Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 86.4% → 99.5%

Time: 10.5s

Alternatives: 15

Speedup: 1.2×

• 23.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{2}{t}, \frac{1}{z} + \left(1 - t\right), \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma (/ 2.0 t) (+ (/ 1.0 z) (- 1.0 t)) (/ x y)))

C

double code(double x, double y, double z, double t) {
	return fma((2.0 / t), ((1.0 / z) + (1.0 - t)), (x / y));
}

Julia

function code(x, y, z, t)
	return fma(Float64(2.0 / t), Float64(Float64(1.0 / z) + Float64(1.0 - t)), Float64(x / y))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(2.0 / t), $MachinePrecision] * N[(N[(1.0 / z), $MachinePrecision] + N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.4%

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

3. Applied rewrites 86.4%

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

5. Applied rewrites 99.5%

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

Alternative 2: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(2, \frac{1 - t}{t}, 2 \cdot \frac{1}{t \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* t z)))))
   (if (<= (/ x y) -100000.0)
     t_1
     (if (<= (/ x y) 1e-5)
       (fma 2.0 (/ (- 1.0 t) t) (* 2.0 (/ 1.0 (* t z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	double tmp;
	if ((x / y) <= -100000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-5) {
		tmp = fma(2.0, ((1.0 - t) / t), (2.0 * (1.0 / (t * z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(t * z)))
	tmp = 0.0
	if (Float64(x / y) <= -100000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-5)
		tmp = fma(2.0, Float64(Float64(1.0 - t) / t), Float64(2.0 * Float64(1.0 / Float64(t * z))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -100000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-5], N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] + N[(2.0 * N[(1.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e5 or 1.00000000000000008e-5 < (/.f64 x y)

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + 2 \cdot z}}{t \cdot z} \]

   4. Applied rewrites 79.7%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + 2 \cdot z}}{t \cdot z} \]

   if -1e5 < (/.f64 x y) < 1.00000000000000008e-5

   1. Initial program 86.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   4. Applied rewrites 66.5%

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

Alternative 3: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -100000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(2, \frac{1 - t}{t}, \frac{\frac{2}{t}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* t z)))))
   (if (<= (/ x y) -100000.0)
     t_1
     (if (<= (/ x y) 1e-5) (fma 2.0 (/ (- 1.0 t) t) (/ (/ 2.0 t) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	double tmp;
	if ((x / y) <= -100000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-5) {
		tmp = fma(2.0, ((1.0 - t) / t), ((2.0 / t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(t * z)))
	tmp = 0.0
	if (Float64(x / y) <= -100000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-5)
		tmp = fma(2.0, Float64(Float64(1.0 - t) / t), Float64(Float64(2.0 / t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -100000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-5], N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e5 or 1.00000000000000008e-5 < (/.f64 x y)

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + 2 \cdot z}}{t \cdot z} \]

   4. Applied rewrites 79.7%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + 2 \cdot z}}{t \cdot z} \]

   if -1e5 < (/.f64 x y) < 1.00000000000000008e-5

   1. Initial program 86.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   4. Applied rewrites 66.5%

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

   6. Applied rewrites 66.4%

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

Alternative 4: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - \left(\frac{-2}{t} + 2\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{t}, \frac{1}{z}, \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) (+ (/ -2.0 t) 2.0))))
   (if (<= z -1.2e-22)
     t_1
     (if (<= z 1.32e-8) (fma (/ 2.0 t) (/ 1.0 z) (/ x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - ((-2.0 / t) + 2.0);
	double tmp;
	if (z <= -1.2e-22) {
		tmp = t_1;
	} else if (z <= 1.32e-8) {
		tmp = fma((2.0 / t), (1.0 / z), (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - Float64(Float64(-2.0 / t) + 2.0))
	tmp = 0.0
	if (z <= -1.2e-22)
		tmp = t_1;
	elseif (z <= 1.32e-8)
		tmp = fma(Float64(2.0 / t), Float64(1.0 / z), Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - N[(N[(-2.0 / t), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e-22], t$95$1, If[LessEqual[z, 1.32e-8], N[(N[(2.0 / t), $MachinePrecision] * N[(1.0 / z), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000001e-22 or 1.32000000000000007e-8 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + \frac{x}{y}} \]

