Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Percentage Accurate: 88.7% → 99.6%

Time: 1.2min

Alternatives: 10

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 / ((y - z) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.4× speedup

Math

\[\mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), 0, \left(\frac{-2}{t}\right)\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (134-z0z1z2z3z4 x (/ 2 (- z y)) (/ 1/2 (- z t)) 0 (/ -2 t)))

Derivation

1. Initial program 88.7%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. frac-2neg N/A

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

   3. distribute-frac-neg2 N/A

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

   4. distribute-neg-frac N/A

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

   5. mult-flip N/A

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

   6. remove-double-neg N/A

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

   7. metadata-eval N/A

      \[\leadsto x \cdot \frac{\color{blue}{1 - 0}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   8. div-sub N/A

      \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right)} \]

   9. *-inverses N/A

      \[\leadsto x \cdot \left(\frac{\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   10. mult-flip N/A

       \[\leadsto x \cdot \left(\frac{\color{blue}{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   11. lift-*.f64 N/A

       \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right) \cdot \left(t - z\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   12. lift--.f64 N/A

       \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   13. sub-negate-rev N/A

       \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

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

       \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - z\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   15. distribute-rgt-neg-in N/A

       \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   16. lift--.f64 N/A

       \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   17. sub-negate-rev N/A

       \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   18. times-frac N/A

       \[\leadsto x \cdot \left(\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{z - y} \cdot \frac{\frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{z - t}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

3. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), \left(\frac{0}{z - y}\right), \left(\frac{2}{z - t}\right)\right)} \]

4. Taylor expanded in y around 0

   \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), \color{blue}{0}, \left(\frac{2}{z - t}\right)\right) \]
5. Step-by-step derivation

6. Applied rewrites 99.6%

   \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), \color{blue}{0}, \left(\frac{2}{z - t}\right)\right) \]

7. Taylor expanded in z around 0

   \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), 0, \color{blue}{\left(\frac{-2}{t}\right)}\right) \]
8. Step-by-step derivation

   1. lower-/.f64 99.6%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), 0, \left(\frac{-2}{\color{blue}{t}}\right)\right) \]

9. Applied rewrites 99.6%

   \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), 0, \color{blue}{\left(\frac{-2}{t}\right)}\right) \]
10. Add Preprocessing

Alternative 2: 97.1% accurate, 0.1× speedup

Math

\[\frac{\frac{x}{z - \mathsf{max}\left(y, t\right)}}{z - \mathsf{min}\left(y, t\right)} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (/ (/ x (- z (fmax y t))) (- z (fmin y t))))

C

double code(double x, double y, double z, double t) {
	return (x / (z - fmax(y, t))) / (z - fmin(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 / (z - fmax(y, t))) / (z - fmin(y, t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.7%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. lift--.f64 N/A

