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

Percentage Accurate: 93.5% → 99.5%

Time: 12.7s

Alternatives: 14

Speedup: 1.0×

• 32.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 93.5% accurate, 1.0× speedup

Math

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

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: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\\ \mathbf{if}\;x \leq 4.4 \cdot 10^{+30}:\\ \;\;\;\;t\_0 + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)))
   (if (<= x 4.4e+30)
     (+
      t_0
      (/
       (+
        (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
        0.083333333333333)
       x))
     (+ t_0 (* (* (/ (- y -0.0007936500793651) x) 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 (x <= 4.4e+30) {
		tmp = t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = t_0 + ((((y - -0.0007936500793651) / x) * 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 (x <= 4.4d+30) then
        tmp = t_0 + ((((((y + 0.0007936500793651d0) * z) - 0.0027777777777778d0) * z) + 0.083333333333333d0) / x)
    else
        tmp = t_0 + ((((y - (-0.0007936500793651d0)) / x) * 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 (x <= 4.4e+30) {
		tmp = t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	} else {
		tmp = t_0 + ((((y - -0.0007936500793651) / x) * z) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (((x - 0.5) * math.log(x)) - x) + 0.91893853320467
	tmp = 0
	if x <= 4.4e+30:
		tmp = t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x)
	else:
		tmp = t_0 + ((((y - -0.0007936500793651) / x) * 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 (x <= 4.4e+30)
		tmp = Float64(t_0 + Float64(Float64(Float64(Float64(Float64(Float64(y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x));
	else
		tmp = Float64(t_0 + Float64(Float64(Float64(Float64(y - -0.0007936500793651) / x) * 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 (x <= 4.4e+30)
		tmp = t_0 + ((((((y + 0.0007936500793651) * z) - 0.0027777777777778) * z) + 0.083333333333333) / x);
	else
		tmp = t_0 + ((((y - -0.0007936500793651) / x) * 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[x, 4.4e+30], 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], N[(t$95$0 + N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 4.4e30

   1. Initial program 99.7%

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

   if 4.4e30 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. div-add-rev N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. unpow2 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 99.5%

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

Alternative 2: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+216}:\\ \;\;\;\;\left(\frac{z}{x} \cdot z\right) \cdot y\\ \mathbf{elif}\;t\_0 \leq 10^{+306}:\\ \;\;\;\;\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - \frac{-0.083333333333333}{x}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z\\ \end{array} \end{array} \]

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 -1e+216)
     (* (* (/ z x) z) y)
     (if (<= t_0 1e+306)
       (-
        (fma (log x) (- x 0.5) (- 0.91893853320467 (/ -0.083333333333333 x)))
        x)
       (* (* (/ (- y -0.0007936500793651) x) 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 <= -1e+216) {
		tmp = ((z / x) * z) * y;
	} else if (t_0 <= 1e+306) {
		tmp = fma(log(x), (x - 0.5), (0.91893853320467 - (-0.083333333333333 / x))) - x;
	} else {
		tmp = (((y - -0.0007936500793651) / x) * 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 <= -1e+216)
		tmp = Float64(Float64(Float64(z / x) * z) * y);
	elseif (t_0 <= 1e+306)
		tmp = Float64(fma(log(x), Float64(x - 0.5), Float64(0.91893853320467 - Float64(-0.083333333333333 / x))) - x);
	else
		tmp = Float64(Float64(Float64(Float64(y - -0.0007936500793651) / x) * z) * z);
	end
	return 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, -1e+216], N[(N[(N[(z / x), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$0, 1e+306], N[(N[(N[Log[x], $MachinePrecision] * N[(x - 0.5), $MachinePrecision] + N[(0.91893853320467 - N[(-0.083333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 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)) < -1e216

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 84.0

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

   5. Applied rewrites 84.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l/ N/A

         \[\leadsto \frac{z \cdot z}{x} \cdot \color{blue}{y} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{x} \cdot y \]

      5. associate-*r/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 93.2

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

   7. Applied rewrites 93.2%

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

   if -1e216 < (+.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)) < 1.00000000000000002e306

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 N/A

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

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

         \[\leadsto \mathsf{fma}\left(\log x, x - \frac{1}{2}, \frac{91893853320467}{100000000000000} - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right) \cdot \frac{1}{x}\right) - x \]