   4. Applied rewrites 70.9%

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

   6. Applied rewrites 70.9%

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

   if -1.20000000000000001e-22 < z < 1.32000000000000007e-8

   1. Initial program 86.4%

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

   3. Applied rewrites 86.4%

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 63.5%

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

Alternative 5: 92.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - \left(\frac{-2}{t} + 2\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) (+ (/ -2.0 t) 2.0))))
   (if (<= z -1.2e-22)
     t_1
     (if (<= z 1.32e-8) (+ (/ x y) (/ 2.0 (* t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - ((-2.0 / t) + 2.0);
	double tmp;
	if (z <= -1.2e-22) {
		tmp = t_1;
	} else if (z <= 1.32e-8) {
		tmp = (x / y) + (2.0 / (t * 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 / y) - (((-2.0d0) / t) + 2.0d0)
    if (z <= (-1.2d-22)) then
        tmp = t_1
    else if (z <= 1.32d-8) then
        tmp = (x / y) + (2.0d0 / (t * 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 / y) - ((-2.0 / t) + 2.0);
	double tmp;
	if (z <= -1.2e-22) {
		tmp = t_1;
	} else if (z <= 1.32e-8) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - ((-2.0 / t) + 2.0)
	tmp = 0
	if z <= -1.2e-22:
		tmp = t_1
	elif z <= 1.32e-8:
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - Float64(Float64(-2.0 / t) + 2.0))
	tmp = 0.0
	if (z <= -1.2e-22)
		tmp = t_1;
	elseif (z <= 1.32e-8)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - ((-2.0 / t) + 2.0);
	tmp = 0.0;
	if (z <= -1.2e-22)
		tmp = t_1;
	elseif (z <= 1.32e-8)
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - N[(N[(-2.0 / t), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e-22], t$95$1, If[LessEqual[z, 1.32e-8], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000001e-22 or 1.32000000000000007e-8 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + \frac{x}{y}} \]

   4. Applied rewrites 70.9%

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

   6. Applied rewrites 70.9%

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

   if -1.20000000000000001e-22 < z < 1.32000000000000007e-8

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2}}{t \cdot z} \]

   4. Applied rewrites 63.2%

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

Alternative 6: 86.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - \left(\frac{-2}{t} + 2\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(2, -1, \frac{2}{t \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) (+ (/ -2.0 t) 2.0))))
   (if (<= z -5.5e-63)
     t_1
     (if (<= z 1.6e-11) (fma 2.0 -1.0 (/ 2.0 (* t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - ((-2.0 / t) + 2.0);
	double tmp;
	if (z <= -5.5e-63) {
		tmp = t_1;
	} else if (z <= 1.6e-11) {
		tmp = fma(2.0, -1.0, (2.0 / (t * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - Float64(Float64(-2.0 / t) + 2.0))
	tmp = 0.0
	if (z <= -5.5e-63)
		tmp = t_1;
	elseif (z <= 1.6e-11)
		tmp = fma(2.0, -1.0, Float64(2.0 / Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - N[(N[(-2.0 / t), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e-63], t$95$1, If[LessEqual[z, 1.6e-11], N[(2.0 * -1.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000043e-63 or 1.59999999999999997e-11 < z

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + \frac{x}{y}} \]

   4. Applied rewrites 70.9%

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

   6. Applied rewrites 70.9%

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

   if -5.50000000000000043e-63 < z < 1.59999999999999997e-11

   1. Initial program 86.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   4. Applied rewrites 66.5%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 49.8%