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

   6. sub-negate-rev N/A

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

   7. distribute-frac-neg2 N/A

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

   8. lift--.f64 N/A

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

   9. sub-negate-rev N/A

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

   10. frac-2neg-rev N/A

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

   11. lower-/.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lower--.f64 N/A

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

   14. lower--.f64 97.0%

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

3. Applied rewrites 97.0%

   \[\leadsto \color{blue}{\frac{\frac{x}{z - t}}{z - y}} \]
4. Add Preprocessing

Alternative 3: 91.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -620000000000000028564426977836206701965470623707109973387378688:\\ \;\;\;\;\frac{\frac{x}{z - \mathsf{max}\left(y, t\right)}}{z}\\ \mathbf{elif}\;z \leq 230000000000000000519191460181802526018234812242782878790299156480:\\ \;\;\;\;\frac{x}{\left(\mathsf{min}\left(y, t\right) - z\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - \mathsf{min}\left(y, t\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     z
     -620000000000000028564426977836206701965470623707109973387378688)
  (/ (/ x (- z (fmax y t))) z)
  (if (<=
       z
       230000000000000000519191460181802526018234812242782878790299156480)
    (/ x (* (- (fmin y t) z) (- (fmax y t) z)))
    (/ (/ x z) (- z (fmin y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e+62) {
		tmp = (x / (z - fmax(y, t))) / z;
	} else if (z <= 2.3e+65) {
		tmp = x / ((fmin(y, t) - z) * (fmax(y, t) - z));
	} else {
		tmp = (x / z) / (z - fmin(y, 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 <= (-6.2d+62)) then
        tmp = (x / (z - fmax(y, t))) / z
    else if (z <= 2.3d+65) then
        tmp = x / ((fmin(y, t) - z) * (fmax(y, t) - z))
    else
        tmp = (x / z) / (z - fmin(y, t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e+62) {
		tmp = (x / (z - fmax(y, t))) / z;
	} else if (z <= 2.3e+65) {
		tmp = x / ((fmin(y, t) - z) * (fmax(y, t) - z));
	} else {
		tmp = (x / z) / (z - fmin(y, t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.2e+62:
		tmp = (x / (z - fmax(y, t))) / z
	elif z <= 2.3e+65:
		tmp = x / ((fmin(y, t) - z) * (fmax(y, t) - z))
	else:
		tmp = (x / z) / (z - fmin(y, t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.2e+62)
		tmp = Float64(Float64(x / Float64(z - fmax(y, t))) / z);
	elseif (z <= 2.3e+65)
		tmp = Float64(x / Float64(Float64(fmin(y, t) - z) * Float64(fmax(y, t) - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - fmin(y, t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.2e+62)
		tmp = (x / (z - max(y, t))) / z;
	elseif (z <= 2.3e+65)
		tmp = x / ((min(y, t) - z) * (max(y, t) - z));
	else
		tmp = (x / z) / (z - min(y, t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -620000000000000028564426977836206701965470623707109973387378688], N[(N[(x / N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 230000000000000000519191460181802526018234812242782878790299156480], N[(x / N[(N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000003e62

   1. Initial program 88.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. distribute-frac-neg2 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. frac-2neg-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 97.0%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{x}{z - t}}{\color{blue}{z}} \]
   5. Step-by-step derivation

   6. Applied rewrites 59.4%

      \[\leadsto \frac{\frac{x}{z - t}}{\color{blue}{z}} \]

   if -6.2000000000000003e62 < z < 2.3e65

   1. Initial program 88.7%

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

   if 2.3e65 < z

   1. Initial program 88.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. distribute-frac-neg2 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. frac-2neg-rev N/A

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

      11. mult-flip N/A

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \frac{1}{z - y}} \]

      12. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \frac{1}{z - y}} \]

      13. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{x}{z - t}} \cdot \frac{1}{z - y} \]

      14. lower--.f64 N/A

          \[\leadsto \frac{x}{\color{blue}{z - t}} \cdot \frac{1}{z - y} \]

      15. metadata-eval N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. frac-2neg-rev N/A

          \[\leadsto \frac{x}{z - t} \cdot \color{blue}{\frac{-1}{y - z}} \]

      19. lower-/.f64 96.9%

          \[\leadsto \frac{x}{z - t} \cdot \color{blue}{\frac{-1}{y - z}} \]

   3. Applied rewrites 96.9%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \frac{-1}{y - z}} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{-1}{y - z} \]
   5. Step-by-step derivation

      1. lower-/.f64 56.5%

         \[\leadsto \frac{x}{\color{blue}{z}} \cdot \frac{-1}{y - z} \]

   6. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{-1}{y - z} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{-1}{y - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-1}{y - z}} \]

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\color{blue}{z - y}} \]

      7. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{x}{z} \cdot 1}{z - y}} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{x}{z} \cdot 1}{z - y}} \]

