + \frac{83333333333333}{1000000000000000}}{x}} \]

   6. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\frac{\left(\log x \cdot \left(x - 0.5\right) - \left(x - 0.91893853320467\right)\right) \cdot x + 0.083333333333333}{x}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + \color{blue}{z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \color{blue}{\left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \color{blue}{\frac{13888888888889}{5000000000000000}}\right)}{x} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]

      5. lower-+.f64 63.7%

         \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   9. Applied rewrites 63.7%

      \[\leadsto \frac{\color{blue}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}}{x} \]

   if 6.1e10 < x

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      7. lower-*.f64 43.5%

         \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      8. lift-+.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      10. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      11. mult-flip-rev N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      13. div-add-rev N/A

          \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      15. add-flip N/A

          \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

      16. metadata-eval N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      17. lift--.f64 N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      18. lower-/.f64 43.5%

          \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

   8. Applied rewrites 43.5%

      \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      5. lift--.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      6. metadata-eval N/A

         \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

      7. add-flip N/A

         \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      8. distribute-lft-out N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      11. lift-+.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      12. lower-/.f64 43.6%

          \[\leadsto \frac{z \cdot y + z \cdot 0.0007936500793651}{x} \cdot z \]

      13. lift-+.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      14. lift-*.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      15. lift-*.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      16. distribute-lft-out N/A

          \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      17. add-flip N/A

          \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

      18. metadata-eval N/A

          \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      19. lift--.f64 N/A

          \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      20. *-commutative N/A

          \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

      21. lift-*.f64 43.6%

          \[\leadsto \frac{\left(y - -0.0007936500793651\right) \cdot z}{x} \cdot z \]

   10. Applied rewrites 43.6%

       \[\leadsto \frac{\left(y - -0.0007936500793651\right) \cdot z}{x} \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 65.5% accurate, 3.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 61000000000:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (if (<= x 61000000000.0)
  (/
   (+
    0.083333333333333
    (* z (- (* z (+ 0.0007936500793651 y)) 0.0027777777777778)))
   x)
  (* (/ 1.0 (/ x (* (- y -0.0007936500793651) z))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 61000000000.0) {
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 61000000000.0d0) then
        tmp = (0.083333333333333d0 + (z * ((z * (0.0007936500793651d0 + y)) - 0.0027777777777778d0))) / x
    else
        tmp = (1.0d0 / (x / ((y - (-0.0007936500793651d0)) * z))) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 61000000000.0) {
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	} else {
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 61000000000.0:
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x
	else:
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 61000000000.0)
		tmp = Float64(Float64(0.083333333333333 + Float64(z * Float64(Float64(z * Float64(0.0007936500793651 + y)) - 0.0027777777777778))) / x);
	else
		tmp = Float64(Float64(1.0 / Float64(x / Float64(Float64(y - -0.0007936500793651) * z))) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 61000000000.0)
		tmp = (0.083333333333333 + (z * ((z * (0.0007936500793651 + y)) - 0.0027777777777778))) / x;
	else
		tmp = (1.0 / (x / ((y - -0.0007936500793651) * z))) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 61000000000.0], N[(N[(0.083333333333333 + N[(z * N[(N[(z * N[(0.0007936500793651 + y), $MachinePrecision]), $MachinePrecision] - 0.0027777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(1.0 / N[(x / N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.1e10

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]

   2. Taylor expanded in z around 0

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\frac{83333333333333}{1000000000000000}}}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 57.5%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{0.083333333333333}}{x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{\frac{83333333333333}{1000000000000000}}{x}} \]

      3. add-to-fraction N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) \cdot x + \frac{83333333333333}{1000000000000000}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) \cdot x + \frac{83333333333333}{1000000000000000}}{x}} \]

   6. Applied rewrites 40.6%

      \[\leadsto \color{blue}{\frac{\left(\log x \cdot \left(x - 0.5\right) - \left(x - 0.91893853320467\right)\right) \cdot x + 0.083333333333333}{x}} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + \color{blue}{z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \color{blue}{\left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}}{x} \]

