Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2

Percentage Accurate: 90.0% → 99.5%

Time: 6.7s

Alternatives: 18

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
}

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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)))) - t;
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * log(Float64(1.0 - y)))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Initial Program: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
}

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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)))) - t;
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * log(Float64(1.0 - y)))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(\left(-0.3333333333333333 \cdot y - 0.5\right) \cdot y - 1\right) \cdot y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (+
   (* (- x 1.0) (log y))
   (* (- z 1.0) (* (- (* (- (* -0.3333333333333333 y) 0.5) y) 1.0) y)))
  t))

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * (((((-0.3333333333333333 * y) - 0.5) * y) - 1.0) * y))) - t;
}

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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x - 1.0d0) * log(y)) + ((z - 1.0d0) * ((((((-0.3333333333333333d0) * y) - 0.5d0) * y) - 1.0d0) * y))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * (((((-0.3333333333333333 * y) - 0.5) * y) - 1.0) * y))) - t;
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * (((((-0.3333333333333333 * y) - 0.5) * y) - 1.0) * y))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * Float64(Float64(Float64(Float64(Float64(-0.3333333333333333 * y) - 0.5) * y) - 1.0) * y))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x - 1.0) * log(y)) + ((z - 1.0) * (((((-0.3333333333333333 * y) - 0.5) * y) - 1.0) * y))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(-0.3333333333333333 * y), $MachinePrecision] - 0.5), $MachinePrecision] * y), $MachinePrecision] - 1.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 90.0%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

2. Taylor expanded in y around 0

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

   1. *-commutative N/A

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) - 1\right) \cdot \color{blue}{y}\right)\right) - t \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) - 1\right) \cdot \color{blue}{y}\right)\right) - t \]

   3. lower--.f64 N/A

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(y \cdot \left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) - 1\right) \cdot y\right)\right) - t \]

   4. *-commutative N/A

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(\left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) \cdot y - 1\right) \cdot y\right)\right) - t \]

   5. lower-*.f64 N/A

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(\left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) \cdot y - 1\right) \cdot y\right)\right) - t \]

   6. lower--.f64 N/A

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(\left(\frac{-1}{3} \cdot y - \frac{1}{2}\right) \cdot y - 1\right) \cdot y\right)\right) - t \]

   7. lower-*.f64 99.5

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(\left(-0.3333333333333333 \cdot y - 0.5\right) \cdot y - 1\right) \cdot y\right)\right) - t \]

4. Applied rewrites 99.5%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(\left(\left(-0.3333333333333333 \cdot y - 0.5\right) \cdot y - 1\right) \cdot y\right)}\right) - t \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (fma (* -0.5 y) (- z 1.0) (- (- z 1.0))) y (* (log y) (- x 1.0))) t))

C

double code(double x, double y, double z, double t) {
	return fma(fma((-0.5 * y), (z - 1.0), -(z - 1.0)), y, (log(y) * (x - 1.0))) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(fma(Float64(-0.5 * y), Float64(z - 1.0), Float64(-Float64(z - 1.0))), y, Float64(log(y) * Float64(x - 1.0))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(-0.5 * y), $MachinePrecision] * N[(z - 1.0), $MachinePrecision] + (-N[(z - 1.0), $MachinePrecision])), $MachinePrecision] * y + N[(N[Log[y], $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 90.0%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

2. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(-1 \cdot \left(z - 1\right) + \frac{-1}{2} \cdot \left(y \cdot \left(z - 1\right)\right), \color{blue}{y}, \log y \cdot \left(x - 1\right)\right) - t \]

   3. +-commutative N/A

      \[\leadsto \mathsf{fma}\left(\frac{-1}{2} \cdot \left(y \cdot \left(z - 1\right)\right) + -1 \cdot \left(z - 1\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   4. associate-*r* N/A

      \[\leadsto \mathsf{fma}\left(\left(\frac{-1}{2} \cdot y\right) \cdot \left(z - 1\right) + -1 \cdot \left(z - 1\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   5. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   7. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   8. mul-1-neg N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, \mathsf{neg}\left(\left(z - 1\right)\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   9. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   10. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   11. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   12. lift-log.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   13. lift--.f64 99.4

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

4. Applied rewrites 99.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right)} - t \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(-0.5 \cdot y - 1\right) \cdot y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (* (- (* -0.5 y) 1.0) y))) t))

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * (((-0.5 * y) - 1.0) * y))) - t;
}

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

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * (((-0.5 * y) - 1.0) * y))) - t;
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * (((-0.5 * y) - 1.0) * y))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * Float64(Float64(Float64(-0.5 * y) - 1.0) * y))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x - 1.0) * log(y)) + ((z - 1.0) * (((-0.5 * y) - 1.0) * y))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[(N[(N[(-0.5 * y), $MachinePrecision] - 1.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 90.0%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

2. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-*.f64 99.4

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \left(\left(-0.5 \cdot y - 1\right) \cdot y\right)\right) - t \]

4. Applied rewrites 99.4%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(\left(-0.5 \cdot y - 1\right) \cdot y\right)}\right) - t \]
5. Add Preprocessing

Alternative 4: 99.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (- y) (- z 1.0) (* (log y) (- x 1.0))) t))

C

double code(double x, double y, double z, double t) {
	return fma(-y, (z - 1.0), (log(y) * (x - 1.0))) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(Float64(-y), Float64(z - 1.0), Float64(log(y) * Float64(x - 1.0))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[((-y) * N[(z - 1.0), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 90.0%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
3. Step-by-step derivation

