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

Percentage Accurate: 89.3% → 97.5%

Time: 3.5s

Alternatives: 16

Speedup: 0.7×

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: 89.3% 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: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left|x\right|}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 10^{-275}:\\ \;\;\;\;\frac{\frac{\left|x\right|}{z - t}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fabs x) (* (- y z) (- t z)))))
   (*
    (copysign 1.0 x)
    (if (<= t_1 1e-275) (/ (/ (fabs x) (- z t)) (- z y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fabs(x) / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 1e-275) {
		tmp = (fabs(x) / (z - t)) / (z - y);
	} else {
		tmp = t_1;
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.abs(x) / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 1e-275) {
		tmp = (Math.abs(x) / (z - t)) / (z - y);
	} else {
		tmp = t_1;
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.fabs(x) / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= 1e-275:
		tmp = (math.fabs(x) / (z - t)) / (z - y)
	else:
		tmp = t_1
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(abs(x) / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= 1e-275)
		tmp = Float64(Float64(abs(x) / Float64(z - t)) / Float64(z - y));
	else
		tmp = t_1;
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = abs(x) / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= 1e-275)
		tmp = (abs(x) / (z - t)) / (z - y);
	else
		tmp = t_1;
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Abs[x], $MachinePrecision] / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, 1e-275], N[(N[(N[Abs[x], $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < 9.99999999999999934e-276

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 96.8%

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

   3. Applied rewrites 96.8%

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

   if 9.99999999999999934e-276 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 89.3%

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

Alternative 2: 96.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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. associate-/r* N/A

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

   4. frac-2neg N/A

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

   5. lift--.f64 N/A

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

   6. sub-negate-rev N/A

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

   7. lower-/.f64 N/A

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

   8. distribute-neg-frac2 N/A

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

   9. lift--.f64 N/A

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

   10. sub-negate-rev N/A

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

   11. lower-/.f64 N/A

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

   12. lower--.f64 N/A

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

   13. lower--.f64 96.8%

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

3. Applied rewrites 96.8%

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

Alternative 3: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e+164)
   (/ (/ x z) (- z y))
   (if (<= z 1.3e+81) (/ x (* (- y z) (- t z))) (/ (/ x z) (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+164) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.3e+81) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - 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 <= (-3.3d+164)) then
        tmp = (x / z) / (z - y)
    else if (z <= 1.3d+81) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / z) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e+164) {
		tmp = (x / z) / (z - y);
	} else if (z <= 1.3e+81) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e+164:
		tmp = (x / z) / (z - y)
	elif z <= 1.3e+81:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e+164)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 1.3e+81)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.3e+164)
		tmp = (x / z) / (z - y);
	elseif (z <= 1.3e+81)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e+164], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+81], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999995e164

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 57.5%

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

   8. Applied rewrites 57.5%

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

   if -3.29999999999999995e164 < z < 1.29999999999999996e81

   1. Initial program 89.3%

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

   if 1.29999999999999996e81 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 57.4%

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

Alternative 4: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - \mathsf{max}\left(y, t\right)}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\mathsf{min}\left(y, t\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{min}\left(y, t\right) - z}}{\mathsf{max}\left(y, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - \mathsf{min}\left(y, t\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.2e-17)
   (/ (/ x z) (- z (fmax y t)))
   (if (<= z 7.6e-185)
     (/ x (* (fmin y t) (- (fmax y t) z)))
     (if (<= z 8e-38)
       (/ (/ x (- (fmin y t) z)) (fmax y t))
       (/ (/ x z) (- z (fmin y t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e-17) {
		tmp = (x / z) / (z - fmax(y, t));
	} else if (z <= 7.6e-185) {
		tmp = x / (fmin(y, t) * (fmax(y, t) - z));
	} else if (z <= 8e-38) {
		tmp = (x / (fmin(y, t) - z)) / fmax(y, t);
	} 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 <= (-8.2d-17)) then
        tmp = (x / z) / (z - fmax(y, t))
    else if (z <= 7.6d-185) then
        tmp = x / (fmin(y, t) * (fmax(y, t) - z))
    else if (z <= 8d-38) then
        tmp = (x / (fmin(y, t) - z)) / fmax(y, t)
    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 <= -8.2e-17) {
		tmp = (x / z) / (z - fmax(y, t));
	} else if (z <= 7.6e-185) {
		tmp = x / (fmin(y, t) * (fmax(y, t) - z));
	} else if (z <= 8e-38) {
		tmp = (x / (fmin(y, t) - z)) / fmax(y, t);
	} else {
		tmp = (x / z) / (z - fmin(y, t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.2e-17:
		tmp = (x / z) / (z - fmax(y, t))
	elif z <= 7.6e-185:
		tmp = x / (fmin(y, t) * (fmax(y, t) - z))
	elif z <= 8e-38:
		tmp = (x / (fmin(y, t) - z)) / fmax(y, t)
	else:
		tmp = (x / z) / (z - fmin(y, t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.2e-17)
		tmp = Float64(Float64(x / z) / Float64(z - fmax(y, t)));
	elseif (z <= 7.6e-185)
		tmp = Float64(x / Float64(fmin(y, t) * Float64(fmax(y, t) - z)));
	elseif (z <= 8e-38)
		tmp = Float64(Float64(x / Float64(fmin(y, t) - z)) / fmax(y, t));
	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 <= -8.2e-17)
		tmp = (x / z) / (z - max(y, t));
	elseif (z <= 7.6e-185)
		tmp = x / (min(y, t) * (max(y, t) - z));
	elseif (z <= 8e-38)
		tmp = (x / (min(y, t) - z)) / max(y, t);
	else
		tmp = (x / z) / (z - min(y, t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.2e-17], N[(N[(x / z), $MachinePrecision] / N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-185], N[(x / N[(N[Min[y, t], $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-38], N[(N[(x / N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / N[Max[y, t], $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2000000000000001e-17

