Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 88.2% → 99.8%

Time: 4.8s

Alternatives: 13

Speedup: 0.8×

• 20.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * ((y - z) + 1.0d0)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * ((y - z) + 1.0d0)) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y - \left(z - 1\right)\\ t_1 := \frac{t\_0}{z} \cdot x\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-39}:\\ \;\;\;\;t\_0 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- y (- z 1.0))) (t_1 (* (/ t_0 z) x)))
   (if (<= z -9.6e+28) t_1 (if (<= z 2e-39) (* t_0 (/ x z)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y - (z - 1.0);
	double t_1 = (t_0 / z) * x;
	double tmp;
	if (z <= -9.6e+28) {
		tmp = t_1;
	} else if (z <= 2e-39) {
		tmp = t_0 * (x / 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y - (z - 1.0d0)
    t_1 = (t_0 / z) * x
    if (z <= (-9.6d+28)) then
        tmp = t_1
    else if (z <= 2d-39) then
        tmp = t_0 * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y - (z - 1.0);
	double t_1 = (t_0 / z) * x;
	double tmp;
	if (z <= -9.6e+28) {
		tmp = t_1;
	} else if (z <= 2e-39) {
		tmp = t_0 * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y - (z - 1.0)
	t_1 = (t_0 / z) * x
	tmp = 0
	if z <= -9.6e+28:
		tmp = t_1
	elif z <= 2e-39:
		tmp = t_0 * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y - Float64(z - 1.0))
	t_1 = Float64(Float64(t_0 / z) * x)
	tmp = 0.0
	if (z <= -9.6e+28)
		tmp = t_1;
	elseif (z <= 2e-39)
		tmp = Float64(t_0 * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y - (z - 1.0);
	t_1 = (t_0 / z) * x;
	tmp = 0.0;
	if (z <= -9.6e+28)
		tmp = t_1;
	elseif (z <= 2e-39)
		tmp = t_0 * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y - N[(z - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(t$95$0 / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -9.6e+28], t$95$1, If[LessEqual[z, 2e-39], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.59999999999999925e28 or 1.99999999999999986e-39 < z

   1. Initial program 88.2%

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 58.9%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 96.0%

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

   if -9.59999999999999925e28 < z < 1.99999999999999986e-39

   1. Initial program 88.2%

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

   3. Applied rewrites 88.8%

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

Alternative 2: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-22}:\\ \;\;\;\;\mathsf{fma}\left(-1, x, \frac{x \cdot \left(1 + y\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - \left(z - 1\right)\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5e-22)
   (fma -1.0 x (/ (* x (+ 1.0 y)) z))
   (* (- y (- z 1.0)) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e-22) {
		tmp = fma(-1.0, x, ((x * (1.0 + y)) / z));
	} else {
		tmp = (y - (z - 1.0)) * (x / z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5e-22)
		tmp = fma(-1.0, x, Float64(Float64(x * Float64(1.0 + y)) / z));
	else
		tmp = Float64(Float64(y - Float64(z - 1.0)) * Float64(x / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5e-22], N[(-1.0 * x + N[(N[(x * N[(1.0 + y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.99999999999999954e-22

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 96.0%

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

   if 4.99999999999999954e-22 < x

   1. Initial program 88.2%

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

   3. Applied rewrites 88.8%

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

Alternative 3: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - \left(z - 1\right)\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4.8e-22) (/ (* x (+ (- y z) 1.0)) z) (* (- y (- z 1.0)) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.8e-22) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (y - (z - 1.0)) * (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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 4.8d-22) then
        tmp = (x * ((y - z) + 1.0d0)) / z
    else
        tmp = (y - (z - 1.0d0)) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.8e-22) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (y - (z - 1.0)) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.8e-22:
		tmp = (x * ((y - z) + 1.0)) / z
	else:
		tmp = (y - (z - 1.0)) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.8e-22)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(Float64(y - Float64(z - 1.0)) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4.8e-22)
		tmp = (x * ((y - z) + 1.0)) / z;
	else
		tmp = (y - (z - 1.0)) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.8e-22], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(y - N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.80000000000000005e-22