      3. lower--.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \color{blue}{\frac{13888888888889}{5000000000000000}}\right)}{x} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\frac{83333333333333}{1000000000000000} + z \cdot \left(z \cdot \left(\frac{7936500793651}{10000000000000000} + y\right) - \frac{13888888888889}{5000000000000000}\right)}{x} \]

      5. lower-+.f64 63.7%

         \[\leadsto \frac{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}{x} \]

   9. Applied rewrites 63.7%

      \[\leadsto \frac{\color{blue}{0.083333333333333 + z \cdot \left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778\right)}}{x} \]

   if 6.1e10 < x

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      7. lower-*.f64 43.5%

         \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      8. lift-+.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      10. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      11. mult-flip-rev N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      13. div-add-rev N/A

          \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      15. add-flip N/A

          \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

      16. metadata-eval N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      17. lift--.f64 N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      18. lower-/.f64 43.5%

          \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

   8. Applied rewrites 43.5%

      \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      2. lift-/.f64 N/A

         \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      3. associate-*l/ N/A

         \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

      4. *-commutative N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      5. lift--.f64 N/A

         \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      6. metadata-eval N/A

         \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

      7. add-flip N/A

         \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

      8. distribute-lft-out N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      10. lift-*.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      11. lift-+.f64 N/A

          \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

      12. div-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      13. lower-unsound-/.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      14. lower-unsound-/.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot 0.0007936500793651}} \cdot z \]

      15. lift-+.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      16. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      17. lift-*.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}} \cdot z \]

      18. distribute-lft-out N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}} \cdot z \]

      19. add-flip N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}} \cdot z \]

      20. metadata-eval N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      21. lift--.f64 N/A

          \[\leadsto \frac{1}{\frac{x}{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}} \cdot z \]

      22. *-commutative N/A

          \[\leadsto \frac{1}{\frac{x}{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}} \cdot z \]

      23. lift-*.f64 43.6%

          \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]

   10. Applied rewrites 43.6%

       \[\leadsto \frac{1}{\frac{x}{\left(y - -0.0007936500793651\right) \cdot z}} \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 44.4% accurate, 5.9× speedup

Math

\[\frac{\left(y - -0.0007936500793651\right) \cdot z}{x} \cdot z \]

FPCore

(FPCore (x y z)
  :precision binary64
  (* (/ (* (- y -0.0007936500793651) z) x) z))

C

double code(double x, double y, double z) {
	return (((y - -0.0007936500793651) * z) / x) * z;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (((y - (-0.0007936500793651d0)) * z) / x) * z
end function

Java

public static double code(double x, double y, double z) {
	return (((y - -0.0007936500793651) * z) / x) * z;
}

Python

def code(x, y, z):
	return (((y - -0.0007936500793651) * z) / x) * z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(y - -0.0007936500793651) * z) / x) * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (((y - -0.0007936500793651) * z) / x) * z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] * z), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 94.2%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

   2. *-commutative N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   3. lift--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   4. sub-flip N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   5. distribute-rgt-in N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   6. fp-cancel-sign-sub-inv N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   7. lower--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   8. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   10. *-commutative N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   12. lift-+.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   13. add-flip N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   14. lower--.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   15. metadata-eval N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   16. remove-double-neg N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   17. lower-*.f64 94.2%

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

3. Applied rewrites 94.2%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

4. Taylor expanded in z around inf

   \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
5. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

   2. lower-pow.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

   3. lower-+.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

   5. lower-/.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

   6. lower-/.f64 41.7%

      \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

6. Applied rewrites 41.7%

   \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

   2. *-commutative N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

   3. lift-pow.f64 N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

   4. unpow2 N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

   5. associate-*r* N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

   7. lower-*.f64 43.5%

      \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   8. lift-+.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   10. lift-/.f64 N/A

       \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   11. mult-flip-rev N/A

       \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   12. lift-/.f64 N/A

       \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   13. div-add-rev N/A

       \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

   14. +-commutative N/A

       \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   15. add-flip N/A

       \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

   16. metadata-eval N/A

       \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   17. lift--.f64 N/A

       \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   18. lower-/.f64 43.5%

       \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

8. Applied rewrites 43.5%

   \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
9. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   2. lift-/.f64 N/A