   1. associate-*r* N/A

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

   2. mul-1-neg N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

   3. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

   4. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   5. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   7. lift-log.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   8. lift--.f64 99.1

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

4. Applied rewrites 99.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-y, z, \log y \cdot \left(x - 1\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (- y) z (* (log y) (- x 1.0))) t))

C

double code(double x, double y, double z, double t) {
	return fma(-y, z, (log(y) * (x - 1.0))) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(Float64(-y), z, Float64(log(y) * Float64(x - 1.0))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[((-y) * z + N[(N[Log[y], $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 90.0%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
3. Step-by-step derivation

   1. associate-*r* N/A

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

   2. mul-1-neg N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

   3. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

   4. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   5. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   7. lift-log.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   8. lift--.f64 99.1

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

4. Applied rewrites 99.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

5. Taylor expanded in z around inf

   \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot \left(x - 1\right)\right) - t \]
6. Step-by-step derivation

7. Applied rewrites 99.0%

   \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot \left(x - 1\right)\right) - t \]
8. Add Preprocessing

Alternative 6: 98.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, \log y \cdot x\right) - t\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05:\\ \;\;\;\;\mathsf{fma}\left(-y, z - 1, -\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (fma (- y) z (* (log y) x)) t)))
   (if (<= x -1.0)
     t_1
     (if (<= x 1.05) (- (fma (- y) (- z 1.0) (- (log y))) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(-y, z, (log(y) * x)) - t;
	double tmp;
	if (x <= -1.0) {
		tmp = t_1;
	} else if (x <= 1.05) {
		tmp = fma(-y, (z - 1.0), -log(y)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(Float64(-y), z, Float64(log(y) * x)) - t)
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_1;
	elseif (x <= 1.05)
		tmp = Float64(fma(Float64(-y), Float64(z - 1.0), Float64(-log(y))) - t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-y) * z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$1, If[LessEqual[x, 1.05], N[(N[((-y) * N[(z - 1.0), $MachinePrecision] + (-N[Log[y], $MachinePrecision])), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.05000000000000004 < x

   1. Initial program 94.2%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 99.3

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot \left(x - 1\right)\right) - t \]
   6. Step-by-step derivation

   7. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot \left(x - 1\right)\right) - t \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot x\right) - t \]
   9. Step-by-step derivation

   10. Applied rewrites 98.4%

       \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot x\right) - t \]

   if -1 < x < 1.05000000000000004

   1. Initial program 85.9%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 98.9

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \log y + \color{blue}{-1 \cdot \left(y \cdot \left(z - 1\right)\right)}\right) - t \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + -1 \cdot \color{blue}{\log y}\right) - t \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      3. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      4. lift-neg.f64 N/A

         \[\leadsto \left(\left(-y\right) \cdot \left(z - 1\right) + -1 \cdot \log y\right) - t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, -1 \cdot \log y\right) - t \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -1 \cdot \log y\right) - t \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \mathsf{neg}\left(\log y\right)\right) - t \]

      8. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

      9. lift-log.f64 98.0

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

   7. Applied rewrites 98.0%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z - 1}, -\log y\right) - t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 98.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-y, z, \log y \cdot x\right) - t\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05:\\ \;\;\;\;\mathsf{fma}\left(-y, z, -\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (fma (- y) z (* (log y) x)) t)))
   (if (<= x -1.0) t_1 (if (<= x 1.05) (- (fma (- y) z (- (log y))) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(-y, z, (log(y) * x)) - t;
	double tmp;
	if (x <= -1.0) {
		tmp = t_1;
	} else if (x <= 1.05) {
		tmp = fma(-y, z, -log(y)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(Float64(-y), z, Float64(log(y) * x)) - t)
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_1;
	elseif (x <= 1.05)
		tmp = Float64(fma(Float64(-y), z, Float64(-log(y))) - t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-y) * z + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$1, If[LessEqual[x, 1.05], N[(N[((-y) * z + (-N[Log[y], $MachinePrecision])), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.05000000000000004 < x

   1. Initial program 94.2%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 99.3

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot \left(x - 1\right)\right) - t \]
   6. Step-by-step derivation

   7. Applied rewrites 99.3%

      \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot \left(x - 1\right)\right) - t \]

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot x\right) - t \]
   9. Step-by-step derivation

   10. Applied rewrites 98.4%

       \[\leadsto \mathsf{fma}\left(-y, z, \log y \cdot x\right) - t \]

   if -1 < x < 1.05000000000000004

   1. Initial program 85.9%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 98.9

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \log y + \color{blue}{-1 \cdot \left(y \cdot \left(z - 1\right)\right)}\right) - t \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + -1 \cdot \color{blue}{\log y}\right) - t \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      3. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      4. lift-neg.f64 N/A

         \[\leadsto \left(\left(-y\right) \cdot \left(z - 1\right) + -1 \cdot \log y\right) - t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, -1 \cdot \log y\right) - t \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -1 \cdot \log y\right) - t \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \mathsf{neg}\left(\log y\right)\right) - t \]

      8. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

      9. lift-log.f64 98.0

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

   7. Applied rewrites 98.0%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z - 1}, -\log y\right) - t \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(-y, z, -\log y\right) - t \]
   9. Step-by-step derivation