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 57.4%

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

   if -8.2000000000000001e-17 < z < 7.5999999999999998e-185

   1. Initial program 89.3%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.9%

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

   4. Applied rewrites 57.9%

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

   if 7.5999999999999998e-185 < z < 7.9999999999999997e-38

   1. Initial program 89.3%

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

   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%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. distribute-neg-frac2 N/A

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

      8. lift-/.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-rgt-identity N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. distribute-neg-frac2 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. metadata-eval N/A

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

      19. *-rgt-identity 63.1%

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

   6. Applied rewrites 63.1%

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

   if 7.9999999999999997e-38 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 57.5%

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

   8. Applied rewrites 57.5%

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

Alternative 5: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - \mathsf{max}\left(y, t\right)}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{\mathsf{min}\left(y, t\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{max}\left(y, t\right)}}{\mathsf{min}\left(y, t\right) - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - \mathsf{min}\left(y, t\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.2e-17)
   (/ (/ x z) (- z (fmax y t)))
   (if (<= z 1.35e-172)
     (/ x (* (fmin y t) (- (fmax y t) z)))
     (if (<= z 8e-38)
       (/ (/ x (fmax y t)) (- (fmin y t) z))
       (/ (/ x z) (- z (fmin y t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e-17) {
		tmp = (x / z) / (z - fmax(y, t));
	} else if (z <= 1.35e-172) {
		tmp = x / (fmin(y, t) * (fmax(y, t) - z));
	} else if (z <= 8e-38) {
		tmp = (x / fmax(y, t)) / (fmin(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 <= (-8.2d-17)) then
        tmp = (x / z) / (z - fmax(y, t))
    else if (z <= 1.35d-172) then
        tmp = x / (fmin(y, t) * (fmax(y, t) - z))
    else if (z <= 8d-38) then
        tmp = (x / fmax(y, t)) / (fmin(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 <= -8.2e-17) {
		tmp = (x / z) / (z - fmax(y, t));
	} else if (z <= 1.35e-172) {
		tmp = x / (fmin(y, t) * (fmax(y, t) - z));
	} else if (z <= 8e-38) {
		tmp = (x / fmax(y, t)) / (fmin(y, t) - z);
	} else {
		tmp = (x / z) / (z - fmin(y, t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.2e-17:
		tmp = (x / z) / (z - fmax(y, t))
	elif z <= 1.35e-172:
		tmp = x / (fmin(y, t) * (fmax(y, t) - z))
	elif z <= 8e-38:
		tmp = (x / fmax(y, t)) / (fmin(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 <= -8.2e-17)
		tmp = Float64(Float64(x / z) / Float64(z - fmax(y, t)));
	elseif (z <= 1.35e-172)
		tmp = Float64(x / Float64(fmin(y, t) * Float64(fmax(y, t) - z)));
	elseif (z <= 8e-38)
		tmp = Float64(Float64(x / fmax(y, t)) / Float64(fmin(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 <= -8.2e-17)
		tmp = (x / z) / (z - max(y, t));
	elseif (z <= 1.35e-172)
		tmp = x / (min(y, t) * (max(y, t) - z));
	elseif (z <= 8e-38)
		tmp = (x / max(y, t)) / (min(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, -8.2e-17], N[(N[(x / z), $MachinePrecision] / N[(z - N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-172], N[(x / N[(N[Min[y, t], $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-38], N[(N[(x / N[Max[y, t], $MachinePrecision]), $MachinePrecision] / N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2000000000000001e-17

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 57.4%

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

   if -8.2000000000000001e-17 < z < 1.35000000000000013e-172

   1. Initial program 89.3%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.9%

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

   4. Applied rewrites 57.9%

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

   if 1.35000000000000013e-172 < z < 7.9999999999999997e-38

   1. Initial program 89.3%

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

   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%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. *-rgt-identity N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 N/A

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

      9. metadata-eval N/A

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

      10. *-rgt-identity 59.0%

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

   6. Applied rewrites 59.0%

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

   if 7.9999999999999997e-38 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 57.5%