      \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   3. associate-*l/ N/A

      \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

   4. *-commutative N/A

      \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

   5. lift--.f64 N/A

      \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

   6. metadata-eval N/A

      \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

   7. add-flip N/A

      \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

   8. distribute-lft-out N/A

      \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

   9. lift-*.f64 N/A

      \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

   10. lift-*.f64 N/A

       \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

   11. lift-+.f64 N/A

       \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

   12. lower-/.f64 43.6%

       \[\leadsto \frac{z \cdot y + z \cdot 0.0007936500793651}{x} \cdot z \]

   13. lift-+.f64 N/A

       \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

   14. lift-*.f64 N/A

       \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

   15. lift-*.f64 N/A

       \[\leadsto \frac{z \cdot y + z \cdot \frac{7936500793651}{10000000000000000}}{x} \cdot z \]

   16. distribute-lft-out N/A

       \[\leadsto \frac{z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)}{x} \cdot z \]

   17. add-flip N/A

       \[\leadsto \frac{z \cdot \left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}{x} \cdot z \]

   18. metadata-eval N/A

       \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

   19. lift--.f64 N/A

       \[\leadsto \frac{z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)}{x} \cdot z \]

   20. *-commutative N/A

       \[\leadsto \frac{\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot z}{x} \cdot z \]

   21. lift-*.f64 43.6%

       \[\leadsto \frac{\left(y - -0.0007936500793651\right) \cdot z}{x} \cdot z \]

10. Applied rewrites 43.6%

    \[\leadsto \frac{\left(y - -0.0007936500793651\right) \cdot z}{x} \cdot z \]
11. Add Preprocessing

Alternative 18: 43.6% accurate, 5.9× speedup

Math

\[\left(y - -0.0007936500793651\right) \cdot \left(z \cdot \frac{z}{x}\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  (* (- y -0.0007936500793651) (* z (/ z x))))

C

double code(double x, double y, double z) {
	return (y - -0.0007936500793651) * (z * (z / x));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y - (-0.0007936500793651d0)) * (z * (z / x))
end function

Java

public static double code(double x, double y, double z) {
	return (y - -0.0007936500793651) * (z * (z / x));
}

Python

def code(x, y, z):
	return (y - -0.0007936500793651) * (z * (z / x))

Julia

function code(x, y, z)
	return Float64(Float64(y - -0.0007936500793651) * Float64(z * Float64(z / x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y - -0.0007936500793651) * (z * (z / x));
end

Wolfram

code[x_, y_, z_] := N[(N[(y - -0.0007936500793651), $MachinePrecision] * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.2%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

   2. *-commutative N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   3. lift--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   4. sub-flip N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   5. distribute-rgt-in N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   6. fp-cancel-sign-sub-inv N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   7. lower--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   8. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   10. *-commutative N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   12. lift-+.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   13. add-flip N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   14. lower--.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   15. metadata-eval N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   16. remove-double-neg N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   17. lower-*.f64 94.2%

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

3. Applied rewrites 94.2%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

4. Taylor expanded in z around inf

   \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
5. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

   2. lower-pow.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

   3. lower-+.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

   5. lower-/.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

   6. lower-/.f64 41.7%

      \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

6. Applied rewrites 41.7%

   \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

   2. *-commutative N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

   3. lift-pow.f64 N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

   4. unpow2 N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

   5. associate-*r* N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

   7. lower-*.f64 43.5%

      \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   8. lift-+.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   10. lift-/.f64 N/A

       \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   11. mult-flip-rev N/A

       \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   12. lift-/.f64 N/A

       \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   13. div-add-rev N/A

       \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

   14. +-commutative N/A

       \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   15. add-flip N/A

       \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

   16. metadata-eval N/A

       \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   17. lift--.f64 N/A

       \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   18. lower-/.f64 43.5%

       \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

8. Applied rewrites 43.5%

   \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
9. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot \color{blue}{z} \]

   2. lift-*.f64 N/A

      \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   3. associate-*l* N/A

      \[\leadsto \frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot \color{blue}{\left(z \cdot z\right)} \]