   1. Initial program 88.2%

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

   if 4.80000000000000005e-22 < x

   1. Initial program 88.2%

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

   3. Applied rewrites 88.8%

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

Alternative 4: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot \left(y - 1\right) - x\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+47}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;\left(y - \left(z - 1\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (/ x z) (- y 1.0)) x)))
   (if (<= z -3.4e+47)
     t_0
     (if (<= z 9.5e+15) (* (- y (- z 1.0)) (/ x z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((x / z) * (y - 1.0)) - x;
	double tmp;
	if (z <= -3.4e+47) {
		tmp = t_0;
	} else if (z <= 9.5e+15) {
		tmp = (y - (z - 1.0)) * (x / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((x / z) * (y - 1.0d0)) - x
    if (z <= (-3.4d+47)) then
        tmp = t_0
    else if (z <= 9.5d+15) then
        tmp = (y - (z - 1.0d0)) * (x / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((x / z) * (y - 1.0)) - x;
	double tmp;
	if (z <= -3.4e+47) {
		tmp = t_0;
	} else if (z <= 9.5e+15) {
		tmp = (y - (z - 1.0)) * (x / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((x / z) * (y - 1.0)) - x
	tmp = 0
	if z <= -3.4e+47:
		tmp = t_0
	elif z <= 9.5e+15:
		tmp = (y - (z - 1.0)) * (x / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x / z) * Float64(y - 1.0)) - x)
	tmp = 0.0
	if (z <= -3.4e+47)
		tmp = t_0;
	elseif (z <= 9.5e+15)
		tmp = Float64(Float64(y - Float64(z - 1.0)) * Float64(x / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((x / z) * (y - 1.0)) - x;
	tmp = 0.0;
	if (z <= -3.4e+47)
		tmp = t_0;
	elseif (z <= 9.5e+15)
		tmp = (y - (z - 1.0)) * (x / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x / z), $MachinePrecision] * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[z, -3.4e+47], t$95$0, If[LessEqual[z, 9.5e+15], N[(N[(y - N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3999999999999998e47 or 9.5e15 < z

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 96.0%

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

   6. Applied rewrites 72.2%

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

   8. Applied rewrites 72.2%

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

   if -3.3999999999999998e47 < z < 9.5e15

   1. Initial program 88.2%

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

   3. Applied rewrites 88.8%

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

Alternative 5: 93.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot \left(y - 1\right) - x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2:\\ \;\;\;\;\mathsf{fma}\left(-1, x, \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (/ x z) (- y 1.0)) x)))
   (if (<= y -1.0) t_0 (if (<= y 2.0) (fma -1.0 x (/ x z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((x / z) * (y - 1.0)) - x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 2.0) {
		tmp = fma(-1.0, x, (x / z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(x / z) * Float64(y - 1.0)) - x)
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 2.0)
		tmp = fma(-1.0, x, Float64(x / z));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(x / z), $MachinePrecision] * N[(y - 1.0), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 2.0], N[(-1.0 * x + N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2 < y

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 96.0%

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

   6. Applied rewrites 72.2%

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

   8. Applied rewrites 72.2%

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

   if -1 < y < 2

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(-1, x, \frac{x}{z}\right) \]

   7. Applied rewrites 66.4%

      \[\leadsto \mathsf{fma}\left(-1, x, \frac{x}{z}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 42000:\\ \;\;\;\;\mathsf{fma}\left(-1, x, \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - 1, \frac{x}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+28)
   (/ (* x y) z)
   (if (<= y 42000.0) (fma -1.0 x (/ x z)) (fma (- y 1.0) (/ x z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+28) {
		tmp = (x * y) / z;
	} else if (y <= 42000.0) {
		tmp = fma(-1.0, x, (x / z));
	} else {
		tmp = fma((y - 1.0), (x / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e+28)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 42000.0)
		tmp = fma(-1.0, x, Float64(x / z));
	else
		tmp = fma(Float64(y - 1.0), Float64(x / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e+28], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 42000.0], N[(-1.0 * x + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000003e28

   1. Initial program 88.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 37.7%

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

   if -5.5000000000000003e28 < y < 42000

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(-1, x, \frac{x}{z}\right) \]