   10. Applied rewrites 97.8%

       \[\leadsto \mathsf{fma}\left(-y, z, -\log y\right) - t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 95.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x - 1, \log y, -t\right)\\ \mathbf{if}\;x \leq -0.00062:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-61}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, -\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (- x 1.0) (log y) (- t))))
   (if (<= x -0.00062)
     t_1
     (if (<= x 4.5e-61) (- (fma (- y) z (- (log y))) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((x - 1.0), log(y), -t);
	double tmp;
	if (x <= -0.00062) {
		tmp = t_1;
	} else if (x <= 4.5e-61) {
		tmp = fma(-y, z, -log(y)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(x - 1.0), log(y), Float64(-t))
	tmp = 0.0
	if (x <= -0.00062)
		tmp = t_1;
	elseif (x <= 4.5e-61)
		tmp = Float64(fma(Float64(-y), z, Float64(-log(y))) - t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision] + (-t)), $MachinePrecision]}, If[LessEqual[x, -0.00062], t$95$1, If[LessEqual[x, 4.5e-61], N[(N[((-y) * z + (-N[Log[y], $MachinePrecision])), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e-4 or 4.5e-61 < x

   1. Initial program 93.5%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--l+ N/A

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

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x - 1, \log y, \left(z - 1\right) \cdot \log \left(1 - y\right) - t\right)} \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{x - 1}, \log y, \left(z - 1\right) \cdot \log \left(1 - y\right) - t\right) \]

      13. lift-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \color{blue}{\log y}, \left(z - 1\right) \cdot \log \left(1 - y\right) - t\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{\left(z - 1\right) \cdot \log \left(1 - y\right) - t}\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{\log \left(1 - y\right) \cdot \left(z - 1\right)} - t\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{\log \left(1 - y\right) \cdot \left(z - 1\right)} - t\right) \]

      17. lift-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{\log \left(1 - y\right)} \cdot \left(z - 1\right) - t\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \log \color{blue}{\left(1 - y\right)} \cdot \left(z - 1\right) - t\right) \]

      19. lift--.f64 93.5

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \log \left(1 - y\right) \cdot \color{blue}{\left(z - 1\right)} - t\right) \]

   3. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - 1, \log y, \log \left(1 - y\right) \cdot \left(z - 1\right) - t\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{-1 \cdot t}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(x - 1, \log y, \mathsf{neg}\left(t\right)\right) \]

      2. lower-neg.f64 92.9

         \[\leadsto \mathsf{fma}\left(x - 1, \log y, -t\right) \]

   6. Applied rewrites 92.9%

      \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{-t}\right) \]

   if -6.2e-4 < x < 4.5e-61

   1. Initial program 85.8%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 98.8

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \log y + \color{blue}{-1 \cdot \left(y \cdot \left(z - 1\right)\right)}\right) - t \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + -1 \cdot \color{blue}{\log y}\right) - t \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      3. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      4. lift-neg.f64 N/A

         \[\leadsto \left(\left(-y\right) \cdot \left(z - 1\right) + -1 \cdot \log y\right) - t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, -1 \cdot \log y\right) - t \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -1 \cdot \log y\right) - t \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \mathsf{neg}\left(\log y\right)\right) - t \]

      8. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

      9. lift-log.f64 98.6

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

   7. Applied rewrites 98.6%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z - 1}, -\log y\right) - t \]

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(-y, z, -\log y\right) - t \]
   9. Step-by-step derivation

   10. Applied rewrites 98.4%

       \[\leadsto \mathsf{fma}\left(-y, z, -\log y\right) - t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 90.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+239}:\\ \;\;\;\;\mathsf{fma}\left(x - 1, \log y, -t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (* (- (* -0.5 y) 1.0) z) y) t)))
   (if (<= z -4.5e+189)
     t_1
     (if (<= z 1.95e+239) (fma (- x 1.0) (log y) (- t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((((-0.5 * y) - 1.0) * z) * y) - t;
	double tmp;
	if (z <= -4.5e+189) {
		tmp = t_1;
	} else if (z <= 1.95e+239) {
		tmp = fma((x - 1.0), log(y), -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(Float64(-0.5 * y) - 1.0) * z) * y) - t)
	tmp = 0.0
	if (z <= -4.5e+189)
		tmp = t_1;
	elseif (z <= 1.95e+239)
		tmp = fma(Float64(x - 1.0), log(y), Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(N[(-0.5 * y), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[z, -4.5e+189], t$95$1, If[LessEqual[z, 1.95e+239], N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision] + (-t)), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999973e189 or 1.9499999999999999e239 < z

   1. Initial program 61.6%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(z - 1\right) + \frac{-1}{2} \cdot \left(y \cdot \left(z - 1\right)\right), \color{blue}{y}, \log y \cdot \left(x - 1\right)\right) - t \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{2} \cdot \left(y \cdot \left(z - 1\right)\right) + -1 \cdot \left(z - 1\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{-1}{2} \cdot y\right) \cdot \left(z - 1\right) + -1 \cdot \left(z - 1\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, \mathsf{neg}\left(\left(z - 1\right)\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      12. lift-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      13. lift--.f64 99.2

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in z around inf

      \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right)} - t \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right) \cdot y - t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right) \cdot y - t \]