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

   8. Applied rewrites 57.5%

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

Alternative 6: 78.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{\frac{x}{\mathsf{max}\left(y, t\right)}}{\mathsf{min}\left(y, t\right) - z}\\ t_2 := z - \mathsf{min}\left(y, t\right)\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+30}:\\ \;\;\;\;\frac{\frac{x}{t\_2}}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{\mathsf{min}\left(y, t\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t\_2}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (fmax y t)) (- (fmin y t) z))) (t_2 (- z (fmin y t))))
   (if (<= z -1.06e+30)
     (/ (/ x t_2) z)
     (if (<= z -1.4e-31)
       t_1
       (if (<= z 1.35e-172)
         (/ x (* (fmin y t) (- (fmax y t) z)))
         (if (<= z 8e-38) t_1 (/ (/ x z) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / fmax(y, t)) / (fmin(y, t) - z);
	double t_2 = z - fmin(y, t);
	double tmp;
	if (z <= -1.06e+30) {
		tmp = (x / t_2) / z;
	} else if (z <= -1.4e-31) {
		tmp = t_1;
	} else if (z <= 1.35e-172) {
		tmp = x / (fmin(y, t) * (fmax(y, t) - z));
	} else if (z <= 8e-38) {
		tmp = t_1;
	} else {
		tmp = (x / z) / t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / fmax(y, t)) / (fmin(y, t) - z)
    t_2 = z - fmin(y, t)
    if (z <= (-1.06d+30)) then
        tmp = (x / t_2) / z
    else if (z <= (-1.4d-31)) then
        tmp = t_1
    else if (z <= 1.35d-172) then
        tmp = x / (fmin(y, t) * (fmax(y, t) - z))
    else if (z <= 8d-38) then
        tmp = t_1
    else
        tmp = (x / z) / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / fmax(y, t)) / (fmin(y, t) - z);
	double t_2 = z - fmin(y, t);
	double tmp;
	if (z <= -1.06e+30) {
		tmp = (x / t_2) / z;
	} else if (z <= -1.4e-31) {
		tmp = t_1;
	} else if (z <= 1.35e-172) {
		tmp = x / (fmin(y, t) * (fmax(y, t) - z));
	} else if (z <= 8e-38) {
		tmp = t_1;
	} else {
		tmp = (x / z) / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / fmax(y, t)) / (fmin(y, t) - z)
	t_2 = z - fmin(y, t)
	tmp = 0
	if z <= -1.06e+30:
		tmp = (x / t_2) / z
	elif z <= -1.4e-31:
		tmp = t_1
	elif z <= 1.35e-172:
		tmp = x / (fmin(y, t) * (fmax(y, t) - z))
	elif z <= 8e-38:
		tmp = t_1
	else:
		tmp = (x / z) / t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / fmax(y, t)) / Float64(fmin(y, t) - z))
	t_2 = Float64(z - fmin(y, t))
	tmp = 0.0
	if (z <= -1.06e+30)
		tmp = Float64(Float64(x / t_2) / z);
	elseif (z <= -1.4e-31)
		tmp = t_1;
	elseif (z <= 1.35e-172)
		tmp = Float64(x / Float64(fmin(y, t) * Float64(fmax(y, t) - z)));
	elseif (z <= 8e-38)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / max(y, t)) / (min(y, t) - z);
	t_2 = z - min(y, t);
	tmp = 0.0;
	if (z <= -1.06e+30)
		tmp = (x / t_2) / z;
	elseif (z <= -1.4e-31)
		tmp = t_1;
	elseif (z <= 1.35e-172)
		tmp = x / (min(y, t) * (max(y, t) - z));
	elseif (z <= 8e-38)
		tmp = t_1;
	else
		tmp = (x / z) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[Max[y, t], $MachinePrecision]), $MachinePrecision] / N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.06e+30], N[(N[(x / t$95$2), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.4e-31], t$95$1, If[LessEqual[z, 1.35e-172], N[(x / N[(N[Min[y, t], $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-38], t$95$1, N[(N[(x / z), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.06e30

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

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

      13. mult-flip N/A

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

      14. lower-/.f64 59.6%

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

   8. Applied rewrites 59.6%

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

   if -1.06e30 < z < -1.3999999999999999e-31 or 1.35000000000000013e-172 < z < 7.9999999999999997e-38

   1. Initial program 89.3%

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

   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%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. *-rgt-identity N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 N/A

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

      9. metadata-eval N/A

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

      10. *-rgt-identity 59.0%

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

   6. Applied rewrites 59.0%

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

   if -1.3999999999999999e-31 < z < 1.35000000000000013e-172

   1. Initial program 89.3%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.9%

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

   4. Applied rewrites 57.9%

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

   if 7.9999999999999997e-38 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 57.5%