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

   9. Applied rewrites 49.8%

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

Alternative 7: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_3 (- (/ x y) 2.0)))
   (if (<= t_2 -1e+58)
     t_1
     (if (<= t_2 10000000000.0) t_3 (if (<= t_2 INFINITY) t_1 t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t_2 <= -1e+58) {
		tmp = t_1;
	} else if (t_2 <= 10000000000.0) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t_2 <= -1e+58) {
		tmp = t_1;
	} else if (t_2 <= 10000000000.0) {
		tmp = t_3;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / z) - -2.0) / t
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_3 = (x / y) - 2.0
	tmp = 0
	if t_2 <= -1e+58:
		tmp = t_1
	elif t_2 <= 10000000000.0:
		tmp = t_3
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_3 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t_2 <= -1e+58)
		tmp = t_1;
	elseif (t_2 <= 10000000000.0)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / z) - -2.0) / t;
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_3 = (x / y) - 2.0;
	tmp = 0.0;
	if (t_2 <= -1e+58)
		tmp = t_1;
	elseif (t_2 <= 10000000000.0)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+58], t$95$1, If[LessEqual[t$95$2, 10000000000.0], t$95$3, If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.99999999999999944e57 or 1e10 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   6. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   if -9.99999999999999944e57 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1e10 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 86.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   4. Applied rewrites 54.3%

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

Alternative 8: 81.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ t_3 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_4 := \frac{x}{y} - \frac{-2}{t}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -50000000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -1.9995:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+269}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ 2.0 z) t))
        (t_2 (- (/ x y) 2.0))
        (t_3 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_4 (- (/ x y) (/ -2.0 t))))
   (if (<= t_3 -1e+308)
     t_1
     (if (<= t_3 -50000000.0)
       t_4
       (if (<= t_3 -1.9995)
         t_2
         (if (<= t_3 5e+269) t_4 (if (<= t_3 INFINITY) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) / t;
	double t_2 = (x / y) - 2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_4 = (x / y) - (-2.0 / t);
	double tmp;
	if (t_3 <= -1e+308) {
		tmp = t_1;
	} else if (t_3 <= -50000000.0) {
		tmp = t_4;
	} else if (t_3 <= -1.9995) {
		tmp = t_2;
	} else if (t_3 <= 5e+269) {
		tmp = t_4;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) / t;
	double t_2 = (x / y) - 2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_4 = (x / y) - (-2.0 / t);
	double tmp;
	if (t_3 <= -1e+308) {
		tmp = t_1;
	} else if (t_3 <= -50000000.0) {
		tmp = t_4;
	} else if (t_3 <= -1.9995) {
		tmp = t_2;
	} else if (t_3 <= 5e+269) {
		tmp = t_4;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) / t
	t_2 = (x / y) - 2.0
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_4 = (x / y) - (-2.0 / t)
	tmp = 0
	if t_3 <= -1e+308:
		tmp = t_1
	elif t_3 <= -50000000.0:
		tmp = t_4
	elif t_3 <= -1.9995:
		tmp = t_2
	elif t_3 <= 5e+269:
		tmp = t_4
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) / t)
	t_2 = Float64(Float64(x / y) - 2.0)
	t_3 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_4 = Float64(Float64(x / y) - Float64(-2.0 / t))
	tmp = 0.0
	if (t_3 <= -1e+308)
		tmp = t_1;
	elseif (t_3 <= -50000000.0)
		tmp = t_4;
	elseif (t_3 <= -1.9995)
		tmp = t_2;
	elseif (t_3 <= 5e+269)
		tmp = t_4;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) / t;
	t_2 = (x / y) - 2.0;
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_4 = (x / y) - (-2.0 / t);
	tmp = 0.0;
	if (t_3 <= -1e+308)
		tmp = t_1;
	elseif (t_3 <= -50000000.0)
		tmp = t_4;
	elseif (t_3 <= -1.9995)
		tmp = t_2;
	elseif (t_3 <= 5e+269)
		tmp = t_4;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / y), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+308], t$95$1, If[LessEqual[t$95$3, -50000000.0], t$95$4, If[LessEqual[t$95$3, -1.9995], t$95$2, If[LessEqual[t$95$3, 5e+269], t$95$4, If[LessEqual[t$95$3, Infinity], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1e308 or 5.0000000000000002e269 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   7. Applied rewrites 31.3%