      9. *-rgt-identity N/A

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

      10. lift--.f64 56.6%

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

   8. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 91.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -620000000000000028564426977836206701965470623707109973387378688:\\ \;\;\;\;\frac{\frac{x}{z}}{z - \mathsf{max}\left(y, t\right)}\\ \mathbf{elif}\;z \leq 230000000000000000519191460181802526018234812242782878790299156480:\\ \;\;\;\;\frac{x}{\left(\mathsf{min}\left(y, t\right) - z\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - \mathsf{min}\left(y, t\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     z
     -620000000000000028564426977836206701965470623707109973387378688)
  (/ (/ x z) (- z (fmax y t)))
  (if (<=
       z
       230000000000000000519191460181802526018234812242782878790299156480)
    (/ x (* (- (fmin y t) z) (- (fmax y t) z)))
    (/ (/ x z) (- z (fmin y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e+62) {
		tmp = (x / z) / (z - fmax(y, t));
	} else if (z <= 2.3e+65) {
		tmp = x / ((fmin(y, t) - z) * (fmax(y, t) - z));
	} else {
		tmp = (x / z) / (z - fmin(y, 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 <= (-6.2d+62)) then
        tmp = (x / z) / (z - fmax(y, t))
    else if (z <= 2.3d+65) then
        tmp = x / ((fmin(y, t) - z) * (fmax(y, t) - z))
    else
        tmp = (x / z) / (z - fmin(y, t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e+62) {
		tmp = (x / z) / (z - fmax(y, t));
	} else if (z <= 2.3e+65) {
		tmp = x / ((fmin(y, t) - z) * (fmax(y, t) - z));
	} else {
		tmp = (x / z) / (z - fmin(y, t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.2e+62:
		tmp = (x / z) / (z - fmax(y, t))
	elif z <= 2.3e+65:
		tmp = x / ((fmin(y, t) - z) * (fmax(y, t) - z))
	else:
		tmp = (x / z) / (z - fmin(y, t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.2e+62)
		tmp = Float64(Float64(x / z) / Float64(z - fmax(y, t)));
	elseif (z <= 2.3e+65)
		tmp = Float64(x / Float64(Float64(fmin(y, t) - z) * Float64(fmax(y, t) - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - fmin(y, t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.2e+62)
		tmp = (x / z) / (z - max(y, t));
	elseif (z <= 2.3e+65)
		tmp = x / ((min(y, t) - z) * (max(y, t) - z));
	else
		tmp = (x / z) / (z - min(y, t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -620000000000000028564426977836206701965470623707109973387378688], N[(N[(x / z), $MachinePrecision] / N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 230000000000000000519191460181802526018234812242782878790299156480], N[(x / N[(N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000003e62

   1. Initial program 88.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg2 N/A

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

      4. distribute-neg-frac N/A

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

      5. mult-flip N/A

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

      6. remove-double-neg N/A

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

      7. metadata-eval N/A

         \[\leadsto x \cdot \frac{\color{blue}{1 - 0}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      8. div-sub N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right)} \]

      9. *-inverses N/A

         \[\leadsto x \cdot \left(\frac{\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      10. mult-flip N/A

          \[\leadsto x \cdot \left(\frac{\color{blue}{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right) \cdot \left(t - z\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      12. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      13. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

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

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - z\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      17. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      18. times-frac N/A

          \[\leadsto x \cdot \left(\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{z - y} \cdot \frac{\frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{z - t}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   3. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), \left(\frac{0}{z - y}\right), \left(\frac{2}{z - t}\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

      5. lower-/.f64 57.3%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z} - t} \]

   8. Applied rewrites 57.3%

      \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

   if -6.2000000000000003e62 < z < 2.3e65

   1. Initial program 88.7%

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

   if 2.3e65 < z

   1. Initial program 88.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. distribute-frac-neg2 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. frac-2neg-rev N/A

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

      11. mult-flip N/A

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \frac{1}{z - y}} \]

      12. lower-*.f64 N/A

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \frac{1}{z - y}} \]

      13. lower-/.f64 N/A

          \[\leadsto \color{blue}{\frac{x}{z - t}} \cdot \frac{1}{z - y} \]

      14. lower--.f64 N/A

          \[\leadsto \frac{x}{\color{blue}{z - t}} \cdot \frac{1}{z - y} \]

      15. metadata-eval N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 N/A

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

      18. frac-2neg-rev N/A

          \[\leadsto \frac{x}{z - t} \cdot \color{blue}{\frac{-1}{y - z}} \]

      19. lower-/.f64 96.9%

          \[\leadsto \frac{x}{z - t} \cdot \color{blue}{\frac{-1}{y - z}} \]

   3. Applied rewrites 96.9%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \frac{-1}{y - z}} \]

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{-1}{y - z} \]
   5. Step-by-step derivation