   4. lift-/.f64 N/A

      \[\leadsto \frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot \left(\color{blue}{z} \cdot z\right) \]

   5. mult-flip N/A

      \[\leadsto \left(\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{1}{x}\right) \cdot \left(\color{blue}{z} \cdot z\right) \]

   6. lift-/.f64 N/A

      \[\leadsto \left(\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{1}{x}\right) \cdot \left(z \cdot z\right) \]

   7. unpow2 N/A

      \[\leadsto \left(\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{1}{x}\right) \cdot {z}^{\color{blue}{2}} \]

   8. lift-pow.f64 N/A

      \[\leadsto \left(\left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{1}{x}\right) \cdot {z}^{\color{blue}{2}} \]

   9. associate-*l* N/A

      \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \color{blue}{\left(\frac{1}{x} \cdot {z}^{2}\right)} \]

   10. *-commutative N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \left({z}^{2} \cdot \color{blue}{\frac{1}{x}}\right) \]

   11. lift-/.f64 N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \left({z}^{2} \cdot \frac{1}{\color{blue}{x}}\right) \]

   12. mult-flip N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{{z}^{2}}{\color{blue}{x}} \]

   13. lift-/.f64 N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{{z}^{2}}{\color{blue}{x}} \]

   14. lower-*.f64 42.8%

       \[\leadsto \left(y - -0.0007936500793651\right) \cdot \color{blue}{\frac{{z}^{2}}{x}} \]

   15. lift-/.f64 N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{{z}^{2}}{\color{blue}{x}} \]

   16. lift-pow.f64 N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{{z}^{2}}{x} \]

   17. unpow2 N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \frac{z \cdot z}{x} \]

   18. associate-/l* N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \left(z \cdot \color{blue}{\frac{z}{x}}\right) \]

   19. lift-/.f64 N/A

       \[\leadsto \left(y - \frac{-7936500793651}{10000000000000000}\right) \cdot \left(z \cdot \frac{z}{\color{blue}{x}}\right) \]

   20. lower-*.f64 44.4%

       \[\leadsto \left(y - -0.0007936500793651\right) \cdot \left(z \cdot \color{blue}{\frac{z}{x}}\right) \]

10. Applied rewrites 44.4%

    \[\leadsto \left(y - -0.0007936500793651\right) \cdot \color{blue}{\left(z \cdot \frac{z}{x}\right)} \]
11. Add Preprocessing

Alternative 19: 43.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} t_0 := \frac{y \cdot z}{x} \cdot z\\ \mathbf{if}\;y + 0.0007936500793651 \leq -2:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y + 0.0007936500793651 \leq 0.000794:\\ \;\;\;\;\left(z \cdot \frac{z}{x}\right) \cdot 0.0007936500793651\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  (let* ((t_0 (* (/ (* y z) x) z)))
  (if (<= (+ y 0.0007936500793651) -2.0)
    t_0
    (if (<= (+ y 0.0007936500793651) 0.000794)
      (* (* z (/ z x)) 0.0007936500793651)
      t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y * z) / x) * z;
	double tmp;
	if ((y + 0.0007936500793651) <= -2.0) {
		tmp = t_0;
	} else if ((y + 0.0007936500793651) <= 0.000794) {
		tmp = (z * (z / x)) * 0.0007936500793651;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y * z) / x) * z
    if ((y + 0.0007936500793651d0) <= (-2.0d0)) then
        tmp = t_0
    else if ((y + 0.0007936500793651d0) <= 0.000794d0) then
        tmp = (z * (z / x)) * 0.0007936500793651d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y * z) / x) * z;
	double tmp;
	if ((y + 0.0007936500793651) <= -2.0) {
		tmp = t_0;
	} else if ((y + 0.0007936500793651) <= 0.000794) {
		tmp = (z * (z / x)) * 0.0007936500793651;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y * z) / x) * z
	tmp = 0
	if (y + 0.0007936500793651) <= -2.0:
		tmp = t_0
	elif (y + 0.0007936500793651) <= 0.000794:
		tmp = (z * (z / x)) * 0.0007936500793651
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y * z) / x) * z)
	tmp = 0.0
	if (Float64(y + 0.0007936500793651) <= -2.0)
		tmp = t_0;
	elseif (Float64(y + 0.0007936500793651) <= 0.000794)
		tmp = Float64(Float64(z * Float64(z / x)) * 0.0007936500793651);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y * z) / x) * z;
	tmp = 0.0;
	if ((y + 0.0007936500793651) <= -2.0)
		tmp = t_0;
	elseif ((y + 0.0007936500793651) <= 0.000794)
		tmp = (z * (z / x)) * 0.0007936500793651;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(y + 0.0007936500793651), $MachinePrecision], -2.0], t$95$0, If[LessEqual[N[(y + 0.0007936500793651), $MachinePrecision], 0.000794], N[(N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision] * 0.0007936500793651), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) < -2 or 7.94e-4 < (+.f64 y #s(literal 7936500793651/10000000000000000 binary64))