      8. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\log x, x - \frac{1}{2}, \frac{91893853320467}{100000000000000} - \left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right) \cdot \frac{1}{x}\right) - x \]

      9. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(\log x, x - \frac{1}{2}, \frac{91893853320467}{100000000000000} - \frac{\left(\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)\right) \cdot 1}{x}\right) - x \]

      10. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\log x, x - \frac{1}{2}, \frac{91893853320467}{100000000000000} - \frac{\mathsf{neg}\left(\frac{83333333333333}{1000000000000000} \cdot 1\right)}{x}\right) - x \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\log x, x - \frac{1}{2}, \frac{91893853320467}{100000000000000} - \frac{\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)}{x}\right) - x \]

      12. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\log x, x - \frac{1}{2}, \frac{91893853320467}{100000000000000} - \frac{\mathsf{neg}\left(\frac{83333333333333}{1000000000000000}\right)}{x}\right) - x \]

      13. metadata-eval 91.9

          \[\leadsto \mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - \frac{-0.083333333333333}{x}\right) - x \]

   5. Applied rewrites 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log x, x - 0.5, 0.91893853320467 - \frac{-0.083333333333333}{x}\right) - x} \]

   if 1.00000000000000002e306 < (+.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 88.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 90.8%

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

Alternative 3: 86.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+216}:\\ \;\;\;\;\left(\frac{z}{x} \cdot z\right) \cdot y\\ \mathbf{elif}\;t\_0 \leq 10^{+306}:\\ \;\;\;\;\left(\log x - 1\right) \cdot x + \frac{0.083333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z\\ \end{array} \end{array} \]

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 -1e+216)
     (* (* (/ z x) z) y)
     (if (<= t_0 1e+306)
       (+ (* (- (log x) 1.0) x) (/ 0.083333333333333 x))
       (* (* (/ (- y -0.0007936500793651) x) 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 <= -1e+216) {
		tmp = ((z / x) * z) * y;
	} else if (t_0 <= 1e+306) {
		tmp = ((log(x) - 1.0) * x) + (0.083333333333333 / x);
	} else {
		tmp = (((y - -0.0007936500793651) / x) * 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 <= (-1d+216)) then
        tmp = ((z / x) * z) * y
    else if (t_0 <= 1d+306) then
        tmp = ((log(x) - 1.0d0) * x) + (0.083333333333333d0 / x)
    else
        tmp = (((y - (-0.0007936500793651d0)) / x) * 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 <= -1e+216) {
		tmp = ((z / x) * z) * y;
	} else if (t_0 <= 1e+306) {
		tmp = ((Math.log(x) - 1.0) * x) + (0.083333333333333 / x);
	} else {
		tmp = (((y - -0.0007936500793651) / x) * 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 <= -1e+216:
		tmp = ((z / x) * z) * y
	elif t_0 <= 1e+306:
		tmp = ((math.log(x) - 1.0) * x) + (0.083333333333333 / x)
	else:
		tmp = (((y - -0.0007936500793651) / x) * 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 <= -1e+216)
		tmp = Float64(Float64(Float64(z / x) * z) * y);
	elseif (t_0 <= 1e+306)
		tmp = Float64(Float64(Float64(log(x) - 1.0) * x) + Float64(0.083333333333333 / x));
	else
		tmp = Float64(Float64(Float64(Float64(y - -0.0007936500793651) / x) * 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 <= -1e+216)
		tmp = ((z / x) * z) * y;
	elseif (t_0 <= 1e+306)
		tmp = ((log(x) - 1.0) * x) + (0.083333333333333 / x);
	else
		tmp = (((y - -0.0007936500793651) / x) * 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, -1e+216], N[(N[(N[(z / x), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$0, 1e+306], N[(N[(N[(N[Log[x], $MachinePrecision] - 1.0), $MachinePrecision] * x), $MachinePrecision] + N[(0.083333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 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)) < -1e216

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 84.0

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

   5. Applied rewrites 84.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l/ N/A

         \[\leadsto \frac{z \cdot z}{x} \cdot \color{blue}{y} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{x} \cdot y \]

      5. associate-*r/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 93.2

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

   7. Applied rewrites 93.2%

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

   if -1e216 < (+.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)) < 1.00000000000000002e306