      3. *-commutative N/A

         \[\leadsto \left(\left(\frac{-1}{2} \cdot y - 1\right) \cdot z\right) \cdot y - t \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{-1}{2} \cdot y - 1\right) \cdot z\right) \cdot y - t \]

      5. lower--.f64 N/A

         \[\leadsto \left(\left(\frac{-1}{2} \cdot y - 1\right) \cdot z\right) \cdot y - t \]

      6. lift-*.f64 68.9

         \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t \]

   7. Applied rewrites 68.9%

      \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot \color{blue}{y} - t \]

   if -4.49999999999999973e189 < z < 1.9499999999999999e239

   1. Initial program 95.0%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate--l+ N/A

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

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x - 1, \log y, \left(z - 1\right) \cdot \log \left(1 - y\right) - t\right)} \]

      12. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{x - 1}, \log y, \left(z - 1\right) \cdot \log \left(1 - y\right) - t\right) \]

      13. lift-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \color{blue}{\log y}, \left(z - 1\right) \cdot \log \left(1 - y\right) - t\right) \]

      14. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{\left(z - 1\right) \cdot \log \left(1 - y\right) - t}\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{\log \left(1 - y\right) \cdot \left(z - 1\right)} - t\right) \]

      16. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{\log \left(1 - y\right) \cdot \left(z - 1\right)} - t\right) \]

      17. lift-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{\log \left(1 - y\right)} \cdot \left(z - 1\right) - t\right) \]

      18. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \log \color{blue}{\left(1 - y\right)} \cdot \left(z - 1\right) - t\right) \]

      19. lift--.f64 95.0

          \[\leadsto \mathsf{fma}\left(x - 1, \log y, \log \left(1 - y\right) \cdot \color{blue}{\left(z - 1\right)} - t\right) \]

   3. Applied rewrites 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - 1, \log y, \log \left(1 - y\right) \cdot \left(z - 1\right) - t\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(x - 1, \log y, \color{blue}{-1 \cdot t}\right) \]
   5. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(x - 1, \log y, \mathsf{neg}\left(t\right)\right) \]

      2. lower-neg.f64 94.1

         \[\leadsto \mathsf{fma}\left(x - 1, \log y, -t\right) \]

   6. Applied rewrites 94.1%

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

Alternative 10: 90.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+239}:\\ \;\;\;\;\log y \cdot \left(x - 1\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (* (- (* -0.5 y) 1.0) z) y) t)))
   (if (<= z -4.5e+189)
     t_1
     (if (<= z 1.95e+239) (- (* (log y) (- x 1.0)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((((-0.5 * y) - 1.0) * z) * y) - t;
	double tmp;
	if (z <= -4.5e+189) {
		tmp = t_1;
	} else if (z <= 1.95e+239) {
		tmp = (log(y) * (x - 1.0)) - t;
	} else {
		tmp = t_1;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((-0.5d0) * y) - 1.0d0) * z) * y) - t
    if (z <= (-4.5d+189)) then
        tmp = t_1
    else if (z <= 1.95d+239) then
        tmp = (log(y) * (x - 1.0d0)) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((((-0.5 * y) - 1.0) * z) * y) - t;
	double tmp;
	if (z <= -4.5e+189) {
		tmp = t_1;
	} else if (z <= 1.95e+239) {
		tmp = (Math.log(y) * (x - 1.0)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((((-0.5 * y) - 1.0) * z) * y) - t
	tmp = 0
	if z <= -4.5e+189:
		tmp = t_1
	elif z <= 1.95e+239:
		tmp = (math.log(y) * (x - 1.0)) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(Float64(-0.5 * y) - 1.0) * z) * y) - t)
	tmp = 0.0
	if (z <= -4.5e+189)
		tmp = t_1;
	elseif (z <= 1.95e+239)
		tmp = Float64(Float64(log(y) * Float64(x - 1.0)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((((-0.5 * y) - 1.0) * z) * y) - t;
	tmp = 0.0;
	if (z <= -4.5e+189)
		tmp = t_1;
	elseif (z <= 1.95e+239)
		tmp = (log(y) * (x - 1.0)) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(N[(-0.5 * y), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[z, -4.5e+189], t$95$1, If[LessEqual[z, 1.95e+239], N[(N[(N[Log[y], $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999973e189 or 1.9499999999999999e239 < z

   1. Initial program 61.6%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-1 \cdot \left(z - 1\right) + \frac{-1}{2} \cdot \left(y \cdot \left(z - 1\right)\right), \color{blue}{y}, \log y \cdot \left(x - 1\right)\right) - t \]

      3. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{2} \cdot \left(y \cdot \left(z - 1\right)\right) + -1 \cdot \left(z - 1\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{-1}{2} \cdot y\right) \cdot \left(z - 1\right) + -1 \cdot \left(z - 1\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -1 \cdot \left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, \mathsf{neg}\left(\left(z - 1\right)\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      9. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      12. lift-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{2} \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

      13. lift--.f64 99.2

          \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-0.5 \cdot y, z - 1, -\left(z - 1\right)\right), y, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in z around inf

      \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right)} - t \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right) \cdot y - t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(z \cdot \left(\frac{-1}{2} \cdot y - 1\right)\right) \cdot y - t \]

      3. *-commutative N/A

         \[\leadsto \left(\left(\frac{-1}{2} \cdot y - 1\right) \cdot z\right) \cdot y - t \]

      4. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{-1}{2} \cdot y - 1\right) \cdot z\right) \cdot y - t \]