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

      3. lift-pow.f64 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

      7. lower-*.f64 43.5%

         \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      8. lift-+.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      10. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      11. mult-flip-rev N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      12. lift-/.f64 N/A

          \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

      13. div-add-rev N/A

          \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

      14. +-commutative N/A

          \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      15. add-flip N/A

          \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

      16. metadata-eval N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      17. lift--.f64 N/A

          \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

      18. lower-/.f64 43.5%

          \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

   8. Applied rewrites 43.5%

      \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]

   9. Taylor expanded in y around inf

      \[\leadsto \frac{y \cdot z}{x} \cdot z \]
   10. Step-by-step derivation

       1. lower-/.f64 N/A

          \[\leadsto \frac{y \cdot z}{x} \cdot z \]

       2. lower-*.f64 29.7%

          \[\leadsto \frac{y \cdot z}{x} \cdot z \]

   11. Applied rewrites 29.7%

       \[\leadsto \frac{y \cdot z}{x} \cdot z \]

   if -2 < (+.f64 y #s(literal 7936500793651/10000000000000000 binary64)) < 7.94e-4

   1. Initial program 94.2%

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      3. lift--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      4. sub-flip N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      5. distribute-rgt-in N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      6. fp-cancel-sign-sub-inv N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      7. lower--.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      9. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      10. *-commutative N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      11. lower-*.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      13. add-flip N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      14. lower--.f64 N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      15. metadata-eval N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      16. remove-double-neg N/A

          \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

      17. lower-*.f64 94.2%

          \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

   3. Applied rewrites 94.2%

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

      2. lower-pow.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

      3. lower-+.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

      4. lower-*.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

      6. lower-/.f64 41.7%

         \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

   6. Applied rewrites 41.7%

      \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \color{blue}{\frac{{z}^{2}}{x}} \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{x} \]

      3. lower-pow.f64 25.8%

         \[\leadsto 0.0007936500793651 \cdot \frac{{z}^{2}}{x} \]

   9. Applied rewrites 25.8%

      \[\leadsto 0.0007936500793651 \cdot \color{blue}{\frac{{z}^{2}}{x}} \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]

       2. *-commutative N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       3. lower-*.f64 25.8%

          \[\leadsto \frac{{z}^{2}}{x} \cdot 0.0007936500793651 \]

       4. lift-/.f64 N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       5. lift-pow.f64 N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       6. unpow2 N/A

          \[\leadsto \frac{z \cdot z}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       7. associate-/l* N/A

          \[\leadsto \left(z \cdot \frac{z}{x}\right) \cdot \frac{7936500793651}{10000000000000000} \]

       8. lift-/.f64 N/A

          \[\leadsto \left(z \cdot \frac{z}{x}\right) \cdot \frac{7936500793651}{10000000000000000} \]

       9. lower-*.f64 26.2%

          \[\leadsto \left(z \cdot \frac{z}{x}\right) \cdot 0.0007936500793651 \]

   11. Applied rewrites 26.2%

       \[\leadsto \left(z \cdot \frac{z}{x}\right) \cdot 0.0007936500793651 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 43.3% accurate, 5.9× speedup