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 37.3

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

   8. Applied rewrites 37.3%

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

   9. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right)} + \frac{\frac{83333333333333}{1000000000000000}}{x} \]
   10. Step-by-step derivation

       1. *-commutative N/A

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

       2. *-commutative N/A

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

       3. mul-1-neg N/A

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

       4. log-rec N/A

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

       5. remove-double-neg N/A

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

       6. lower-*.f64 N/A

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

       7. lower--.f64 N/A

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

       8. lower-log.f64 90.3

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

   11. Applied rewrites 90.3%

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

   if 1.00000000000000002e306 < (+.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 88.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 90.8%

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

Alternative 4: 98.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778, \frac{z}{x}, \frac{0.083333333333333}{x} + \left(\log x \cdot \left(x - 0.5\right) - \left(x - 0.91893853320467\right)\right)\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.5%

   \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x} \]
2. Add Preprocessing
3. 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. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-+.f64 N/A

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

   5. div-add N/A

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

   6. associate-+l+ N/A

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

   7. lift-*.f64 N/A

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

   8. associate-/l* N/A

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

   9. lower-fma.f64 N/A

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

4. Applied rewrites 98.5%

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

Alternative 5: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00029:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y - -0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.00029)
   (/
    (fma
     (fma (- y -0.0007936500793651) z -0.0027777777777778)
     z
     0.083333333333333)
    x)
   (+
    (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
    (* (* (/ (- y -0.0007936500793651) x) z) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.00029) {
		tmp = fma(fma((y - -0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x;
	} else {
		tmp = ((((x - 0.5) * log(x)) - x) + 0.91893853320467) + ((((y - -0.0007936500793651) / x) * z) * z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.00029)
		tmp = Float64(fma(fma(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(y - -0.0007936500793651) / x) * z) * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.00029], N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(N[(N[(x - 0.5), $MachinePrecision] * N[Log[x], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] + 0.91893853320467), $MachinePrecision] + N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.9e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 98.9%

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

   if 2.9e-4 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(x - \frac{1}{2}\right) \cdot \log x - x\right) + \frac{91893853320467}{100000000000000}\right) + \color{blue}{\frac{{z}^{2} \cdot \left(\frac{7936500793651}{10000000000000000} + y\right)}{x}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. div-add-rev N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. *-commutative N/A

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

      6. unpow2 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 98.9%

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

Alternative 6: 84.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y - -0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - 1\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.6e+36)
   (/
    (fma
     (fma (- y -0.0007936500793651) z -0.0027777777777778)
     z
     0.083333333333333)
    x)
   (* (- (log x) 1.0) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.6e+36) {
		tmp = fma(fma((y - -0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x;
	} else {
		tmp = (log(x) - 1.0) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.6e+36)
		tmp = Float64(fma(fma(Float64(y - -0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x);
	else
		tmp = Float64(Float64(log(x) - 1.0) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.6e+36], N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[Log[x], $MachinePrecision] - 1.0), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.5999999999999999e36

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 95.2%

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

   if 1.5999999999999999e36 < x

   1. Initial program 87.5%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto \left(-1 \cdot \log \left(\frac{1}{x}\right) - 1\right) \cdot \color{blue}{x} \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\log \left(\frac{1}{x}\right)\right)\right) - 1\right) \cdot x \]

      3. log-rec N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\log x\right)\right)\right)\right) - 1\right) \cdot x \]

      4. remove-double-neg N/A

         \[\leadsto \left(\log x - 1\right) \cdot x \]

      5. lower-*.f64 N/A

         \[\leadsto \left(\log x - 1\right) \cdot \color{blue}{x} \]

      6. lower--.f64 N/A

         \[\leadsto \left(\log x - 1\right) \cdot x \]

      7. lower-log.f64 79.2

         \[\leadsto \left(\log x - 1\right) \cdot x \]