      1. lower-/.f64 56.5%

         \[\leadsto \frac{x}{\color{blue}{z}} \cdot \frac{-1}{y - z} \]

   6. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\frac{x}{z}} \cdot \frac{-1}{y - z} \]
   7. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{-1}{y - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-1}{y - z}} \]

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

         \[\leadsto \frac{x}{z} \cdot \frac{1}{\color{blue}{z - y}} \]

      7. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{x}{z} \cdot 1}{z - y}} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{x}{z} \cdot 1}{z - y}} \]

      9. *-rgt-identity N/A

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

      10. lift--.f64 56.6%

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

   8. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{z - y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 88.7% accurate, 0.1× speedup

Math

\[\mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;\left|x\right| \leq 53999999999999994460554466293816695728673855464713753691845866347553268068862465361878962243493542853062926547897473848599210925528049937866186001234467342095518149287905599506986073144689734346152409303027578180711881601842433039542400319488:\\ \;\;\;\;\frac{\left|x\right|}{\left(\mathsf{min}\left(y, t\right) - z\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left|x\right|}{z}}{z - \mathsf{max}\left(y, t\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (*
 (copysign 1 x)
 (if (<=
      (fabs x)
      53999999999999994460554466293816695728673855464713753691845866347553268068862465361878962243493542853062926547897473848599210925528049937866186001234467342095518149287905599506986073144689734346152409303027578180711881601842433039542400319488)
   (/ (fabs x) (* (- (fmin y t) z) (- (fmax y t) z)))
   (/ (/ (fabs x) z) (- z (fmax y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (fabs(x) <= 5.4e+241) {
		tmp = fabs(x) / ((fmin(y, t) - z) * (fmax(y, t) - z));
	} else {
		tmp = (fabs(x) / z) / (z - fmax(y, t));
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.abs(x) <= 5.4e+241) {
		tmp = Math.abs(x) / ((fmin(y, t) - z) * (fmax(y, t) - z));
	} else {
		tmp = (Math.abs(x) / z) / (z - fmax(y, t));
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.fabs(x) <= 5.4e+241:
		tmp = math.fabs(x) / ((fmin(y, t) - z) * (fmax(y, t) - z))
	else:
		tmp = (math.fabs(x) / z) / (z - fmax(y, t))
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (abs(x) <= 5.4e+241)
		tmp = Float64(abs(x) / Float64(Float64(fmin(y, t) - z) * Float64(fmax(y, t) - z)));
	else
		tmp = Float64(Float64(abs(x) / z) / Float64(z - fmax(y, t)));
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (abs(x) <= 5.4e+241)
		tmp = abs(x) / ((min(y, t) - z) * (max(y, t) - z));
	else
		tmp = (abs(x) / z) / (z - max(y, t));
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[With[{TMP1 = Abs[1], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[x], $MachinePrecision], 53999999999999994460554466293816695728673855464713753691845866347553268068862465361878962243493542853062926547897473848599210925528049937866186001234467342095518149287905599506986073144689734346152409303027578180711881601842433039542400319488], N[(N[Abs[x], $MachinePrecision] / N[(N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Abs[x], $MachinePrecision] / z), $MachinePrecision] / N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 5.3999999999999994e241

   1. Initial program 88.7%

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

   if 5.3999999999999994e241 < x

   1. Initial program 88.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg2 N/A

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

      4. distribute-neg-frac N/A

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

      5. mult-flip N/A

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

      6. remove-double-neg N/A

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

      7. metadata-eval N/A

         \[\leadsto x \cdot \frac{\color{blue}{1 - 0}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      8. div-sub N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right)} \]

      9. *-inverses N/A

         \[\leadsto x \cdot \left(\frac{\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      10. mult-flip N/A

          \[\leadsto x \cdot \left(\frac{\color{blue}{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right) \cdot \left(t - z\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      12. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      13. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

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

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - z\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      17. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      18. times-frac N/A

          \[\leadsto x \cdot \left(\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{z - y} \cdot \frac{\frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{z - t}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   3. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), \left(\frac{0}{z - y}\right), \left(\frac{2}{z - t}\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

      4. lower-/.f64 N/A

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]

      5. lower-/.f64 57.3%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z} - t} \]