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

   8. Applied rewrites 57.5%

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

Alternative 7: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := z - \mathsf{min}\left(y, t\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{t\_1}}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\left(\mathsf{min}\left(y, t\right) - z\right) \cdot \mathsf{max}\left(y, t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t\_1}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- z (fmin y t))))
   (if (<= z -3.7e-66)
     (/ (/ x t_1) z)
     (if (<= z 3.4e-55)
       (/ x (* (- (fmin y t) z) (fmax y t)))
       (/ (/ x z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z - fmin(y, t);
	double tmp;
	if (z <= -3.7e-66) {
		tmp = (x / t_1) / z;
	} else if (z <= 3.4e-55) {
		tmp = x / ((fmin(y, t) - z) * fmax(y, t));
	} else {
		tmp = (x / z) / 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 = z - fmin(y, t)
    if (z <= (-3.7d-66)) then
        tmp = (x / t_1) / z
    else if (z <= 3.4d-55) then
        tmp = x / ((fmin(y, t) - z) * fmax(y, t))
    else
        tmp = (x / z) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z - fmin(y, t);
	double tmp;
	if (z <= -3.7e-66) {
		tmp = (x / t_1) / z;
	} else if (z <= 3.4e-55) {
		tmp = x / ((fmin(y, t) - z) * fmax(y, t));
	} else {
		tmp = (x / z) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z - fmin(y, t)
	tmp = 0
	if z <= -3.7e-66:
		tmp = (x / t_1) / z
	elif z <= 3.4e-55:
		tmp = x / ((fmin(y, t) - z) * fmax(y, t))
	else:
		tmp = (x / z) / t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z - fmin(y, t))
	tmp = 0.0
	if (z <= -3.7e-66)
		tmp = Float64(Float64(x / t_1) / z);
	elseif (z <= 3.4e-55)
		tmp = Float64(x / Float64(Float64(fmin(y, t) - z) * fmax(y, t)));
	else
		tmp = Float64(Float64(x / z) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z - min(y, t);
	tmp = 0.0;
	if (z <= -3.7e-66)
		tmp = (x / t_1) / z;
	elseif (z <= 3.4e-55)
		tmp = x / ((min(y, t) - z) * max(y, t));
	else
		tmp = (x / z) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-66], N[(N[(x / t$95$1), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.4e-55], N[(x / N[(N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision] * N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7000000000000002e-66

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

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

      13. mult-flip N/A

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

      14. lower-/.f64 59.6%

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

   8. Applied rewrites 59.6%

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

   if -3.7000000000000002e-66 < z < 3.39999999999999973e-55

   1. Initial program 89.3%

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

   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%

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

   if 3.39999999999999973e-55 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 57.5%

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

   8. Applied rewrites 57.5%

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

Alternative 8: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - \mathsf{min}\left(y, t\right)}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\left(\mathsf{min}\left(y, t\right) - z\right) \cdot \mathsf{max}\left(y, t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z (fmin y t)))))
   (if (<= z -3.7e-66)
     t_1
     (if (<= z 3.4e-55) (/ x (* (- (fmin y t) z) (fmax y t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - fmin(y, t));
	double tmp;
	if (z <= -3.7e-66) {
		tmp = t_1;
	} else if (z <= 3.4e-55) {
		tmp = x / ((fmin(y, t) - 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 / z) / (z - fmin(y, t))
    if (z <= (-3.7d-66)) then
        tmp = t_1
    else if (z <= 3.4d-55) then
        tmp = x / ((fmin(y, t) - 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 / z) / (z - fmin(y, t));
	double tmp;
	if (z <= -3.7e-66) {
		tmp = t_1;
	} else if (z <= 3.4e-55) {
		tmp = x / ((fmin(y, t) - z) * fmax(y, t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) / (z - fmin(y, t))
	tmp = 0
	if z <= -3.7e-66:
		tmp = t_1
	elif z <= 3.4e-55:
		tmp = x / ((fmin(y, t) - z) * fmax(y, t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - fmin(y, t)))
	tmp = 0.0
	if (z <= -3.7e-66)
		tmp = t_1;
	elseif (z <= 3.4e-55)
		tmp = Float64(x / Float64(Float64(fmin(y, t) - z) * fmax(y, t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / (z - min(y, t));
	tmp = 0.0;
	if (z <= -3.7e-66)
		tmp = t_1;
	elseif (z <= 3.4e-55)
		tmp = x / ((min(y, t) - z) * max(y, t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-66], t$95$1, If[LessEqual[z, 3.4e-55], N[(x / N[(N[(N[Min[y, t], $MachinePrecision] - z), $MachinePrecision] * N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000002e-66 or 3.39999999999999973e-55 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 57.5%