   5. Applied rewrites 79.2%

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

Alternative 7: 44.1% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0012 \lor \neg \left(y \leq 0.00078\right):\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{x} \cdot 0.0007936500793651\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0012) (not (<= y 0.00078)))
   (* z (* z (/ y x)))
   (* (* (/ z x) 0.0007936500793651) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0012) || !(y <= 0.00078)) {
		tmp = z * (z * (y / x));
	} else {
		tmp = ((z / x) * 0.0007936500793651) * 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 ((y <= (-0.0012d0)) .or. (.not. (y <= 0.00078d0))) then
        tmp = z * (z * (y / x))
    else
        tmp = ((z / x) * 0.0007936500793651d0) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0012) || !(y <= 0.00078)) {
		tmp = z * (z * (y / x));
	} else {
		tmp = ((z / x) * 0.0007936500793651) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0012) or not (y <= 0.00078):
		tmp = z * (z * (y / x))
	else:
		tmp = ((z / x) * 0.0007936500793651) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0012) || !(y <= 0.00078))
		tmp = Float64(z * Float64(z * Float64(y / x)));
	else
		tmp = Float64(Float64(Float64(z / x) * 0.0007936500793651) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0012) || ~((y <= 0.00078)))
		tmp = z * (z * (y / x));
	else
		tmp = ((z / x) * 0.0007936500793651) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0012], N[Not[LessEqual[y, 0.00078]], $MachinePrecision]], N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / x), $MachinePrecision] * 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00119999999999999989 or 7.79999999999999986e-4 < y

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 44.0

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

   5. Applied rewrites 44.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 46.5

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

   7. Applied rewrites 46.5%

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

   if -0.00119999999999999989 < y < 7.79999999999999986e-4

   1. Initial program 94.8%

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

   3. Taylor expanded in y around -inf

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

   5. Applied rewrites 62.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 34.8

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

   8. Applied rewrites 34.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       3. unpow2 N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 38.7

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

   11. Applied rewrites 38.7%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 38.7

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

   13. Applied rewrites 38.7%

       \[\leadsto \left(\frac{z}{x} \cdot 0.0007936500793651\right) \cdot z \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0012 \lor \neg \left(y \leq 0.00078\right):\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{x} \cdot 0.0007936500793651\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 44.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0012:\\ \;\;\;\;\left(\frac{z}{x} \cdot z\right) \cdot y\\ \mathbf{elif}\;y \leq 0.00078:\\ \;\;\;\;\left(\frac{z}{x} \cdot 0.0007936500793651\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0012)
   (* (* (/ z x) z) y)
   (if (<= y 0.00078)
     (* (* (/ z x) 0.0007936500793651) z)
     (* z (* z (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0012) {
		tmp = ((z / x) * z) * y;
	} else if (y <= 0.00078) {
		tmp = ((z / x) * 0.0007936500793651) * z;
	} else {
		tmp = z * (z * (y / 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 (y <= (-0.0012d0)) then
        tmp = ((z / x) * z) * y
    else if (y <= 0.00078d0) then
        tmp = ((z / x) * 0.0007936500793651d0) * z
    else
        tmp = z * (z * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0012) {
		tmp = ((z / x) * z) * y;
	} else if (y <= 0.00078) {
		tmp = ((z / x) * 0.0007936500793651) * z;
	} else {
		tmp = z * (z * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.0012:
		tmp = ((z / x) * z) * y
	elif y <= 0.00078:
		tmp = ((z / x) * 0.0007936500793651) * z
	else:
		tmp = z * (z * (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0012)
		tmp = Float64(Float64(Float64(z / x) * z) * y);
	elseif (y <= 0.00078)
		tmp = Float64(Float64(Float64(z / x) * 0.0007936500793651) * z);
	else
		tmp = Float64(z * Float64(z * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.0012)
		tmp = ((z / x) * z) * y;
	elseif (y <= 0.00078)
		tmp = ((z / x) * 0.0007936500793651) * z;
	else
		tmp = z * (z * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0012], N[(N[(N[(z / x), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 0.00078], N[(N[(N[(z / x), $MachinePrecision] * 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision], N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00119999999999999989

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 43.0

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

   5. Applied rewrites 43.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l/ N/A

         \[\leadsto \frac{z \cdot z}{x} \cdot \color{blue}{y} \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{z \cdot z}{x} \cdot y \]

      5. associate-*r/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 47.5

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

   7. Applied rewrites 47.5%

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

   if -0.00119999999999999989 < y < 7.79999999999999986e-4

   1. Initial program 94.8%

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

   3. Taylor expanded in y around -inf

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

   5. Applied rewrites 62.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 34.8

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

   8. Applied rewrites 34.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       3. unpow2 N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 38.7