   8. Applied rewrites 57.3%

      \[\leadsto \frac{\frac{x}{z}}{\color{blue}{z - t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 77.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\mathsf{min}\left(y, t\right) \leq \frac{-5377774977523043}{32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016}:\\ \;\;\;\;\frac{x}{\mathsf{min}\left(y, t\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{elif}\;\mathsf{min}\left(y, t\right) \leq \frac{5159714252685701}{1842755090244893238399196572748178169393027939656465052918069482541808673043041431682679065028153695088607604995490158642466105776330465152617887818082371115063181312}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - \mathsf{max}\left(y, t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(\mathsf{min}\left(y, t\right) - z\right) \cdot \mathsf{max}\left(y, t\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<=
     (fmin y t)
     -5377774977523043/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016)
  (/ x (* (fmin y t) (- (fmax y t) z)))
  (if (<=
       (fmin y t)
       5159714252685701/1842755090244893238399196572748178169393027939656465052918069482541808673043041431682679065028153695088607604995490158642466105776330465152617887818082371115063181312)
    (/ x (* z (- z (fmax y t))))
    (/ x (* (- (fmin y t) z) (fmax y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (fmin(y, t) <= -1.65e-76) {
		tmp = x / (fmin(y, t) * (fmax(y, t) - z));
	} else if (fmin(y, t) <= 2.8e-150) {
		tmp = x / (z * (z - fmax(y, t)));
	} else {
		tmp = x / ((fmin(y, t) - z) * fmax(y, 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 (fmin(y, t) <= (-1.65d-76)) then
        tmp = x / (fmin(y, t) * (fmax(y, t) - z))
    else if (fmin(y, t) <= 2.8d-150) then
        tmp = x / (z * (z - fmax(y, t)))
    else
        tmp = x / ((fmin(y, t) - z) * fmax(y, t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (fmin(y, t) <= -1.65e-76) {
		tmp = x / (fmin(y, t) * (fmax(y, t) - z));
	} else if (fmin(y, t) <= 2.8e-150) {
		tmp = x / (z * (z - fmax(y, t)));
	} else {
		tmp = x / ((fmin(y, t) - z) * fmax(y, t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if fmin(y, t) <= -1.65e-76:
		tmp = x / (fmin(y, t) * (fmax(y, t) - z))
	elif fmin(y, t) <= 2.8e-150:
		tmp = x / (z * (z - fmax(y, t)))
	else:
		tmp = x / ((fmin(y, t) - z) * fmax(y, t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (fmin(y, t) <= -1.65e-76)
		tmp = Float64(x / Float64(fmin(y, t) * Float64(fmax(y, t) - z)));
	elseif (fmin(y, t) <= 2.8e-150)
		tmp = Float64(x / Float64(z * Float64(z - fmax(y, t))));
	else
		tmp = Float64(x / Float64(Float64(fmin(y, t) - z) * fmax(y, t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (min(y, t) <= -1.65e-76)
		tmp = x / (min(y, t) * (max(y, t) - z));
	elseif (min(y, t) <= 2.8e-150)
		tmp = x / (z * (z - max(y, t)));
	else
		tmp = x / ((min(y, t) - z) * max(y, t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Min[y, t], $MachinePrecision], -5377774977523043/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016], N[(x / N[(N[Min[y, t], $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Min[y, t], $MachinePrecision], 5159714252685701/1842755090244893238399196572748178169393027939656465052918069482541808673043041431682679065028153695088607604995490158642466105776330465152617887818082371115063181312], N[(x / N[(z * N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision] * N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e-76

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.9%

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

   4. Applied rewrites 39.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.2%

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

   7. Applied rewrites 57.2%

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

   if -1.6499999999999999e-76 < y < 2.8e-150

   1. Initial program 88.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg2 N/A

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

      4. distribute-neg-frac N/A

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

      5. mult-flip N/A

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

      6. remove-double-neg N/A

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

      7. metadata-eval N/A

         \[\leadsto x \cdot \frac{\color{blue}{1 - 0}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      8. div-sub N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right)} \]

      9. *-inverses N/A

         \[\leadsto x \cdot \left(\frac{\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      10. mult-flip N/A

          \[\leadsto x \cdot \left(\frac{\color{blue}{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right) \cdot \left(t - z\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      12. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      13. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