      5. lower--.f64 N/A

         \[\leadsto \left(\left(\frac{-1}{2} \cdot y - 1\right) \cdot z\right) \cdot y - t \]

      6. lift-*.f64 68.9

         \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot y - t \]

   7. Applied rewrites 68.9%

      \[\leadsto \left(\left(-0.5 \cdot y - 1\right) \cdot z\right) \cdot \color{blue}{y} - t \]

   if -4.49999999999999973e189 < z < 1.9499999999999999e239

   1. Initial program 95.0%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 94.1

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

   4. Applied rewrites 94.1%

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

Alternative 11: 90.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+189}:\\ \;\;\;\;\left(-y\right) \cdot z - t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+239}:\\ \;\;\;\;\log y \cdot \left(x - 1\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(z - 1\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e+189)
   (- (* (- y) z) t)
   (if (<= z 1.95e+239)
     (- (* (log y) (- x 1.0)) t)
     (- (* (- y) (- z 1.0)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+189) {
		tmp = (-y * z) - t;
	} else if (z <= 1.95e+239) {
		tmp = (log(y) * (x - 1.0)) - t;
	} else {
		tmp = (-y * (z - 1.0)) - t;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.5d+189)) then
        tmp = (-y * z) - t
    else if (z <= 1.95d+239) then
        tmp = (log(y) * (x - 1.0d0)) - t
    else
        tmp = (-y * (z - 1.0d0)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e+189) {
		tmp = (-y * z) - t;
	} else if (z <= 1.95e+239) {
		tmp = (Math.log(y) * (x - 1.0)) - t;
	} else {
		tmp = (-y * (z - 1.0)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e+189:
		tmp = (-y * z) - t
	elif z <= 1.95e+239:
		tmp = (math.log(y) * (x - 1.0)) - t
	else:
		tmp = (-y * (z - 1.0)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e+189)
		tmp = Float64(Float64(Float64(-y) * z) - t);
	elseif (z <= 1.95e+239)
		tmp = Float64(Float64(log(y) * Float64(x - 1.0)) - t);
	else
		tmp = Float64(Float64(Float64(-y) * Float64(z - 1.0)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.5e+189)
		tmp = (-y * z) - t;
	elseif (z <= 1.95e+239)
		tmp = (log(y) * (x - 1.0)) - t;
	else
		tmp = (-y * (z - 1.0)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e+189], N[(N[((-y) * z), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[z, 1.95e+239], N[(N[(N[Log[y], $MachinePrecision] * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[((-y) * N[(z - 1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999973e189

   1. Initial program 62.0%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 98.6

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot z\right)} - t \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y\right) \cdot z - t \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot z - t \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot z - t \]

      4. lower-*.f64 69.8

         \[\leadsto \left(-y\right) \cdot z - t \]

   7. Applied rewrites 69.8%

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

   if -4.49999999999999973e189 < z < 1.9499999999999999e239

   1. Initial program 95.0%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 94.1

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

   4. Applied rewrites 94.1%

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

   if 1.9499999999999999e239 < z

   1. Initial program 61.0%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 97.8

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 97.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(z - 1\right)\right)} - t \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) - t \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - \color{blue}{1}\right) - t \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot \left(z - 1\right) - t \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-y\right) \cdot \left(z - \color{blue}{1}\right) - t \]

      5. lift--.f64 65.3

         \[\leadsto \left(-y\right) \cdot \left(z - 1\right) - t \]

   7. Applied rewrites 65.3%

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

Alternative 12: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x - t\\ t_2 := \left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 220:\\ \;\;\;\;\left(-y\right) \cdot \left(z - 1\right) - t\\ \mathbf{elif}\;t\_2 \leq 700:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (log y) x) t))
        (t_2 (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))))
   (if (<= t_2 -4e+25)
     t_1
     (if (<= t_2 220.0)
       (- (* (- y) (- z 1.0)) t)
       (if (<= t_2 700.0) (- (- (log y)) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (log(y) * x) - t;
	double t_2 = ((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)));
	double tmp;
	if (t_2 <= -4e+25) {
		tmp = t_1;
	} else if (t_2 <= 220.0) {
		tmp = (-y * (z - 1.0)) - t;
	} else if (t_2 <= 700.0) {
		tmp = -log(y) - t;
	} else {
		tmp = t_1;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (log(y) * x) - t
    t_2 = ((x - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))
    if (t_2 <= (-4d+25)) then
        tmp = t_1
    else if (t_2 <= 220.0d0) then
        tmp = (-y * (z - 1.0d0)) - t
    else if (t_2 <= 700.0d0) then
        tmp = -log(y) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (Math.log(y) * x) - t;
	double t_2 = ((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)));
	double tmp;
	if (t_2 <= -4e+25) {
		tmp = t_1;
	} else if (t_2 <= 220.0) {
		tmp = (-y * (z - 1.0)) - t;
	} else if (t_2 <= 700.0) {
		tmp = -Math.log(y) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (math.log(y) * x) - t
	t_2 = ((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))
	tmp = 0
	if t_2 <= -4e+25:
		tmp = t_1
	elif t_2 <= 220.0:
		tmp = (-y * (z - 1.0)) - t
	elif t_2 <= 700.0:
		tmp = -math.log(y) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(log(y) * x) - t)
	t_2 = Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * log(Float64(1.0 - y))))
	tmp = 0.0
	if (t_2 <= -4e+25)
		tmp = t_1;
	elseif (t_2 <= 220.0)
		tmp = Float64(Float64(Float64(-y) * Float64(z - 1.0)) - t);
	elseif (t_2 <= 700.0)
		tmp = Float64(Float64(-log(y)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (log(y) * x) - t;
	t_2 = ((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)));
	tmp = 0.0;
	if (t_2 <= -4e+25)
		tmp = t_1;
	elseif (t_2 <= 220.0)
		tmp = (-y * (z - 1.0)) - t;
	elseif (t_2 <= 700.0)
		tmp = -log(y) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+25], t$95$1, If[LessEqual[t$95$2, 220.0], N[(N[((-y) * N[(z - 1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[t$95$2, 700.0], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) < -4.00000000000000036e25 or 700 < (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y))))