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   if -1e308 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5e7 or -1.99950000000000006 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5.0000000000000002e269

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + \frac{x}{y}} \]

   4. Applied rewrites 70.9%

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

   6. Applied rewrites 70.9%

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

   7. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} - \frac{-2}{\color{blue}{t}} \]

   9. Applied rewrites 51.8%

      \[\leadsto \frac{x}{y} - \frac{-2}{\color{blue}{t}} \]

   if -5e7 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.99950000000000006 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 86.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   4. Applied rewrites 54.3%

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

Alternative 9: 69.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{\frac{2}{z}}{t}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+287}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;2 \cdot \frac{1 - t}{t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 10^{+240}:\\ \;\;\;\;2 \cdot \frac{1}{t} - 2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_2 (/ (/ 2.0 z) t))
        (t_3 (- (/ x y) 2.0)))
   (if (<= t_1 -1e+287)
     (/ 2.0 (* t z))
     (if (<= t_1 -1e+141)
       (* 2.0 (/ (- 1.0 t) t))
       (if (<= t_1 -1e+78)
         t_2
         (if (<= t_1 10000000000.0)
           t_3
           (if (<= t_1 1e+240)
             (- (* 2.0 (/ 1.0 t)) 2.0)
             (if (<= t_1 INFINITY) t_2 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_2 = (2.0 / z) / t;
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t_1 <= -1e+287) {
		tmp = 2.0 / (t * z);
	} else if (t_1 <= -1e+141) {
		tmp = 2.0 * ((1.0 - t) / t);
	} else if (t_1 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 10000000000.0) {
		tmp = t_3;
	} else if (t_1 <= 1e+240) {
		tmp = (2.0 * (1.0 / t)) - 2.0;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_2 = (2.0 / z) / t;
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t_1 <= -1e+287) {
		tmp = 2.0 / (t * z);
	} else if (t_1 <= -1e+141) {
		tmp = 2.0 * ((1.0 - t) / t);
	} else if (t_1 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 10000000000.0) {
		tmp = t_3;
	} else if (t_1 <= 1e+240) {
		tmp = (2.0 * (1.0 / t)) - 2.0;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_2 = (2.0 / z) / t
	t_3 = (x / y) - 2.0
	tmp = 0
	if t_1 <= -1e+287:
		tmp = 2.0 / (t * z)
	elif t_1 <= -1e+141:
		tmp = 2.0 * ((1.0 - t) / t)
	elif t_1 <= -1e+78:
		tmp = t_2
	elif t_1 <= 10000000000.0:
		tmp = t_3
	elif t_1 <= 1e+240:
		tmp = (2.0 * (1.0 / t)) - 2.0
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_2 = Float64(Float64(2.0 / z) / t)
	t_3 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t_1 <= -1e+287)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t_1 <= -1e+141)
		tmp = Float64(2.0 * Float64(Float64(1.0 - t) / t));
	elseif (t_1 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 10000000000.0)
		tmp = t_3;
	elseif (t_1 <= 1e+240)
		tmp = Float64(Float64(2.0 * Float64(1.0 / t)) - 2.0);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_2 = (2.0 / z) / t;
	t_3 = (x / y) - 2.0;
	tmp = 0.0;
	if (t_1 <= -1e+287)
		tmp = 2.0 / (t * z);
	elseif (t_1 <= -1e+141)
		tmp = 2.0 * ((1.0 - t) / t);
	elseif (t_1 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 10000000000.0)
		tmp = t_3;
	elseif (t_1 <= 1e+240)
		tmp = (2.0 * (1.0 / t)) - 2.0;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+287], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+141], N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+78], t$95$2, If[LessEqual[t$95$1, 10000000000.0], t$95$3, If[LessEqual[t$95$1, 1e+240], N[(N[(2.0 * N[(1.0 / t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.0000000000000001e287

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   4. Applied rewrites 31.3%

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   if -1.0000000000000001e287 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000002e141

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + \frac{x}{y}} \]