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

   8. Applied rewrites 57.5%

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

   if -3.7000000000000002e-66 < z < 3.39999999999999973e-55

   1. Initial program 89.3%

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

   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 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z y)))))
   (if (<= z -4.1e+164)
     (/ (/ x z) z)
     (if (<= z -3.7e-66) t_1 (if (<= z 3.4e-55) (/ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double tmp;
	if (z <= -4.1e+164) {
		tmp = (x / z) / z;
	} else if (z <= -3.7e-66) {
		tmp = t_1;
	} else if (z <= 3.4e-55) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z * (z - y))
    if (z <= (-4.1d+164)) then
        tmp = (x / z) / z
    else if (z <= (-3.7d-66)) then
        tmp = t_1
    else if (z <= 3.4d-55) then
        tmp = x / ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double tmp;
	if (z <= -4.1e+164) {
		tmp = (x / z) / z;
	} else if (z <= -3.7e-66) {
		tmp = t_1;
	} else if (z <= 3.4e-55) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (z - y))
	tmp = 0
	if z <= -4.1e+164:
		tmp = (x / z) / z
	elif z <= -3.7e-66:
		tmp = t_1
	elif z <= 3.4e-55:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (z <= -4.1e+164)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= -3.7e-66)
		tmp = t_1;
	elseif (z <= 3.4e-55)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - y));
	tmp = 0.0;
	if (z <= -4.1e+164)
		tmp = (x / z) / z;
	elseif (z <= -3.7e-66)
		tmp = t_1;
	elseif (z <= 3.4e-55)
		tmp = x / ((y - z) * 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 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+164], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -3.7e-66], t$95$1, If[LessEqual[z, 3.4e-55], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.10000000000000016e164

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

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

      13. mult-flip N/A

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

      14. lower-/.f64 59.6%

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

   8. Applied rewrites 59.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{x}{z}}{z} \]
   10. Step-by-step derivation

       1. lower-/.f64 43.4%

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

   11. Applied rewrites 43.4%

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

   if -4.10000000000000016e164 < z < -3.7000000000000002e-66 or 3.39999999999999973e-55 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

   if -3.7000000000000002e-66 < z < 3.39999999999999973e-55

   1. Initial program 89.3%

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

   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 10: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{-x}{z}}{\mathsf{max}\left(y, t\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{\mathsf{min}\left(y, t\right) \cdot \left(\mathsf{max}\left(y, t\right) - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - \mathsf{min}\left(y, t\right)\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e+80)
   (/ (/ x z) z)
   (if (<= z -8.2e-17)
     (/ (/ (- x) z) (fmax y t))
     (if (<= z 8e-38)
       (/ x (* (fmin y t) (- (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 <= -3.6e+80) {
		tmp = (x / z) / z;
	} else if (z <= -8.2e-17) {
		tmp = (-x / z) / fmax(y, t);
	} else if (z <= 8e-38) {
		tmp = x / (fmin(y, t) * (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 <= (-3.6d+80)) then
        tmp = (x / z) / z
    else if (z <= (-8.2d-17)) then
        tmp = (-x / z) / fmax(y, t)
    else if (z <= 8d-38) then
        tmp = x / (fmin(y, t) * (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 <= -3.6e+80) {
		tmp = (x / z) / z;
	} else if (z <= -8.2e-17) {
		tmp = (-x / z) / fmax(y, t);
	} else if (z <= 8e-38) {
		tmp = x / (fmin(y, t) * (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 <= -3.6e+80:
		tmp = (x / z) / z
	elif z <= -8.2e-17:
		tmp = (-x / z) / fmax(y, t)
	elif z <= 8e-38:
		tmp = x / (fmin(y, t) * (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 <= -3.6e+80)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= -8.2e-17)
		tmp = Float64(Float64(Float64(-x) / z) / fmax(y, t));
	elseif (z <= 8e-38)
		tmp = Float64(x / Float64(fmin(y, t) * Float64(fmax(y, t) - z)));
	else
		tmp = Float64(x / Float64(z * Float64(z - fmin(y, t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.6e+80)
		tmp = (x / z) / z;
	elseif (z <= -8.2e-17)
		tmp = (-x / z) / max(y, t);
	elseif (z <= 8e-38)
		tmp = x / (min(y, t) * (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, -3.6e+80], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8.2e-17], N[(N[((-x) / z), $MachinePrecision] / N[Max[y, t], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-38], N[(x / N[(N[Min[y, t], $MachinePrecision] * N[(N[Max[y, t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[(z - N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.59999999999999995e80

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

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

      13. mult-flip N/A

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

      14. lower-/.f64 59.6%

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

   8. Applied rewrites 59.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{x}{z}}{z} \]
   10. Step-by-step derivation

       1. lower-/.f64 43.4%

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

   11. Applied rewrites 43.4%

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

   if -3.59999999999999995e80 < z < -8.2000000000000001e-17

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. mult-flip N/A

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

      8. lower-*.f64 N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. frac-2neg-rev N/A

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

      18. lower-/.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 57.4%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 34.4%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lift-/.f64 N/A