   1. Initial program 93.9%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} - t \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} - t \]

      2. lower-*.f64 N/A

         \[\leadsto \log y \cdot \color{blue}{x} - t \]

      3. lift-log.f64 90.9

         \[\leadsto \log y \cdot x - t \]

   4. Applied rewrites 90.9%

      \[\leadsto \color{blue}{\log y \cdot x} - t \]

   if -4.00000000000000036e25 < (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) < 220

   1. Initial program 76.7%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 99.1

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(z - 1\right)\right)} - t \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) - t \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - \color{blue}{1}\right) - t \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot \left(z - 1\right) - t \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-y\right) \cdot \left(z - \color{blue}{1}\right) - t \]

      5. lift--.f64 64.3

         \[\leadsto \left(-y\right) \cdot \left(z - 1\right) - t \]

   7. Applied rewrites 64.3%

      \[\leadsto \left(-y\right) \cdot \color{blue}{\left(z - 1\right)} - t \]

   if 220 < (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) < 700

   1. Initial program 90.4%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 100.0

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \log y + \color{blue}{-1 \cdot \left(y \cdot \left(z - 1\right)\right)}\right) - t \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + -1 \cdot \color{blue}{\log y}\right) - t \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      3. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      4. lift-neg.f64 N/A

         \[\leadsto \left(\left(-y\right) \cdot \left(z - 1\right) + -1 \cdot \log y\right) - t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, -1 \cdot \log y\right) - t \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -1 \cdot \log y\right) - t \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \mathsf{neg}\left(\log y\right)\right) - t \]

      8. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

      9. lift-log.f64 99.0

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

   7. Applied rewrites 99.0%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z - 1}, -\log y\right) - t \]

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \log y - t \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\log y\right)\right) - t \]

      2. lift-neg.f64 N/A

         \[\leadsto \left(-\log y\right) - t \]

      3. lift-log.f64 89.5

         \[\leadsto \left(-\log y\right) - t \]

   10. Applied rewrites 89.5%

       \[\leadsto \left(-\log y\right) - t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 220:\\ \;\;\;\;\left(-y\right) \cdot \left(z - 1\right) - t\\ \mathbf{elif}\;t\_2 \leq 6 \cdot 10^{+145}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x))
        (t_2 (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))))
   (if (<= t_2 -1e+103)
     t_1
     (if (<= t_2 220.0)
       (- (* (- y) (- z 1.0)) t)
       (if (<= t_2 6e+145) (- (- (log y)) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double t_2 = ((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)));
	double tmp;
	if (t_2 <= -1e+103) {
		tmp = t_1;
	} else if (t_2 <= 220.0) {
		tmp = (-y * (z - 1.0)) - t;
	} else if (t_2 <= 6e+145) {
		tmp = -log(y) - t;
	} else {
		tmp = t_1;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(y) * x
    t_2 = ((x - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))
    if (t_2 <= (-1d+103)) then
        tmp = t_1
    else if (t_2 <= 220.0d0) then
        tmp = (-y * (z - 1.0d0)) - t
    else if (t_2 <= 6d+145) then
        tmp = -log(y) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * x;
	double t_2 = ((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)));
	double tmp;
	if (t_2 <= -1e+103) {
		tmp = t_1;
	} else if (t_2 <= 220.0) {
		tmp = (-y * (z - 1.0)) - t;
	} else if (t_2 <= 6e+145) {
		tmp = -Math.log(y) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	t_2 = ((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))
	tmp = 0
	if t_2 <= -1e+103:
		tmp = t_1
	elif t_2 <= 220.0:
		tmp = (-y * (z - 1.0)) - t
	elif t_2 <= 6e+145:
		tmp = -math.log(y) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	t_2 = Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * log(Float64(1.0 - y))))
	tmp = 0.0
	if (t_2 <= -1e+103)
		tmp = t_1;
	elseif (t_2 <= 220.0)
		tmp = Float64(Float64(Float64(-y) * Float64(z - 1.0)) - t);
	elseif (t_2 <= 6e+145)
		tmp = Float64(Float64(-log(y)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	t_2 = ((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)));
	tmp = 0.0;
	if (t_2 <= -1e+103)
		tmp = t_1;
	elseif (t_2 <= 220.0)
		tmp = (-y * (z - 1.0)) - t;
	elseif (t_2 <= 6e+145)
		tmp = -log(y) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+103], t$95$1, If[LessEqual[t$95$2, 220.0], N[(N[((-y) * N[(z - 1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[t$95$2, 6e+145], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) < -1e103 or 6.0000000000000005e145 < (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y))))