   4. Applied rewrites 70.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]

   7. Applied rewrites 37.1%

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]

   if -1.00000000000000002e141 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000001e78 or 1.00000000000000001e240 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   7. Applied rewrites 31.3%

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   if -1.00000000000000001e78 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1e10 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 86.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   4. Applied rewrites 54.3%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if 1e10 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.00000000000000001e240

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + \frac{x}{y}} \]

   4. Applied rewrites 70.9%

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

   6. Applied rewrites 70.9%

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

   7. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]

   9. Applied rewrites 37.1%

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{1 - t}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{\frac{2}{z}}{t}\\ t_4 := \frac{x}{y} - 2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+287}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10000000000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 10^{+240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (- 1.0 t) t)))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_3 (/ (/ 2.0 z) t))
        (t_4 (- (/ x y) 2.0)))
   (if (<= t_2 -1e+287)
     (/ 2.0 (* t z))
     (if (<= t_2 -1e+141)
       t_1
       (if (<= t_2 -1e+78)
         t_3
         (if (<= t_2 10000000000.0)
           t_4
           (if (<= t_2 1e+240) t_1 (if (<= t_2 INFINITY) t_3 t_4))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((1.0 - t) / t);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (2.0 / z) / t;
	double t_4 = (x / y) - 2.0;
	double tmp;
	if (t_2 <= -1e+287) {
		tmp = 2.0 / (t * z);
	} else if (t_2 <= -1e+141) {
		tmp = t_1;
	} else if (t_2 <= -1e+78) {
		tmp = t_3;
	} else if (t_2 <= 10000000000.0) {
		tmp = t_4;
	} else if (t_2 <= 1e+240) {
		tmp = t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((1.0 - t) / t);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (2.0 / z) / t;
	double t_4 = (x / y) - 2.0;
	double tmp;
	if (t_2 <= -1e+287) {
		tmp = 2.0 / (t * z);
	} else if (t_2 <= -1e+141) {
		tmp = t_1;
	} else if (t_2 <= -1e+78) {
		tmp = t_3;
	} else if (t_2 <= 10000000000.0) {
		tmp = t_4;
	} else if (t_2 <= 1e+240) {
		tmp = t_1;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((1.0 - t) / t)
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_3 = (2.0 / z) / t
	t_4 = (x / y) - 2.0
	tmp = 0
	if t_2 <= -1e+287:
		tmp = 2.0 / (t * z)
	elif t_2 <= -1e+141:
		tmp = t_1
	elif t_2 <= -1e+78:
		tmp = t_3
	elif t_2 <= 10000000000.0:
		tmp = t_4
	elif t_2 <= 1e+240:
		tmp = t_1
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(1.0 - t) / t))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_3 = Float64(Float64(2.0 / z) / t)
	t_4 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t_2 <= -1e+287)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t_2 <= -1e+141)
		tmp = t_1;
	elseif (t_2 <= -1e+78)
		tmp = t_3;
	elseif (t_2 <= 10000000000.0)
		tmp = t_4;
	elseif (t_2 <= 1e+240)
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((1.0 - t) / t);
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_3 = (2.0 / z) / t;
	t_4 = (x / y) - 2.0;
	tmp = 0.0;
	if (t_2 <= -1e+287)
		tmp = 2.0 / (t * z);
	elseif (t_2 <= -1e+141)
		tmp = t_1;
	elseif (t_2 <= -1e+78)
		tmp = t_3;
	elseif (t_2 <= 10000000000.0)
		tmp = t_4;
	elseif (t_2 <= 1e+240)
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+287], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e+141], t$95$1, If[LessEqual[t$95$2, -1e+78], t$95$3, If[LessEqual[t$95$2, 10000000000.0], t$95$4, If[LessEqual[t$95$2, 1e+240], t$95$1, If[LessEqual[t$95$2, Infinity], t$95$3, t$95$4]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.0000000000000001e287

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   4. Applied rewrites 31.3%

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   if -1.0000000000000001e287 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000002e141 or 1e10 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.00000000000000001e240