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

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - z\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      17. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      18. times-frac N/A

          \[\leadsto x \cdot \left(\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{z - y} \cdot \frac{\frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{z - t}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   3. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), \left(\frac{0}{z - y}\right), \left(\frac{2}{z - t}\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

   if 2.8e-150 < y

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 57.9%

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

Alternative 7: 75.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{\mathsf{min}\left(y, t\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{if}\;\mathsf{min}\left(y, t\right) \leq \frac{-5377774977523043}{32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\mathsf{min}\left(y, t\right) \leq \frac{8583373319263867}{604462909807314587353088}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - \mathsf{max}\left(y, t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ x (* (fmin y t) (- (fmax y t) z)))))
  (if (<=
       (fmin y t)
       -5377774977523043/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016)
    t_1
    (if (<= (fmin y t) 8583373319263867/604462909807314587353088)
      (/ x (* z (- z (fmax y t))))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (fmin(y, t) * (fmax(y, t) - z));
	double tmp;
	if (fmin(y, t) <= -1.65e-76) {
		tmp = t_1;
	} else if (fmin(y, t) <= 1.42e-8) {
		tmp = x / (z * (z - fmax(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) :: tmp
    t_1 = x / (fmin(y, t) * (fmax(y, t) - z))
    if (fmin(y, t) <= (-1.65d-76)) then
        tmp = t_1
    else if (fmin(y, t) <= 1.42d-8) then
        tmp = x / (z * (z - fmax(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 = x / (fmin(y, t) * (fmax(y, t) - z));
	double tmp;
	if (fmin(y, t) <= -1.65e-76) {
		tmp = t_1;
	} else if (fmin(y, t) <= 1.42e-8) {
		tmp = x / (z * (z - fmax(y, t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (fmin(y, t) * (fmax(y, t) - z))
	tmp = 0
	if fmin(y, t) <= -1.65e-76:
		tmp = t_1
	elif fmin(y, t) <= 1.42e-8:
		tmp = x / (z * (z - fmax(y, t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(fmin(y, t) * Float64(fmax(y, t) - z)))
	tmp = 0.0
	if (fmin(y, t) <= -1.65e-76)
		tmp = t_1;
	elseif (fmin(y, t) <= 1.42e-8)
		tmp = Float64(x / Float64(z * Float64(z - fmax(y, t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (min(y, t) * (max(y, t) - z));
	tmp = 0.0;
	if (min(y, t) <= -1.65e-76)
		tmp = t_1;
	elseif (min(y, t) <= 1.42e-8)
		tmp = x / (z * (z - max(y, t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[Min[y, t], $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Min[y, t], $MachinePrecision], -5377774977523043/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016], t$95$1, If[LessEqual[N[Min[y, t], $MachinePrecision], 8583373319263867/604462909807314587353088], N[(x / N[(z * N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999999e-76 or 1.42e-8 < y

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.9%

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

   4. Applied rewrites 39.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.2%

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

   7. Applied rewrites 57.2%

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

   if -1.6499999999999999e-76 < y < 1.42e-8

   1. Initial program 88.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg2 N/A

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

      4. distribute-neg-frac N/A

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

      5. mult-flip N/A

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

      6. remove-double-neg N/A

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

      7. metadata-eval N/A

         \[\leadsto x \cdot \frac{\color{blue}{1 - 0}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      8. div-sub N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right)} \]

      9. *-inverses N/A

         \[\leadsto x \cdot \left(\frac{\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      10. mult-flip N/A

          \[\leadsto x \cdot \left(\frac{\color{blue}{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right) \cdot \left(t - z\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      12. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      13. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

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

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - z\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      17. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      18. times-frac N/A

          \[\leadsto x \cdot \left(\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{z - y} \cdot \frac{\frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{z - t}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   3. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), \left(\frac{0}{z - y}\right), \left(\frac{2}{z - t}\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