   7. Applied rewrites 66.4%

      \[\leadsto \mathsf{fma}\left(-1, x, \frac{x}{z}\right) \]

   if 42000 < y

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 96.0%

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

   6. Applied rewrites 35.5%

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

Alternative 7: 83.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(-1, x, \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - -1}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+28)
   (/ (* x y) z)
   (if (<= y 2.6e-19) (fma -1.0 x (/ x z)) (* (/ (- y -1.0) z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+28) {
		tmp = (x * y) / z;
	} else if (y <= 2.6e-19) {
		tmp = fma(-1.0, x, (x / z));
	} else {
		tmp = ((y - -1.0) / z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e+28)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 2.6e-19)
		tmp = fma(-1.0, x, Float64(x / z));
	else
		tmp = Float64(Float64(Float64(y - -1.0) / z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e+28], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.6e-19], N[(-1.0 * x + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - -1.0), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000003e28

   1. Initial program 88.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 37.7%

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

   if -5.5000000000000003e28 < y < 2.60000000000000013e-19

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(-1, x, \frac{x}{z}\right) \]

   7. Applied rewrites 66.4%

      \[\leadsto \mathsf{fma}\left(-1, x, \frac{x}{z}\right) \]

   if 2.60000000000000013e-19 < y

   1. Initial program 88.2%

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 58.9%

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

Alternative 8: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 42000:\\ \;\;\;\;\mathsf{fma}\left(-1, x, \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+28)
   (/ (* x y) z)
   (if (<= y 42000.0) (fma -1.0 x (/ x z)) (* (/ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+28) {
		tmp = (x * y) / z;
	} else if (y <= 42000.0) {
		tmp = fma(-1.0, x, (x / z));
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e+28)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 42000.0)
		tmp = fma(-1.0, x, Float64(x / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e+28], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 42000.0], N[(-1.0 * x + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000003e28

   1. Initial program 88.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 37.7%

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

   if -5.5000000000000003e28 < y < 42000

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(-1, x, \frac{x}{z}\right) \]

   7. Applied rewrites 66.4%

      \[\leadsto \mathsf{fma}\left(-1, x, \frac{x}{z}\right) \]

   if 42000 < y

   1. Initial program 88.2%

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 35.6%

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

Alternative 9: 61.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot y}{z}\\ t_1 := \frac{x \cdot 1}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-185}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+136}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) z)) (t_1 (/ (* x 1.0) z)))
   (if (<= z -1.0)
     (- x)
     (if (<= z -1.7e-179)
       t_1
       (if (<= z 1.42e-185)
         t_0
         (if (<= z 2.1e-134) t_1 (if (<= z 1.25e+136) t_0 (- x))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double t_1 = (x * 1.0) / z;
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -1.7e-179) {
		tmp = t_1;
	} else if (z <= 1.42e-185) {
		tmp = t_0;
	} else if (z <= 2.1e-134) {
		tmp = t_1;
	} else if (z <= 1.25e+136) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x * y) / z
    t_1 = (x * 1.0d0) / z
    if (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= (-1.7d-179)) then
        tmp = t_1
    else if (z <= 1.42d-185) then
        tmp = t_0
    else if (z <= 2.1d-134) then
        tmp = t_1
    else if (z <= 1.25d+136) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * y) / z;
	double t_1 = (x * 1.0) / z;
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -1.7e-179) {
		tmp = t_1;
	} else if (z <= 1.42e-185) {
		tmp = t_0;
	} else if (z <= 2.1e-134) {
		tmp = t_1;
	} else if (z <= 1.25e+136) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) / z
	t_1 = (x * 1.0) / z
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= -1.7e-179:
		tmp = t_1
	elif z <= 1.42e-185:
		tmp = t_0
	elif z <= 2.1e-134:
		tmp = t_1
	elif z <= 1.25e+136:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) / z)
	t_1 = Float64(Float64(x * 1.0) / z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= -1.7e-179)
		tmp = t_1;
	elseif (z <= 1.42e-185)
		tmp = t_0;
	elseif (z <= 2.1e-134)
		tmp = t_1;
	elseif (z <= 1.25e+136)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) / z;
	t_1 = (x * 1.0) / z;
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -x;
	elseif (z <= -1.7e-179)
		tmp = t_1;
	elseif (z <= 1.42e-185)
		tmp = t_0;
	elseif (z <= 2.1e-134)
		tmp = t_1;
	elseif (z <= 1.25e+136)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * 1.0), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.0], (-x), If[LessEqual[z, -1.7e-179], t$95$1, If[LessEqual[z, 1.42e-185], t$95$0, If[LessEqual[z, 2.1e-134], t$95$1, If[LessEqual[z, 1.25e+136], t$95$0, (-x)]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1.25e136 < z