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

   11. Applied rewrites 38.7%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 38.7

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

   13. Applied rewrites 38.7%

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

   if 7.79999999999999986e-4 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 45.0

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

   5. Applied rewrites 45.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 47.2

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

   7. Applied rewrites 47.2%

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

Alternative 9: 44.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0012:\\ \;\;\;\;\left(y \cdot \frac{z}{x}\right) \cdot z\\ \mathbf{elif}\;y \leq 0.00078:\\ \;\;\;\;\left(\frac{z}{x} \cdot 0.0007936500793651\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0012)
   (* (* y (/ z x)) z)
   (if (<= y 0.00078)
     (* (* (/ z x) 0.0007936500793651) z)
     (* z (* z (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0012) {
		tmp = (y * (z / x)) * z;
	} else if (y <= 0.00078) {
		tmp = ((z / x) * 0.0007936500793651) * z;
	} else {
		tmp = z * (z * (y / 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 (y <= (-0.0012d0)) then
        tmp = (y * (z / x)) * z
    else if (y <= 0.00078d0) then
        tmp = ((z / x) * 0.0007936500793651d0) * z
    else
        tmp = z * (z * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0012) {
		tmp = (y * (z / x)) * z;
	} else if (y <= 0.00078) {
		tmp = ((z / x) * 0.0007936500793651) * z;
	} else {
		tmp = z * (z * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.0012:
		tmp = (y * (z / x)) * z
	elif y <= 0.00078:
		tmp = ((z / x) * 0.0007936500793651) * z
	else:
		tmp = z * (z * (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0012)
		tmp = Float64(Float64(y * Float64(z / x)) * z);
	elseif (y <= 0.00078)
		tmp = Float64(Float64(Float64(z / x) * 0.0007936500793651) * z);
	else
		tmp = Float64(z * Float64(z * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.0012)
		tmp = (y * (z / x)) * z;
	elseif (y <= 0.00078)
		tmp = ((z / x) * 0.0007936500793651) * z;
	else
		tmp = z * (z * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0012], N[(N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 0.00078], N[(N[(N[(z / x), $MachinePrecision] * 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision], N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00119999999999999989

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 43.0

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

   5. Applied rewrites 43.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-*r/ N/A

         \[\leadsto y \cdot \color{blue}{\frac{z \cdot z}{x}} \]

      5. lift-*.f64 N/A

         \[\leadsto y \cdot \frac{z \cdot z}{x} \]

      6. associate-*l/ N/A

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

      7. lift-/.f64 N/A

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 46.0

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

   7. Applied rewrites 46.0%

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

   if -0.00119999999999999989 < y < 7.79999999999999986e-4

   1. Initial program 94.8%

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

   3. Taylor expanded in y around -inf

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

   5. Applied rewrites 62.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 34.8

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

   8. Applied rewrites 34.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       3. unpow2 N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 38.7

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

   11. Applied rewrites 38.7%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 38.7

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

   13. Applied rewrites 38.7%

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

   if 7.79999999999999986e-4 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 45.0

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

   5. Applied rewrites 45.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 47.2

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

   7. Applied rewrites 47.2%

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

Alternative 10: 44.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0012:\\ \;\;\;\;z \cdot \frac{y \cdot z}{x}\\ \mathbf{elif}\;y \leq 0.00078:\\ \;\;\;\;\left(\frac{z}{x} \cdot 0.0007936500793651\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot \frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0012)
   (* z (/ (* y z) x))
   (if (<= y 0.00078)
     (* (* (/ z x) 0.0007936500793651) z)
     (* z (* z (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0012) {
		tmp = z * ((y * z) / x);
	} else if (y <= 0.00078) {
		tmp = ((z / x) * 0.0007936500793651) * z;
	} else {
		tmp = z * (z * (y / 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 (y <= (-0.0012d0)) then
        tmp = z * ((y * z) / x)
    else if (y <= 0.00078d0) then
        tmp = ((z / x) * 0.0007936500793651d0) * z
    else
        tmp = z * (z * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0012) {
		tmp = z * ((y * z) / x);
	} else if (y <= 0.00078) {
		tmp = ((z / x) * 0.0007936500793651) * z;
	} else {
		tmp = z * (z * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.0012:
		tmp = z * ((y * z) / x)
	elif y <= 0.00078:
		tmp = ((z / x) * 0.0007936500793651) * z
	else:
		tmp = z * (z * (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0012)
		tmp = Float64(z * Float64(Float64(y * z) / x));
	elseif (y <= 0.00078)
		tmp = Float64(Float64(Float64(z / x) * 0.0007936500793651) * z);
	else
		tmp = Float64(z * Float64(z * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.0012)
		tmp = z * ((y * z) / x);
	elseif (y <= 0.00078)
		tmp = ((z / x) * 0.0007936500793651) * z;
	else
		tmp = z * (z * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0012], N[(z * N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00078], N[(N[(N[(z / x), $MachinePrecision] * 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision], N[(z * N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00119999999999999989