Alternative 8: 66.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - \mathsf{max}\left(y, t\right)\right)}\\ \mathbf{if}\;z \leq \frac{-2671230065510023}{14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{2582544170319337}{36893488147419103232}:\\ \;\;\;\;\frac{x}{\mathsf{max}\left(y, t\right) \cdot \mathsf{min}\left(y, t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ x (* z (- z (fmax y t))))))
  (if (<=
       z
       -2671230065510023/14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296)
    t_1
    (if (<= z 2582544170319337/36893488147419103232)
      (/ x (* (fmax y t) (fmin y t)))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - fmax(y, t)));
	double tmp;
	if (z <= -1.9e-145) {
		tmp = t_1;
	} else if (z <= 7e-5) {
		tmp = x / (fmax(y, t) * fmin(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) :: tmp
    t_1 = x / (z * (z - fmax(y, t)))
    if (z <= (-1.9d-145)) then
        tmp = t_1
    else if (z <= 7d-5) then
        tmp = x / (fmax(y, t) * fmin(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 = x / (z * (z - fmax(y, t)));
	double tmp;
	if (z <= -1.9e-145) {
		tmp = t_1;
	} else if (z <= 7e-5) {
		tmp = x / (fmax(y, t) * fmin(y, t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (z - fmax(y, t)))
	tmp = 0
	if z <= -1.9e-145:
		tmp = t_1
	elif z <= 7e-5:
		tmp = x / (fmax(y, t) * fmin(y, t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - fmax(y, t))))
	tmp = 0.0
	if (z <= -1.9e-145)
		tmp = t_1;
	elseif (z <= 7e-5)
		tmp = Float64(x / Float64(fmax(y, t) * fmin(y, t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - max(y, t)));
	tmp = 0.0;
	if (z <= -1.9e-145)
		tmp = t_1;
	elseif (z <= 7e-5)
		tmp = x / (max(y, t) * min(y, t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2671230065510023/14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296], t$95$1, If[LessEqual[z, 2582544170319337/36893488147419103232], N[(x / N[(N[Max[y, t], $MachinePrecision] * N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9000000000000001e-145 or 6.9999999999999994e-5 < z

   1. Initial program 88.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. distribute-frac-neg2 N/A

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

      4. distribute-neg-frac N/A

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

      5. mult-flip N/A

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

      6. remove-double-neg N/A

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

      7. metadata-eval N/A

         \[\leadsto x \cdot \frac{\color{blue}{1 - 0}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      8. div-sub N/A

         \[\leadsto x \cdot \color{blue}{\left(\frac{1}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right)} \]

      9. *-inverses N/A

         \[\leadsto x \cdot \left(\frac{\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      10. mult-flip N/A

          \[\leadsto x \cdot \left(\frac{\color{blue}{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right) \cdot \left(t - z\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      12. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(y - z\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      13. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - z\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

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

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - z\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\color{blue}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      16. lift--.f64 N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      17. sub-negate-rev N/A

          \[\leadsto x \cdot \left(\frac{\left(e^{0} + e^{\mathsf{neg}\left(0\right)}\right) \cdot \frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{\left(z - y\right) \cdot \color{blue}{\left(z - t\right)}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

      18. times-frac N/A

          \[\leadsto x \cdot \left(\color{blue}{\frac{e^{0} + e^{\mathsf{neg}\left(0\right)}}{z - y} \cdot \frac{\frac{1}{e^{0} + e^{\mathsf{neg}\left(0\right)}}}{z - t}} - \frac{0}{\left(y - z\right) \cdot \left(t - z\right)}\right) \]

   3. Applied rewrites 99.6%

      \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(x, \left(\frac{2}{z - y}\right), \left(\frac{\frac{1}{2}}{z - t}\right), \left(\frac{0}{z - y}\right), \left(\frac{2}{z - t}\right)\right)} \]

   4. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

   if -1.9000000000000001e-145 < z < 6.9999999999999994e-5

   1. Initial program 88.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.9%

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

   4. Applied rewrites 39.9%

      \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 39.9% accurate, 1.4× speedup

Math

\[\frac{x}{t \cdot y} \]

FPCore

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

C

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

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 / (t * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.7%

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

2. Taylor expanded in z around 0

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

   1. lower-*.f64 39.9%

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

4. Applied rewrites 39.9%

   \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64
  (/ x (* (- y z) (- t z))))