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

       6. associate-*l/ N/A

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

       7. *-commutative N/A

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

       8. mul-1-neg N/A

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

       9. lower-/.f64 N/A

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

       10. *-rgt-identity N/A

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

       11. metadata-eval N/A

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

       12. distribute-rgt-neg-out N/A

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

       13. *-commutative N/A

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

       14. mul-1-neg N/A

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

       15. lower-neg.f64 N/A

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

       16. mul-1-neg N/A

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

       17. *-commutative N/A

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

       18. distribute-rgt-neg-out N/A

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

       19. metadata-eval N/A

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

       20. *-rgt-identity 34.4%

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

   11. Applied rewrites 34.4%

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

   if -8.2000000000000001e-17 < z < 7.9999999999999997e-38

   1. Initial program 89.3%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 57.9%

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

   4. Applied rewrites 57.9%

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

   if 7.9999999999999997e-38 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

Alternative 11: 70.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z y)))))
   (if (<= z -4.1e+164)
     (/ (/ x z) z)
     (if (<= z -4.8e-66) t_1 (if (<= z 3.4e-55) (/ x (* t y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double tmp;
	if (z <= -4.1e+164) {
		tmp = (x / z) / z;
	} else if (z <= -4.8e-66) {
		tmp = t_1;
	} else if (z <= 3.4e-55) {
		tmp = x / (t * y);
	} 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 - y))
    if (z <= (-4.1d+164)) then
        tmp = (x / z) / z
    else if (z <= (-4.8d-66)) then
        tmp = t_1
    else if (z <= 3.4d-55) then
        tmp = x / (t * y)
    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 - y));
	double tmp;
	if (z <= -4.1e+164) {
		tmp = (x / z) / z;
	} else if (z <= -4.8e-66) {
		tmp = t_1;
	} else if (z <= 3.4e-55) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z * (z - y))
	tmp = 0
	if z <= -4.1e+164:
		tmp = (x / z) / z
	elif z <= -4.8e-66:
		tmp = t_1
	elif z <= 3.4e-55:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (z <= -4.1e+164)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= -4.8e-66)
		tmp = t_1;
	elseif (z <= 3.4e-55)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - y));
	tmp = 0.0;
	if (z <= -4.1e+164)
		tmp = (x / z) / z;
	elseif (z <= -4.8e-66)
		tmp = t_1;
	elseif (z <= 3.4e-55)
		tmp = x / (t * y);
	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 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+164], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -4.8e-66], t$95$1, If[LessEqual[z, 3.4e-55], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.10000000000000016e164

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

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

      13. mult-flip N/A

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

      14. lower-/.f64 59.6%

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

   8. Applied rewrites 59.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{x}{z}}{z} \]
   10. Step-by-step derivation

       1. lower-/.f64 43.4%

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

   11. Applied rewrites 43.4%

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

   if -4.10000000000000016e164 < z < -4.80000000000000052e-66 or 3.39999999999999973e-55 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

   if -4.80000000000000052e-66 < z < 3.39999999999999973e-55

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.8%

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

   4. Applied rewrites 39.8%

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

Alternative 12: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{-x}{z}}{\mathsf{max}\left(y, t\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\mathsf{max}\left(y, t\right) \cdot \mathsf{min}\left(y, t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -3.6e+80)
     t_1
     (if (<= z -8e-17)
       (/ (/ (- x) z) (fmax y t))
       (if (<= z 5e-22) (/ 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;
	double tmp;
	if (z <= -3.6e+80) {
		tmp = t_1;
	} else if (z <= -8e-17) {
		tmp = (-x / z) / fmax(y, t);
	} else if (z <= 5e-22) {
		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
    if (z <= (-3.6d+80)) then
        tmp = t_1
    else if (z <= (-8d-17)) then
        tmp = (-x / z) / fmax(y, t)
    else if (z <= 5d-22) 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;
	double tmp;
	if (z <= -3.6e+80) {
		tmp = t_1;
	} else if (z <= -8e-17) {
		tmp = (-x / z) / fmax(y, t);
	} else if (z <= 5e-22) {
		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
	tmp = 0
	if z <= -3.6e+80:
		tmp = t_1
	elif z <= -8e-17:
		tmp = (-x / z) / fmax(y, t)
	elif z <= 5e-22:
		tmp = x / (fmax(y, t) * fmin(y, t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -3.6e+80)
		tmp = t_1;
	elseif (z <= -8e-17)
		tmp = Float64(Float64(Float64(-x) / z) / fmax(y, t));
	elseif (z <= 5e-22)
		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;
	tmp = 0.0;
	if (z <= -3.6e+80)
		tmp = t_1;
	elseif (z <= -8e-17)
		tmp = (-x / z) / max(y, t);
	elseif (z <= 5e-22)
		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[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -3.6e+80], t$95$1, If[LessEqual[z, -8e-17], N[(N[((-x) / z), $MachinePrecision] / N[Max[y, t], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-22], N[(x / N[(N[Max[y, t], $MachinePrecision] * N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.59999999999999995e80 or 4.99999999999999954e-22 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

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

      13. mult-flip N/A

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

      14. lower-/.f64 59.6%

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

   8. Applied rewrites 59.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{x}{z}}{z} \]
   10. Step-by-step derivation

       1. lower-/.f64 43.4%

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

   11. Applied rewrites 43.4%

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

   if -3.59999999999999995e80 < z < -8.00000000000000057e-17

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. mult-flip N/A

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

      8. lower-*.f64 N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. frac-2neg-rev N/A