   1. Initial program 91.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 43.0

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

   5. Applied rewrites 43.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l* N/A

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

      5. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{z \cdot y}{x}} \]

      6. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\frac{z \cdot y}{x}} \]

      7. lower-/.f64 N/A

         \[\leadsto z \cdot \frac{z \cdot y}{\color{blue}{x}} \]

      8. *-commutative N/A

         \[\leadsto z \cdot \frac{y \cdot z}{x} \]

      9. lower-*.f64 45.9

         \[\leadsto z \cdot \frac{y \cdot z}{x} \]

   7. Applied rewrites 45.9%

      \[\leadsto z \cdot \color{blue}{\frac{y \cdot z}{x}} \]

   if -0.00119999999999999989 < y < 7.79999999999999986e-4

   1. Initial program 94.8%

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

   3. Taylor expanded in y around -inf

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

   5. Applied rewrites 62.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 34.8

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

   8. Applied rewrites 34.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

       3. unpow2 N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. lower-*.f64 N/A

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

       7. lower-/.f64 38.7

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

   11. Applied rewrites 38.7%

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

       1. lift-*.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l* N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. lower-*.f64 N/A

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

       7. lower-*.f64 38.7

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

   13. Applied rewrites 38.7%

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

   if 7.79999999999999986e-4 < y

   1. Initial program 96.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot {z}^{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{y \cdot {z}^{2}}{\color{blue}{x}} \]

      2. *-commutative N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{{z}^{2} \cdot y}{x} \]

      4. unpow2 N/A

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

      5. lower-*.f64 45.0

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

   5. Applied rewrites 45.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lift-*.f64 N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 47.2

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

   7. Applied rewrites 47.2%

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

Alternative 11: 65.2% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(y - -0.0007936500793651, z, -0.0027777777777778\right), z, 0.083333333333333\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5.3e+39)
   (/
    (fma
     (fma (- y -0.0007936500793651) z -0.0027777777777778)
     z
     0.083333333333333)
    x)
   (* (* (/ (- y -0.0007936500793651) x) z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5.3e+39) {
		tmp = fma(fma((y - -0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x;
	} else {
		tmp = (((y - -0.0007936500793651) / x) * z) * z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5.3e+39)
		tmp = Float64(fma(fma(Float64(y - -0.0007936500793651), z, -0.0027777777777778), z, 0.083333333333333) / x);
	else
		tmp = Float64(Float64(Float64(Float64(y - -0.0007936500793651) / x) * z) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5.3e+39], N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] * z + -0.0027777777777778), $MachinePrecision] * z + 0.083333333333333), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(N[(y - -0.0007936500793651), $MachinePrecision] / x), $MachinePrecision] * z), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.29999999999999979e39

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 93.4%

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

   if 5.29999999999999979e39 < x

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   5. Applied rewrites 23.7%

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

Alternative 12: 44.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \left(\frac{y - -0.0007936500793651}{x} \cdot z\right) \cdot z \end{array} \]

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 94.5%

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

3. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. unpow2 N/A

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

   3. associate-*r* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

5. Applied rewrites 42.5%

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

Alternative 13: 26.2% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \frac{z \cdot \left(0.0007936500793651 \cdot z\right)}{x} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* z (* 0.0007936500793651 z)) x))

C

double code(double x, double y, double z) {
	return (z * (0.0007936500793651 * 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 = (z * (0.0007936500793651d0 * z)) / x
end function

Java

public static double code(double x, double y, double z) {
	return (z * (0.0007936500793651 * z)) / x;
}

