Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.7% → 96.6%

Time: 11.0s

Alternatives: 14

Speedup: 0.5×

• 21.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-323}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{z}{z - 1}, t, y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 4e-323) (/ (* (fma (/ z (- z 1.0)) t y) x) z) (* x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 4e-323) {
		tmp = (fma((z / (z - 1.0)), t, y) * x) / z;
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 4e-323)
		tmp = Float64(Float64(fma(Float64(z / Float64(z - 1.0)), t, y) * x) / z);
	else
		tmp = Float64(x * t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-323], N[(N[(N[(N[(z / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], N[(x * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 3.95253e-323

   1. Initial program 94.7%

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

   3. Applied rewrites 91.4%

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

   if 3.95253e-323 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 94.7%

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

Alternative 2: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 (- INFINITY)) (/ (* x y) z) (* x t_1))))

C

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

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * y) / z;
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x * y) / z;
	else
		tmp = x * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 61.1%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 94.7%

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

Alternative 3: 93.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -19000000000:\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\mathsf{fma}\left(-1 \cdot z, t, y\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - -1 \cdot t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -19000000000.0)
   (* x (/ (+ t y) z))
   (if (<= z 1.0)
     (/ (* (fma (* -1.0 z) t y) x) z)
     (/ (* x (- y (* -1.0 t))) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -19000000000.0) {
		tmp = x * ((t + y) / z);
	} else if (z <= 1.0) {
		tmp = (fma((-1.0 * z), t, y) * x) / z;
	} else {
		tmp = (x * (y - (-1.0 * t))) / z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -19000000000.0)
		tmp = Float64(x * Float64(Float64(t + y) / z));
	elseif (z <= 1.0)
		tmp = Float64(Float64(fma(Float64(-1.0 * z), t, y) * x) / z);
	else
		tmp = Float64(Float64(x * Float64(y - Float64(-1.0 * t))) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -19000000000.0], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(N[(N[(-1.0 * z), $MachinePrecision] * t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], N[(N[(x * N[(y - N[(-1.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e10

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 73.6%

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

   if -1.9e10 < z < 1

   1. Initial program 94.7%

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

   3. Applied rewrites 91.4%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 64.4%

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

   if 1 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 71.6%

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

Alternative 4: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -19000000000:\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{elif}\;z \leq 480:\\ \;\;\;\;\mathsf{fma}\left(-z, t, y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - -1 \cdot t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -19000000000.0)
   (* x (/ (+ t y) z))
   (if (<= z 480.0) (* (fma (- z) t y) (/ x z)) (/ (* x (- y (* -1.0 t))) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -19000000000.0) {
		tmp = x * ((t + y) / z);
	} else if (z <= 480.0) {
		tmp = fma(-z, t, y) * (x / z);
	} else {
		tmp = (x * (y - (-1.0 * t))) / z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -19000000000.0)
		tmp = Float64(x * Float64(Float64(t + y) / z));
	elseif (z <= 480.0)
		tmp = Float64(fma(Float64(-z), t, y) * Float64(x / z));
	else
		tmp = Float64(Float64(x * Float64(y - Float64(-1.0 * t))) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -19000000000.0], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 480.0], N[(N[((-z) * t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - N[(-1.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e10

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 73.6%

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

   if -1.9e10 < z < 480

   1. Initial program 94.7%

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

   3. Applied rewrites 90.6%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 65.5%

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

   8. Applied rewrites 65.5%

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

   if 480 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 71.6%

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

Alternative 5: 92.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -19000000000:\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{elif}\;z \leq 480:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - -1 \cdot t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -19000000000.0)
   (* x (/ (+ t y) z))
   (if (<= z 480.0) (* x (- (/ y z) t)) (/ (* x (- y (* -1.0 t))) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -19000000000.0) {
		tmp = x * ((t + y) / z);
	} else if (z <= 480.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (x * (y - (-1.0 * t))) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 <= (-19000000000.0d0)) then
        tmp = x * ((t + y) / z)
    else if (z <= 480.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = (x * (y - ((-1.0d0) * t))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -19000000000.0) {
		tmp = x * ((t + y) / z);
	} else if (z <= 480.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (x * (y - (-1.0 * t))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -19000000000.0:
		tmp = x * ((t + y) / z)
	elif z <= 480.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = (x * (y - (-1.0 * t))) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -19000000000.0)
		tmp = Float64(x * Float64(Float64(t + y) / z));
	elseif (z <= 480.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(Float64(x * Float64(y - Float64(-1.0 * t))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -19000000000.0)
		tmp = x * ((t + y) / z);
	elseif (z <= 480.0)
		tmp = x * ((y / z) - t);
	else
		tmp = (x * (y - (-1.0 * t))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -19000000000.0], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 480.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - N[(-1.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e10