Math

\[\left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

FPCore

(FPCore (x y z)
  :precision binary64
  (* (* (/ (- y -0.0007936500793651) x) z) z))

C

double code(double x, double y, double z) {
	return (((y - -0.0007936500793651) / x) * z) * z;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (((y - (-0.0007936500793651d0)) / x) * z) * z
end function

Java

public static double code(double x, double y, double z) {
	return (((y - -0.0007936500793651) / x) * z) * z;
}

Python

def code(x, y, z):
	return (((y - -0.0007936500793651) / x) * z) * z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(y - -0.0007936500793651) / x) * z) * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (((y - -0.0007936500793651) / x) * z) * z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 94.2%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

   2. *-commutative N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   3. lift--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   4. sub-flip N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   5. distribute-rgt-in N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   6. fp-cancel-sign-sub-inv N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   7. lower--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   8. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   10. *-commutative N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   12. lift-+.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   13. add-flip N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   14. lower--.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   15. metadata-eval N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   16. remove-double-neg N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   17. lower-*.f64 94.2%

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

3. Applied rewrites 94.2%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

4. Taylor expanded in z around inf

   \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
5. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

   2. lower-pow.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

   3. lower-+.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

   5. lower-/.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

   6. lower-/.f64 41.7%

      \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

6. Applied rewrites 41.7%

   \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

   2. *-commutative N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \color{blue}{{z}^{2}} \]

   3. lift-pow.f64 N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot {z}^{\color{blue}{2}} \]

   4. unpow2 N/A

      \[\leadsto \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot \left(z \cdot \color{blue}{z}\right) \]

   5. associate-*r* N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

   6. lower-*.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot \color{blue}{z} \]

   7. lower-*.f64 43.5%

      \[\leadsto \left(\left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   8. lift-+.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   10. lift-/.f64 N/A

       \[\leadsto \left(\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   11. mult-flip-rev N/A

       \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   12. lift-/.f64 N/A

       \[\leadsto \left(\left(\frac{\frac{7936500793651}{10000000000000000}}{x} + \frac{y}{x}\right) \cdot z\right) \cdot z \]

   13. div-add-rev N/A

       \[\leadsto \left(\frac{\frac{7936500793651}{10000000000000000} + y}{x} \cdot z\right) \cdot z \]

   14. +-commutative N/A

       \[\leadsto \left(\frac{y + \frac{7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   15. add-flip N/A

       \[\leadsto \left(\frac{y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)}{x} \cdot z\right) \cdot z \]

   16. metadata-eval N/A

       \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   17. lift--.f64 N/A

       \[\leadsto \left(\frac{y - \frac{-7936500793651}{10000000000000000}}{x} \cdot z\right) \cdot z \]

   18. lower-/.f64 43.5%

       \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \]

8. Applied rewrites 43.5%

   \[\leadsto \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot \color{blue}{z} \]
9. Add Preprocessing

Alternative 21: 26.2% accurate, 6.7× speedup

Math

\[\left(z \cdot \frac{z}{x}\right) \cdot 0.0007936500793651 \]

FPCore

(FPCore (x y z)
  :precision binary64
  (* (* z (/ z x)) 0.0007936500793651))

C

double code(double x, double y, double z) {
	return (z * (z / x)) * 0.0007936500793651;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (z * (z / x)) * 0.0007936500793651d0
end function

Java

public static double code(double x, double y, double z) {
	return (z * (z / x)) * 0.0007936500793651;
}

Python

def code(x, y, z):
	return (z * (z / x)) * 0.0007936500793651

Julia

function code(x, y, z)
	return Float64(Float64(z * Float64(z / x)) * 0.0007936500793651)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (z * (z / x)) * 0.0007936500793651;
end

Wolfram

code[x_, y_, z_] := N[(N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision] * 0.0007936500793651), $MachinePrecision]

Derivation

1. Initial program 94.2%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right) \cdot z} + \frac{83333333333333}{1000000000000000}}{x} \]

   2. *-commutative N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{z \cdot \left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   3. lift--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z - \frac{13888888888889}{5000000000000000}\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   4. sub-flip N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{z \cdot \color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   5. distribute-rgt-in N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z + \left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   6. fp-cancel-sign-sub-inv N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   7. lower--.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\color{blue}{\left(\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right)} + \frac{83333333333333}{1000000000000000}}{x} \]