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

      18. lower-/.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 57.4%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 34.4%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lift-/.f64 N/A

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

       6. associate-*l/ N/A

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

       7. *-commutative N/A

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

       8. mul-1-neg N/A

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

       9. lower-/.f64 N/A

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

       10. *-rgt-identity N/A

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

       11. metadata-eval N/A

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

       12. distribute-rgt-neg-out N/A

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

       13. *-commutative N/A

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

       14. mul-1-neg N/A

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

       15. lower-neg.f64 N/A

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

       16. mul-1-neg N/A

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

       17. *-commutative N/A

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

       18. distribute-rgt-neg-out N/A

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

       19. metadata-eval N/A

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

       20. *-rgt-identity 34.4%

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

   11. Applied rewrites 34.4%

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

   if -8.00000000000000057e-17 < z < 4.99999999999999954e-22

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.8%

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

   4. Applied rewrites 39.8%

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

Alternative 13: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;\frac{\frac{-x}{\mathsf{max}\left(y, t\right)}}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\mathsf{max}\left(y, t\right) \cdot \mathsf{min}\left(y, t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -5.3e+54)
     t_1
     (if (<= z -8e-17)
       (/ (/ (- x) (fmax y t)) z)
       (if (<= z 5e-22) (/ 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;
	double tmp;
	if (z <= -5.3e+54) {
		tmp = t_1;
	} else if (z <= -8e-17) {
		tmp = (-x / fmax(y, t)) / z;
	} else if (z <= 5e-22) {
		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
    if (z <= (-5.3d+54)) then
        tmp = t_1
    else if (z <= (-8d-17)) then
        tmp = (-x / fmax(y, t)) / z
    else if (z <= 5d-22) 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;
	double tmp;
	if (z <= -5.3e+54) {
		tmp = t_1;
	} else if (z <= -8e-17) {
		tmp = (-x / fmax(y, t)) / z;
	} else if (z <= 5e-22) {
		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
	tmp = 0
	if z <= -5.3e+54:
		tmp = t_1
	elif z <= -8e-17:
		tmp = (-x / fmax(y, t)) / z
	elif z <= 5e-22:
		tmp = x / (fmax(y, t) * fmin(y, t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -5.3e+54)
		tmp = t_1;
	elseif (z <= -8e-17)
		tmp = Float64(Float64(Float64(-x) / fmax(y, t)) / z);
	elseif (z <= 5e-22)
		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;
	tmp = 0.0;
	if (z <= -5.3e+54)
		tmp = t_1;
	elseif (z <= -8e-17)
		tmp = (-x / max(y, t)) / z;
	elseif (z <= 5e-22)
		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[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -5.3e+54], t$95$1, If[LessEqual[z, -8e-17], N[(N[((-x) / N[Max[y, t], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5e-22], N[(x / N[(N[Max[y, t], $MachinePrecision] * N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.30000000000000018e54 or 4.99999999999999954e-22 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

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

      13. mult-flip N/A

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

      14. lower-/.f64 59.6%

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

   8. Applied rewrites 59.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{x}{z}}{z} \]
   10. Step-by-step derivation

       1. lower-/.f64 43.4%

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

   11. Applied rewrites 43.4%

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

   if -5.30000000000000018e54 < z < -8.00000000000000057e-17

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. mult-flip N/A

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

      8. lower-*.f64 N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. frac-2neg-rev N/A

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

      18. lower-/.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 57.4%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 34.4%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lift-/.f64 N/A

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

       5. frac-2neg N/A

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

       6. metadata-eval N/A

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

       7. mult-flip-rev N/A

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

       8. distribute-neg-frac2 N/A

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

       9. lift-/.f64 N/A

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

       10. lower-/.f64 N/A

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

   11. Applied rewrites 33.1%

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

   if -8.00000000000000057e-17 < z < 4.99999999999999954e-22

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.8%

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

   4. Applied rewrites 39.8%

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

Alternative 14: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;\frac{-x}{z \cdot \mathsf{max}\left(y, t\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\mathsf{max}\left(y, t\right) \cdot \mathsf{min}\left(y, t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -5.3e+54)
     t_1
     (if (<= z -8e-17)
       (/ (- x) (* z (fmax y t)))
       (if (<= z 5e-22) (/ 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;
	double tmp;
	if (z <= -5.3e+54) {
		tmp = t_1;
	} else if (z <= -8e-17) {
		tmp = -x / (z * fmax(y, t));
	} else if (z <= 5e-22) {
		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
    if (z <= (-5.3d+54)) then
        tmp = t_1
    else if (z <= (-8d-17)) then
        tmp = -x / (z * fmax(y, t))
    else if (z <= 5d-22) 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;
	double tmp;
	if (z <= -5.3e+54) {
		tmp = t_1;
	} else if (z <= -8e-17) {
		tmp = -x / (z * fmax(y, t));
	} else if (z <= 5e-22) {
		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
	tmp = 0
	if z <= -5.3e+54:
		tmp = t_1
	elif z <= -8e-17:
		tmp = -x / (z * fmax(y, t))
	elif z <= 5e-22:
		tmp = x / (fmax(y, t) * fmin(y, t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -5.3e+54)
		tmp = t_1;
	elseif (z <= -8e-17)
		tmp = Float64(Float64(-x) / Float64(z * fmax(y, t)));
	elseif (z <= 5e-22)
		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;
	tmp = 0.0;
	if (z <= -5.3e+54)
		tmp = t_1;
	elseif (z <= -8e-17)
		tmp = -x / (z * max(y, t));
	elseif (z <= 5e-22)
		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[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -5.3e+54], t$95$1, If[LessEqual[z, -8e-17], N[((-x) / N[(z * N[Max[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-22], N[(x / N[(N[Max[y, t], $MachinePrecision] * N[Min[y, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.30000000000000018e54 or 4.99999999999999954e-22 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