Python

def code(x, y, z):
	return (z * (0.0007936500793651 * z)) / x

Julia

function code(x, y, z)
	return Float64(Float64(z * Float64(0.0007936500793651 * z)) / x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (z * (0.0007936500793651 * z)) / x;
end

Wolfram

code[x_, y_, z_] := N[(N[(z * N[(0.0007936500793651 * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]

Derivation

1. Initial program 94.5%

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

3. Taylor expanded in y around -inf

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

5. Applied rewrites 70.3%

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

6. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-+.f64 N/A

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

   7. associate-*r/ N/A

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

   8. metadata-eval N/A

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

   9. lower-/.f64 N/A

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

   10. lower-*.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. unpow2 N/A

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

   13. lower-*.f64 40.3

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

8. Applied rewrites 40.3%

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

9. Taylor expanded in y around 0

   \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]
10. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

    2. lower-*.f64 N/A

       \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

    3. unpow2 N/A

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

    4. associate-*r/ N/A

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

    5. *-commutative N/A

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

    6. lower-*.f64 N/A

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

    7. lower-/.f64 26.1

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

11. Applied rewrites 26.1%

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

    1. lift-*.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. associate-*l* N/A

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

    4. lift-/.f64 N/A

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

    5. *-commutative N/A

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

    6. associate-*l/ N/A

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

    7. lower-/.f64 N/A

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

    8. lower-*.f64 N/A

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

    9. lower-*.f64 26.5

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

13. Applied rewrites 26.5%

    \[\leadsto \frac{z \cdot \left(0.0007936500793651 \cdot z\right)}{x} \]
14. Add Preprocessing

Alternative 14: 26.4% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \left(\frac{z}{x} \cdot 0.0007936500793651\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (* (/ z x) 0.0007936500793651) z))

C

double code(double x, double y, double z) {
	return ((z / x) * 0.0007936500793651) * 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 = ((z / x) * 0.0007936500793651d0) * z
end function

Java

public static double code(double x, double y, double z) {
	return ((z / x) * 0.0007936500793651) * z;
}

Python

def code(x, y, z):
	return ((z / x) * 0.0007936500793651) * z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(z / x) * 0.0007936500793651) * z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((z / x) * 0.0007936500793651) * z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(z / x), $MachinePrecision] * 0.0007936500793651), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 94.5%

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

3. Taylor expanded in y around -inf

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

5. Applied rewrites 70.3%

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

6. Taylor expanded in z around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-+.f64 N/A

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

   7. associate-*r/ N/A

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

   8. metadata-eval N/A

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

   9. lower-/.f64 N/A

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

   10. lower-*.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. unpow2 N/A

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

   13. lower-*.f64 40.3

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

8. Applied rewrites 40.3%

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

9. Taylor expanded in y around 0

   \[\leadsto \frac{7936500793651}{10000000000000000} \cdot \frac{{z}^{2}}{\color{blue}{x}} \]
10. Step-by-step derivation

    1. *-commutative N/A

       \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

    2. lower-*.f64 N/A

       \[\leadsto \frac{{z}^{2}}{x} \cdot \frac{7936500793651}{10000000000000000} \]

    3. unpow2 N/A

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

    4. associate-*r/ N/A

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

    5. *-commutative N/A

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

    6. lower-*.f64 N/A

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

    7. lower-/.f64 26.1

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

11. Applied rewrites 26.1%

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

    1. lift-*.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. associate-*l* N/A

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

    4. *-commutative N/A

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

    5. associate-*r* N/A

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

    6. lower-*.f64 N/A

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

    7. lower-*.f64 26.1

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

13. Applied rewrites 26.1%

    \[\leadsto \left(\frac{z}{x} \cdot 0.0007936500793651\right) \cdot z \]
14. Add Preprocessing

Developer Target 1: 98.5% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

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)) + (0.91893853320467d0 - x)) + (0.083333333333333d0 / x)) + ((z / x) * ((z * (y + 0.0007936500793651d0)) - 0.0027777777777778d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025026 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (+ (+ (* (- x 1/2) (log x)) (- 91893853320467/100000000000000 x)) (/ 83333333333333/1000000000000000 x)) (* (/ z x) (- (* z (+ y 7936500793651/10000000000000000)) 13888888888889/5000000000000000))))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))