   1. Initial program 96.3%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      3. lift-log.f64 78.8

         \[\leadsto \log y \cdot x \]

   4. Applied rewrites 78.8%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -1e103 < (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) < 220

   1. Initial program 80.7%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 99.1

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(z - 1\right)\right)} - t \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) - t \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - \color{blue}{1}\right) - t \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot \left(z - 1\right) - t \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-y\right) \cdot \left(z - \color{blue}{1}\right) - t \]

      5. lift--.f64 60.1

         \[\leadsto \left(-y\right) \cdot \left(z - 1\right) - t \]

   7. Applied rewrites 60.1%

      \[\leadsto \left(-y\right) \cdot \color{blue}{\left(z - 1\right)} - t \]

   if 220 < (+.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (log.f64 y)) (*.f64 (-.f64 z #s(literal 1 binary64)) (log.f64 (-.f64 #s(literal 1 binary64) y)))) < 6.0000000000000005e145

   1. Initial program 90.3%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 99.6

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in x around 0

      \[\leadsto \left(-1 \cdot \log y + \color{blue}{-1 \cdot \left(y \cdot \left(z - 1\right)\right)}\right) - t \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + -1 \cdot \color{blue}{\log y}\right) - t \]

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      3. distribute-lft-neg-out N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + -1 \cdot \log \color{blue}{y}\right) - t \]

      4. lift-neg.f64 N/A

         \[\leadsto \left(\left(-y\right) \cdot \left(z - 1\right) + -1 \cdot \log y\right) - t \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, -1 \cdot \log y\right) - t \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -1 \cdot \log y\right) - t \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \mathsf{neg}\left(\log y\right)\right) - t \]

      8. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

      9. lift-log.f64 87.0

         \[\leadsto \mathsf{fma}\left(-y, z - 1, -\log y\right) - t \]

   7. Applied rewrites 87.0%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z - 1}, -\log y\right) - t \]

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \log y - t \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\log y\right)\right) - t \]

      2. lift-neg.f64 N/A

         \[\leadsto \left(-\log y\right) - t \]

      3. lift-log.f64 77.4

         \[\leadsto \left(-\log y\right) - t \]

   10. Applied rewrites 77.4%

       \[\leadsto \left(-\log y\right) - t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 64.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+44}:\\ \;\;\;\;\left(-y\right) \cdot \left(z - 1\right) - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -4.8e+143)
     t_1
     (if (<= x 7.6e+44) (- (* (- y) (- z 1.0)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -4.8e+143) {
		tmp = t_1;
	} else if (x <= 7.6e+44) {
		tmp = (-y * (z - 1.0)) - t;
	} else {
		tmp = t_1;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(y) * x
    if (x <= (-4.8d+143)) then
        tmp = t_1
    else if (x <= 7.6d+44) then
        tmp = (-y * (z - 1.0d0)) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * x;
	double tmp;
	if (x <= -4.8e+143) {
		tmp = t_1;
	} else if (x <= 7.6e+44) {
		tmp = (-y * (z - 1.0)) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -4.8e+143:
		tmp = t_1
	elif x <= 7.6e+44:
		tmp = (-y * (z - 1.0)) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -4.8e+143)
		tmp = t_1;
	elseif (x <= 7.6e+44)
		tmp = Float64(Float64(Float64(-y) * Float64(z - 1.0)) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -4.8e+143)
		tmp = t_1;
	elseif (x <= 7.6e+44)
		tmp = (-y * (z - 1.0)) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -4.8e+143], t$95$1, If[LessEqual[x, 7.6e+44], N[(N[((-y) * N[(z - 1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999959e143 or 7.6000000000000004e44 < x

   1. Initial program 96.6%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      3. lift-log.f64 77.9

         \[\leadsto \log y \cdot x \]

   4. Applied rewrites 77.9%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -4.79999999999999959e143 < x < 7.6000000000000004e44

   1. Initial program 86.6%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 99.0

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot \left(z - 1\right)\right)} - t \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y \cdot \left(z - 1\right)\right)\right) - t \]

      2. distribute-lft-neg-out N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - \color{blue}{1}\right) - t \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot \left(z - 1\right) - t \]

      4. lower-*.f64 N/A

         \[\leadsto \left(-y\right) \cdot \left(z - \color{blue}{1}\right) - t \]

      5. lift--.f64 58.1

         \[\leadsto \left(-y\right) \cdot \left(z - 1\right) - t \]

   7. Applied rewrites 58.1%

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

Alternative 15: 64.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+44}:\\ \;\;\;\;\left(-y\right) \cdot z - t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -4.8e+143) t_1 (if (<= x 7.6e+44) (- (* (- y) z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -4.8e+143) {
		tmp = t_1;
	} else if (x <= 7.6e+44) {
		tmp = (-y * z) - t;
	} else {
		tmp = t_1;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(y) * x
    if (x <= (-4.8d+143)) then
        tmp = t_1
    else if (x <= 7.6d+44) then
        tmp = (-y * z) - t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * x;
	double tmp;
	if (x <= -4.8e+143) {
		tmp = t_1;
	} else if (x <= 7.6e+44) {
		tmp = (-y * z) - t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -4.8e+143:
		tmp = t_1
	elif x <= 7.6e+44:
		tmp = (-y * z) - t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -4.8e+143)
		tmp = t_1;
	elseif (x <= 7.6e+44)
		tmp = Float64(Float64(Float64(-y) * z) - t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -4.8e+143)
		tmp = t_1;
	elseif (x <= 7.6e+44)
		tmp = (-y * z) - t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -4.8e+143], t$95$1, If[LessEqual[x, 7.6e+44], N[(N[((-y) * z), $MachinePrecision] - t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999959e143 or 7.6000000000000004e44 < x