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

      13. mult-flip N/A

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

      14. lower-/.f64 59.6%

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

   8. Applied rewrites 59.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{x}{z}}{z} \]
   10. Step-by-step derivation

       1. lower-/.f64 43.4%

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

   11. Applied rewrites 43.4%

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

   if -5.30000000000000018e54 < z < -8.00000000000000057e-17

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. mult-flip N/A

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

      8. lower-*.f64 N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. metadata-eval N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. frac-2neg-rev N/A

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

      18. lower-/.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 57.4%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 34.4%

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

       1. lift-*.f64 N/A

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

       2. *-commutative N/A

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

       3. lift-/.f64 N/A

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

       4. lift-/.f64 N/A

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

       5. frac-times N/A

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

       6. mul-1-neg N/A

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

       7. *-commutative N/A

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

       8. lower-/.f64 N/A

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

       9. *-rgt-identity N/A

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

       10. metadata-eval N/A

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

       11. distribute-rgt-neg-out N/A

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

       12. *-commutative N/A

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

       13. mul-1-neg N/A

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

       14. lower-neg.f64 N/A

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

       15. mul-1-neg N/A

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

       16. *-commutative N/A

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

       17. distribute-rgt-neg-out N/A

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

       18. metadata-eval N/A

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

       19. *-rgt-identity N/A

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

       20. lower-*.f64 31.9%

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

   11. Applied rewrites 31.9%

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

   if -8.00000000000000057e-17 < z < 4.99999999999999954e-22

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-*.f64 39.8%

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

   4. Applied rewrites 39.8%

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

Alternative 15: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -1.1e-17) t_1 (if (<= z 5e-22) (/ x (* t y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.1e-17) {
		tmp = t_1;
	} else if (z <= 5e-22) {
		tmp = x / (t * y);
	} 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
    if (z <= (-1.1d-17)) then
        tmp = t_1
    else if (z <= 5d-22) then
        tmp = x / (t * y)
    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;
	double tmp;
	if (z <= -1.1e-17) {
		tmp = t_1;
	} else if (z <= 5e-22) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -1.1e-17:
		tmp = t_1
	elif z <= 5e-22:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.1e-17)
		tmp = t_1;
	elseif (z <= 5e-22)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.1e-17)
		tmp = t_1;
	elseif (z <= 5e-22)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.1e-17], t$95$1, If[LessEqual[z, 5e-22], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e-17 or 4.99999999999999954e-22 < z

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* N/A

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

      4. frac-2neg N/A

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

      5. lift--.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lower-/.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower--.f64 96.8%

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 52.8%

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

   6. Applied rewrites 52.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. mult-flip N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. lower-/.f64 59.6%

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-/.f64 N/A

          \[\leadsto \frac{x \cdot \frac{1}{z - y}}{z} \]

      13. mult-flip N/A

          \[\leadsto \frac{\frac{x}{z - y}}{z} \]

      14. lower-/.f64 59.6%

          \[\leadsto \frac{\frac{x}{z - y}}{z} \]

   8. Applied rewrites 59.6%

      \[\leadsto \frac{\frac{x}{z - y}}{\color{blue}{z}} \]

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{x}{z}}{z} \]
   10. Step-by-step derivation

       1. lower-/.f64 43.4%

          \[\leadsto \frac{\frac{x}{z}}{z} \]

   11. Applied rewrites 43.4%

       \[\leadsto \frac{\frac{x}{z}}{z} \]

   if -1.1e-17 < z < 4.99999999999999954e-22

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. Taylor expanded in z around 0

      \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
   3. Step-by-step derivation

      1. lower-*.f64 39.8%

         \[\leadsto \frac{x}{t \cdot \color{blue}{y}} \]

   4. Applied rewrites 39.8%

      \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 39.8% accurate, 1.7× 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 89.3%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]

2. Taylor expanded in z around 0

   \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
3. Step-by-step derivation

   1. lower-*.f64 39.8%

      \[\leadsto \frac{x}{t \cdot \color{blue}{y}} \]

4. Applied rewrites 39.8%

   \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025179 
(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))))