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 38.9%

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

   6. Applied rewrites 38.9%

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

   if -1 < z < -1.6999999999999999e-179 or 1.42000000000000003e-185 < z < 2.0999999999999999e-134

   1. Initial program 88.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 61.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 30.1%

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

   if -1.6999999999999999e-179 < z < 1.42000000000000003e-185 or 2.0999999999999999e-134 < z < 1.25e136

   1. Initial program 88.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 37.7%

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

Alternative 10: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+28) (/ (* x y) z) (if (<= y 8.5e-20) (- x) (* (/ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+28) {
		tmp = (x * y) / z;
	} else if (y <= 8.5e-20) {
		tmp = -x;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.5d+28)) then
        tmp = (x * y) / z
    else if (y <= 8.5d-20) then
        tmp = -x
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+28) {
		tmp = (x * y) / z;
	} else if (y <= 8.5e-20) {
		tmp = -x;
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.5e+28:
		tmp = (x * y) / z
	elif y <= 8.5e-20:
		tmp = -x
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e+28)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 8.5e-20)
		tmp = Float64(-x);
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.5e+28)
		tmp = (x * y) / z;
	elseif (y <= 8.5e-20)
		tmp = -x;
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e+28], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 8.5e-20], (-x), N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000003e28

   1. Initial program 88.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 37.7%

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

   if -5.5000000000000003e28 < y < 8.5000000000000005e-20

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 38.9%

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

   6. Applied rewrites 38.9%

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

   if 8.5000000000000005e-20 < y

   1. Initial program 88.2%

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 35.6%

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

Alternative 11: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{z} \cdot x\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ y z) x)))
   (if (<= y -3.7e+29) t_0 (if (<= y 8.5e-20) (- x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y / z) * x;
	double tmp;
	if (y <= -3.7e+29) {
		tmp = t_0;
	} else if (y <= 8.5e-20) {
		tmp = -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y / z) * x
    if (y <= (-3.7d+29)) then
        tmp = t_0
    else if (y <= 8.5d-20) then
        tmp = -x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y / z) * x;
	double tmp;
	if (y <= -3.7e+29) {
		tmp = t_0;
	} else if (y <= 8.5e-20) {
		tmp = -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y / z) * x
	tmp = 0
	if y <= -3.7e+29:
		tmp = t_0
	elif y <= 8.5e-20:
		tmp = -x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y / z) * x)
	tmp = 0.0
	if (y <= -3.7e+29)
		tmp = t_0;
	elseif (y <= 8.5e-20)
		tmp = Float64(-x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y / z) * x;
	tmp = 0.0;
	if (y <= -3.7e+29)
		tmp = t_0;
	elseif (y <= 8.5e-20)
		tmp = -x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -3.7e+29], t$95$0, If[LessEqual[y, 8.5e-20], (-x), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.69999999999999974e29 or 8.5000000000000005e-20 < y

   1. Initial program 88.2%

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in y around inf

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

   6. Applied rewrites 35.6%

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

   if -3.69999999999999974e29 < y < 8.5000000000000005e-20

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 38.9%

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

   6. Applied rewrites 38.9%

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

Alternative 12: 38.9% accurate, 6.4× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 38.9%

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

6. Applied rewrites 38.9%

   \[\leadsto \color{blue}{-x} \]
7. Add Preprocessing

Alternative 13: 3.0% accurate, 12.7× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 88.2%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 38.9%

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

6. Applied rewrites 38.9%

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

8. Applied rewrites 3.0%

   \[\leadsto \color{blue}{x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025159 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64
  (/ (* x (+ (- y z) 1.0)) z))