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 73.6%

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

   if -1.9e10 < z < 480

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 64.9%

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

   if 480 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 71.6%

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

Alternative 6: 91.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t + y}{z}\\ \mathbf{if}\;z \leq -19000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ t y) z))))
   (if (<= z -19000000000.0) t_1 (if (<= z 1.0) (* x (- (/ y z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((t + y) / z);
	double tmp;
	if (z <= -19000000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		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 * ((t + y) / z)
    if (z <= (-19000000000.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) 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 * ((t + y) / z);
	double tmp;
	if (z <= -19000000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((t + y) / z)
	tmp = 0
	if z <= -19000000000.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(t + y) / z))
	tmp = 0.0
	if (z <= -19000000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		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 * ((t + y) / z);
	tmp = 0.0;
	if (z <= -19000000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		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[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -19000000000.0], t$95$1, If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e10 or 1 < z

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 73.6%

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

   if -1.9e10 < z < 1

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 64.9%

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

Alternative 7: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z - 1}\\ \mathbf{if}\;t \leq -14800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- z 1.0)))))
   (if (<= t -14800000000000.0) t_1 (if (<= t 3.7e+65) (/ (* x y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z - 1.0));
	double tmp;
	if (t <= -14800000000000.0) {
		tmp = t_1;
	} else if (t <= 3.7e+65) {
		tmp = (x * y) / z;
	} 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 * (t / (z - 1.0d0))
    if (t <= (-14800000000000.0d0)) then
        tmp = t_1
    else if (t <= 3.7d+65) then
        tmp = (x * y) / z
    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 * (t / (z - 1.0));
	double tmp;
	if (t <= -14800000000000.0) {
		tmp = t_1;
	} else if (t <= 3.7e+65) {
		tmp = (x * y) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z - 1.0))
	tmp = 0
	if t <= -14800000000000.0:
		tmp = t_1
	elif t <= 3.7e+65:
		tmp = (x * y) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z - 1.0)))
	tmp = 0.0
	if (t <= -14800000000000.0)
		tmp = t_1;
	elseif (t <= 3.7e+65)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z - 1.0));
	tmp = 0.0;
	if (t <= -14800000000000.0)
		tmp = t_1;
	elseif (t <= 3.7e+65)
		tmp = (x * y) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -14800000000000.0], t$95$1, If[LessEqual[t, 3.7e+65], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.48e13 or 3.69999999999999995e65 < t

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.7%

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

   6. Applied rewrites 45.7%

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

   if -1.48e13 < t < 3.69999999999999995e65

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 61.1%

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

Alternative 8: 71.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot x}{z - 1}\\ \mathbf{if}\;t \leq -14800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+65}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* t x) (- z 1.0))))
   (if (<= t -14800000000000.0) t_1 (if (<= t 3.7e+65) (/ (* x y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * x) / (z - 1.0);
	double tmp;
	if (t <= -14800000000000.0) {
		tmp = t_1;
	} else if (t <= 3.7e+65) {
		tmp = (x * y) / z;
	} 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 = (t * x) / (z - 1.0d0)
    if (t <= (-14800000000000.0d0)) then
        tmp = t_1
    else if (t <= 3.7d+65) then
        tmp = (x * y) / z
    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 = (t * x) / (z - 1.0);
	double tmp;
	if (t <= -14800000000000.0) {
		tmp = t_1;
	} else if (t <= 3.7e+65) {
		tmp = (x * y) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * x) / (z - 1.0)
	tmp = 0
	if t <= -14800000000000.0:
		tmp = t_1
	elif t <= 3.7e+65:
		tmp = (x * y) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * x) / Float64(z - 1.0))
	tmp = 0.0
	if (t <= -14800000000000.0)
		tmp = t_1;
	elseif (t <= 3.7e+65)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * x) / (z - 1.0);
	tmp = 0.0;
	if (t <= -14800000000000.0)
		tmp = t_1;
	elseif (t <= 3.7e+65)
		tmp = (x * y) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * x), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -14800000000000.0], t$95$1, If[LessEqual[t, 3.7e+65], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.48e13 or 3.69999999999999995e65 < t