   1. Initial program 96.6%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      3. lift-log.f64 77.9

         \[\leadsto \log y \cdot x \]

   4. Applied rewrites 77.9%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -4.79999999999999959e143 < x < 7.6000000000000004e44

   1. Initial program 86.6%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   3. Step-by-step derivation

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

      4. lower-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      5. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      7. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

      8. lift--.f64 99.0

         \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   4. Applied rewrites 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

   5. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \color{blue}{\left(y \cdot z\right)} - t \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-1 \cdot y\right) \cdot z - t \]

      2. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot z - t \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(-y\right) \cdot z - t \]

      4. lower-*.f64 57.7

         \[\leadsto \left(-y\right) \cdot z - t \]

   7. Applied rewrites 57.7%

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

Alternative 16: 45.5% accurate, 4.2× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (- (* (- y) z) t))

C

double code(double x, double y, double z, double t) {
	return (-y * z) - t;
}

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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (-y * z) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (-y * z) - t;
}

Python

def code(x, y, z, t):
	return (-y * z) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(-y) * z) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (-y * z) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[((-y) * z), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 90.0%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
3. Step-by-step derivation

   1. associate-*r* N/A

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

   2. mul-1-neg N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(z - 1\right) + \log \color{blue}{y} \cdot \left(x - 1\right)\right) - t \]

   3. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), \color{blue}{z - 1}, \log y \cdot \left(x - 1\right)\right) - t \]

   4. lower-neg.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z} - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   5. lift--.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - \color{blue}{1}, \log y \cdot \left(x - 1\right)\right) - t \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   7. lift-log.f64 N/A

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

   8. lift--.f64 99.1

      \[\leadsto \mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right) - t \]

4. Applied rewrites 99.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \log y \cdot \left(x - 1\right)\right)} - t \]

5. Taylor expanded in z around inf

   \[\leadsto -1 \cdot \color{blue}{\left(y \cdot z\right)} - t \]
6. Step-by-step derivation

   1. associate-*r* N/A

      \[\leadsto \left(-1 \cdot y\right) \cdot z - t \]

   2. mul-1-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot z - t \]

   3. lift-neg.f64 N/A

      \[\leadsto \left(-y\right) \cdot z - t \]

   4. lower-*.f64 45.5

      \[\leadsto \left(-y\right) \cdot z - t \]

7. Applied rewrites 45.5%

   \[\leadsto \left(-y\right) \cdot \color{blue}{z} - t \]
8. Add Preprocessing

Alternative 17: 42.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+17}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+14}:\\ \;\;\;\;\left(-y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.32e+17) (- t) (if (<= t 2.65e+14) (* (- y) z) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.32e+17) {
		tmp = -t;
	} else if (t <= 2.65e+14) {
		tmp = -y * z;
	} else {
		tmp = -t;
	}
	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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.32d+17)) then
        tmp = -t
    else if (t <= 2.65d+14) then
        tmp = -y * z
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.32e+17) {
		tmp = -t;
	} else if (t <= 2.65e+14) {
		tmp = -y * z;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.32e+17:
		tmp = -t
	elif t <= 2.65e+14:
		tmp = -y * z
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.32e+17)
		tmp = Float64(-t);
	elseif (t <= 2.65e+14)
		tmp = Float64(Float64(-y) * z);
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.32e+17)
		tmp = -t;
	elseif (t <= 2.65e+14)
		tmp = -y * z;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.32e+17], (-t), If[LessEqual[t, 2.65e+14], N[((-y) * z), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -1.32e17 or 2.65e14 < t

   1. Initial program 95.3%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-1 \cdot t} \]
   3. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(t\right) \]

      2. lower-neg.f64 72.2

         \[\leadsto -t \]

   4. Applied rewrites 72.2%

      \[\leadsto \color{blue}{-t} \]

   if -1.32e17 < t < 2.65e14

   1. Initial program 85.3%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \log \left(1 - y\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift--.f64 3.8

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

   4. Applied rewrites 3.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot y\right) \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(y\right)\right) \cdot z \]

      2. lift-neg.f64 16.8

         \[\leadsto \left(-y\right) \cdot z \]

   7. Applied rewrites 16.8%

      \[\leadsto \left(-y\right) \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 35.9% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ -t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- t))

C

double code(double x, double y, double z, double t) {
	return -t;
}

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, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = -t
end function

Java

public static double code(double x, double y, double z, double t) {
	return -t;
}

Python

def code(x, y, z, t):
	return -t

Julia

function code(x, y, z, t)
	return Float64(-t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = -t;
end

Wolfram

code[x_, y_, z_, t_] := (-t)

Derivation

1. Initial program 90.0%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]

2. Taylor expanded in t around inf

   \[\leadsto \color{blue}{-1 \cdot t} \]
3. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(t\right) \]

   2. lower-neg.f64 35.9

      \[\leadsto -t \]

4. Applied rewrites 35.9%

   \[\leadsto \color{blue}{-t} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025120 
(FPCore (x y z t)
  :name "Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2"
  :precision binary64
  (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))