   8. lower-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right) \cdot z} - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   9. lift-*.f64 N/A

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(\left(y + \frac{7936500793651}{10000000000000000}\right) \cdot z\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   10. *-commutative N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   11. lower-*.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\color{blue}{\left(z \cdot \left(y + \frac{7936500793651}{10000000000000000}\right)\right)} \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   12. lift-+.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y + \frac{7936500793651}{10000000000000000}\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   13. add-flip N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   14. lower--.f64 N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \color{blue}{\left(y - \left(\mathsf{neg}\left(\frac{7936500793651}{10000000000000000}\right)\right)\right)}\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   15. metadata-eval N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \color{blue}{\frac{-7936500793651}{10000000000000000}}\right)\right) \cdot z - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{13888888888889}{5000000000000000}\right)\right)\right)\right) \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   16. remove-double-neg N/A

       \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \frac{\left(\left(z \cdot \left(y - \frac{-7936500793651}{10000000000000000}\right)\right) \cdot z - \color{blue}{\frac{13888888888889}{5000000000000000}} \cdot z\right) + \frac{83333333333333}{1000000000000000}}{x} \]

   17. lower-*.f64 94.2%

       \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - \color{blue}{0.0027777777777778 \cdot z}\right) + 0.083333333333333}{x} \]

3. Applied rewrites 94.2%

   \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\color{blue}{\left(\left(z \cdot \left(y - -0.0007936500793651\right)\right) \cdot z - 0.0027777777777778 \cdot z\right)} + 0.083333333333333}{x} \]

4. Taylor expanded in z around inf

   \[\leadsto \color{blue}{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]
5. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \color{blue}{\left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

   2. lower-pow.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\color{blue}{\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x}} + \frac{y}{x}\right) \]

   3. lower-+.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \color{blue}{\frac{y}{x}}\right) \]

   4. lower-*.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{\color{blue}{y}}{x}\right) \]

   5. lower-/.f64 N/A

      \[\leadsto {z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} \cdot \frac{1}{x} + \frac{y}{x}\right) \]

   6. lower-/.f64 41.7%

      \[\leadsto {z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{\color{blue}{x}}\right) \]

6. Applied rewrites 41.7%

   \[\leadsto \color{blue}{{z}^{2} \cdot \left(0.0007936500793651 \cdot \frac{1}{x} + \frac{y}{x}\right)} \]

7. Taylor expanded in y around 0

   \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \color{blue}{\frac{{z}^{2}}{x}} \]
8. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{x} \]

   3. lower-pow.f64 25.8%

      \[\leadsto 0.0007936500793651 \cdot \frac{{z}^{2}}{x} \]

9. Applied rewrites 25.8%

   \[\leadsto 0.0007936500793651 \cdot \color{blue}{\frac{{z}^{2}}{x}} \]
10. Step-by-step derivation

    1. lift-*.f64 N/A

       \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]

    2. *-commutative N/A

       \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

    3. lower-*.f64 25.8%

       \[\leadsto \frac{{z}^{2}}{x} \cdot 0.0007936500793651 \]

    4. lift-/.f64 N/A

       \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

    5. lift-pow.f64 N/A

       \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

    6. unpow2 N/A

       \[\leadsto \frac{z \cdot z}{x} \cdot \frac{7936500793651}{10000000000000000} \]

    7. associate-/l* N/A

       \[\leadsto \left(z \cdot \frac{z}{x}\right) \cdot \frac{7936500793651}{10000000000000000} \]

    8. lift-/.f64 N/A

       \[\leadsto \left(z \cdot \frac{z}{x}\right) \cdot \frac{7936500793651}{10000000000000000} \]

    9. lower-*.f64 26.2%

       \[\leadsto \left(z \cdot \frac{z}{x}\right) \cdot 0.0007936500793651 \]

11. Applied rewrites 26.2%

    \[\leadsto \left(z \cdot \frac{z}{x}\right) \cdot 0.0007936500793651 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))