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 43.4%

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

   if -1.48e13 < t < 3.69999999999999995e65

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 61.1%

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

Alternative 9: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -1.92 \cdot 10^{+282}:\\ \;\;\;\;x \cdot \left(-1 \cdot t\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -1.92e+282)
     (* x (* -1.0 t))
     (if (<= t -1.12e+46) t_1 (if (<= t 4.5e+136) (/ (* x y) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -1.92e+282) {
		tmp = x * (-1.0 * t);
	} else if (t <= -1.12e+46) {
		tmp = t_1;
	} else if (t <= 4.5e+136) {
		tmp = (x * y) / z;
	} 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 * (t / z)
    if (t <= (-1.92d+282)) then
        tmp = x * ((-1.0d0) * t)
    else if (t <= (-1.12d+46)) then
        tmp = t_1
    else if (t <= 4.5d+136) then
        tmp = (x * y) / z
    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 * (t / z);
	double tmp;
	if (t <= -1.92e+282) {
		tmp = x * (-1.0 * t);
	} else if (t <= -1.12e+46) {
		tmp = t_1;
	} else if (t <= 4.5e+136) {
		tmp = (x * y) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -1.92e+282:
		tmp = x * (-1.0 * t)
	elif t <= -1.12e+46:
		tmp = t_1
	elif t <= 4.5e+136:
		tmp = (x * y) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -1.92e+282)
		tmp = Float64(x * Float64(-1.0 * t));
	elseif (t <= -1.12e+46)
		tmp = t_1;
	elseif (t <= 4.5e+136)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -1.92e+282)
		tmp = x * (-1.0 * t);
	elseif (t <= -1.12e+46)
		tmp = t_1;
	elseif (t <= 4.5e+136)
		tmp = (x * y) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.92e+282], N[(x * N[(-1.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.12e+46], t$95$1, If[LessEqual[t, 4.5e+136], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9200000000000001e282

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 23.2%

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

   if -1.9200000000000001e282 < t < -1.12e46 or 4.4999999999999999e136 < t

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.7%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 35.2%

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

   if -1.12e46 < t < 4.4999999999999999e136

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 61.1%

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

Alternative 10: 64.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-1 \cdot t\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+65}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* -1.0 t))))
   (if (<= t -5.2e+194)
     t_1
     (if (<= t 4.1e+65)
       (* (/ y z) x)
       (if (<= t 3.7e+113) t_1 (/ (* t x) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-1.0 * t);
	double tmp;
	if (t <= -5.2e+194) {
		tmp = t_1;
	} else if (t <= 4.1e+65) {
		tmp = (y / z) * x;
	} else if (t <= 3.7e+113) {
		tmp = t_1;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 * ((-1.0d0) * t)
    if (t <= (-5.2d+194)) then
        tmp = t_1
    else if (t <= 4.1d+65) then
        tmp = (y / z) * x
    else if (t <= 3.7d+113) then
        tmp = t_1
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (-1.0 * t);
	double tmp;
	if (t <= -5.2e+194) {
		tmp = t_1;
	} else if (t <= 4.1e+65) {
		tmp = (y / z) * x;
	} else if (t <= 3.7e+113) {
		tmp = t_1;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-1.0 * t)
	tmp = 0
	if t <= -5.2e+194:
		tmp = t_1
	elif t <= 4.1e+65:
		tmp = (y / z) * x
	elif t <= 3.7e+113:
		tmp = t_1
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-1.0 * t))
	tmp = 0.0
	if (t <= -5.2e+194)
		tmp = t_1;
	elseif (t <= 4.1e+65)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 3.7e+113)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-1.0 * t);
	tmp = 0.0;
	if (t <= -5.2e+194)
		tmp = t_1;
	elseif (t <= 4.1e+65)
		tmp = (y / z) * x;
	elseif (t <= 3.7e+113)
		tmp = t_1;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(-1.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+194], t$95$1, If[LessEqual[t, 4.1e+65], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 3.7e+113], t$95$1, N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1999999999999998e194 or 4.1000000000000001e65 < t < 3.6999999999999998e113

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 23.2%

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

   if -5.1999999999999998e194 < t < 4.1000000000000001e65

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 61.1%

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

   6. Applied rewrites 61.0%

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

   if 3.6999999999999998e113 < t

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 43.4%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 33.1%

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

Alternative 11: 64.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+217}:\\ \;\;\;\;x \cdot \left(-1 \cdot t\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+115}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2e+217)
   (* x (* -1.0 t))
   (if (<= t 1.1e+115) (/ (* x y) z) (/ (* t x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e+217) {
		tmp = x * (-1.0 * t);
	} else if (t <= 1.1e+115) {
		tmp = (x * y) / z;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2d+217)) then
        tmp = x * ((-1.0d0) * t)
    else if (t <= 1.1d+115) then
        tmp = (x * y) / z
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e+217) {
		tmp = x * (-1.0 * t);
	} else if (t <= 1.1e+115) {
		tmp = (x * y) / z;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2e+217:
		tmp = x * (-1.0 * t)
	elif t <= 1.1e+115:
		tmp = (x * y) / z
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2e+217)
		tmp = Float64(x * Float64(-1.0 * t));
	elseif (t <= 1.1e+115)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2e+217)
		tmp = x * (-1.0 * t);
	elseif (t <= 1.1e+115)
		tmp = (x * y) / z;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2e+217], N[(x * N[(-1.0 * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+115], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999992e217

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 23.2%

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

   if -1.99999999999999992e217 < t < 1.1e115

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 61.1%

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

   if 1.1e115 < t

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 43.4%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 33.1%

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

Alternative 12: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-1 \cdot t\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* -1.0 t))))
   (if (<= t -2e+217)
     t_1
     (if (<= t 4.1e+65)
       (* (/ x z) y)
       (if (<= t 3.7e+113) t_1 (/ (* t x) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-1.0 * t);
	double tmp;
	if (t <= -2e+217) {
		tmp = t_1;
	} else if (t <= 4.1e+65) {
		tmp = (x / z) * y;
	} else if (t <= 3.7e+113) {
		tmp = t_1;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, 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 * ((-1.0d0) * t)
    if (t <= (-2d+217)) then
        tmp = t_1
    else if (t <= 4.1d+65) then
        tmp = (x / z) * y
    else if (t <= 3.7d+113) then
        tmp = t_1
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (-1.0 * t);
	double tmp;
	if (t <= -2e+217) {
		tmp = t_1;
	} else if (t <= 4.1e+65) {
		tmp = (x / z) * y;
	} else if (t <= 3.7e+113) {
		tmp = t_1;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-1.0 * t)
	tmp = 0
	if t <= -2e+217:
		tmp = t_1
	elif t <= 4.1e+65:
		tmp = (x / z) * y
	elif t <= 3.7e+113:
		tmp = t_1
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-1.0 * t))
	tmp = 0.0
	if (t <= -2e+217)
		tmp = t_1;
	elseif (t <= 4.1e+65)
		tmp = Float64(Float64(x / z) * y);
	elseif (t <= 3.7e+113)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-1.0 * t);
	tmp = 0.0;
	if (t <= -2e+217)
		tmp = t_1;
	elseif (t <= 4.1e+65)
		tmp = (x / z) * y;
	elseif (t <= 3.7e+113)
		tmp = t_1;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(-1.0 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+217], t$95$1, If[LessEqual[t, 4.1e+65], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t, 3.7e+113], t$95$1, N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999992e217 or 4.1000000000000001e65 < t < 3.6999999999999998e113

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 23.2%

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

   if -1.99999999999999992e217 < t < 4.1000000000000001e65

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 61.1%

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

   6. Applied rewrites 60.8%

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

   if 3.6999999999999998e113 < t

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 43.4%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 33.1%

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

Alternative 13: 42.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot x}{z}\\ \mathbf{if}\;z \leq -19000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(-1 \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* t x) z)))
   (if (<= z -19000000000.0) t_1 (if (<= z 1.2e+20) (* x (* -1.0 t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * x) / z;
	double tmp;
	if (z <= -19000000000.0) {
		tmp = t_1;
	} else if (z <= 1.2e+20) {
		tmp = x * (-1.0 * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * x) / z
    if (z <= (-19000000000.0d0)) then
        tmp = t_1
    else if (z <= 1.2d+20) then
        tmp = x * ((-1.0d0) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * x) / z;
	double tmp;
	if (z <= -19000000000.0) {
		tmp = t_1;
	} else if (z <= 1.2e+20) {
		tmp = x * (-1.0 * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * x) / z
	tmp = 0
	if z <= -19000000000.0:
		tmp = t_1
	elif z <= 1.2e+20:
		tmp = x * (-1.0 * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * x) / z)
	tmp = 0.0
	if (z <= -19000000000.0)
		tmp = t_1;
	elseif (z <= 1.2e+20)
		tmp = Float64(x * Float64(-1.0 * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * x) / z;
	tmp = 0.0;
	if (z <= -19000000000.0)
		tmp = t_1;
	elseif (z <= 1.2e+20)
		tmp = x * (-1.0 * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -19000000000.0], t$95$1, If[LessEqual[z, 1.2e+20], N[(x * N[(-1.0 * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e10 or 1.2e20 < z

   1. Initial program 94.7%

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

   3. Applied rewrites 94.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 43.4%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 33.1%

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

   if -1.9e10 < z < 1.2e20

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 45.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 23.2%

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

Alternative 14: 23.2% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

def code(x, y, z, t):
	return x * (-1.0 * t)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

2. Taylor expanded in y around 0

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

4. Applied rewrites 45.7%

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

5. Taylor expanded in z around 0

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

7. Applied rewrites 23.2%

   \[\leadsto x \cdot \left(-1 \cdot t\right) \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64
  (* x (- (/ y z) (/ t (- 1.0 z)))))