   1. Initial program 86.4%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + \frac{x}{y}} \]

   4. Applied rewrites 70.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]

   7. Applied rewrites 37.1%

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]

   if -1.00000000000000002e141 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000001e78 or 1.00000000000000001e240 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   7. Applied rewrites 31.3%

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   if -1.00000000000000001e78 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1e10 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 86.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   4. Applied rewrites 54.3%

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

Alternative 11: 69.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{\frac{2}{z}}{t}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+287}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 10^{+240}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_2 (/ (/ 2.0 z) t))
        (t_3 (- (/ x y) 2.0)))
   (if (<= t_1 -1e+287)
     (/ 2.0 (* t z))
     (if (<= t_1 -1e+141)
       (/ 2.0 t)
       (if (<= t_1 -1e+78)
         t_2
         (if (<= t_1 10000000000.0)
           t_3
           (if (<= t_1 1e+240) (/ 2.0 t) (if (<= t_1 INFINITY) t_2 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_2 = (2.0 / z) / t;
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t_1 <= -1e+287) {
		tmp = 2.0 / (t * z);
	} else if (t_1 <= -1e+141) {
		tmp = 2.0 / t;
	} else if (t_1 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 10000000000.0) {
		tmp = t_3;
	} else if (t_1 <= 1e+240) {
		tmp = 2.0 / t;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_2 = (2.0 / z) / t;
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t_1 <= -1e+287) {
		tmp = 2.0 / (t * z);
	} else if (t_1 <= -1e+141) {
		tmp = 2.0 / t;
	} else if (t_1 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 10000000000.0) {
		tmp = t_3;
	} else if (t_1 <= 1e+240) {
		tmp = 2.0 / t;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_2 = (2.0 / z) / t
	t_3 = (x / y) - 2.0
	tmp = 0
	if t_1 <= -1e+287:
		tmp = 2.0 / (t * z)
	elif t_1 <= -1e+141:
		tmp = 2.0 / t
	elif t_1 <= -1e+78:
		tmp = t_2
	elif t_1 <= 10000000000.0:
		tmp = t_3
	elif t_1 <= 1e+240:
		tmp = 2.0 / t
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_2 = Float64(Float64(2.0 / z) / t)
	t_3 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t_1 <= -1e+287)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t_1 <= -1e+141)
		tmp = Float64(2.0 / t);
	elseif (t_1 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 10000000000.0)
		tmp = t_3;
	elseif (t_1 <= 1e+240)
		tmp = Float64(2.0 / t);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_2 = (2.0 / z) / t;
	t_3 = (x / y) - 2.0;
	tmp = 0.0;
	if (t_1 <= -1e+287)
		tmp = 2.0 / (t * z);
	elseif (t_1 <= -1e+141)
		tmp = 2.0 / t;
	elseif (t_1 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 10000000000.0)
		tmp = t_3;
	elseif (t_1 <= 1e+240)
		tmp = 2.0 / t;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+287], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e+141], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$1, -1e+78], t$95$2, If[LessEqual[t$95$1, 10000000000.0], t$95$3, If[LessEqual[t$95$1, 1e+240], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.0000000000000001e287

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   4. Applied rewrites 31.3%

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   if -1.0000000000000001e287 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000002e141 or 1e10 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.00000000000000001e240

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \frac{2}{\color{blue}{t}} \]

   7. Applied rewrites 18.6%

      \[\leadsto \frac{2}{\color{blue}{t}} \]

   if -1.00000000000000002e141 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000001e78 or 1.00000000000000001e240 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   7. Applied rewrites 31.3%

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   if -1.00000000000000001e78 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1e10 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 86.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   4. Applied rewrites 54.3%

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

Alternative 12: 69.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+141}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{+240}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_3 (- (/ x y) 2.0)))
   (if (<= t_2 -1e+287)
     t_1
     (if (<= t_2 -1e+141)
       (/ 2.0 t)
       (if (<= t_2 -1e+78)
         t_1
         (if (<= t_2 10000000000.0)
           t_3
           (if (<= t_2 1e+240) (/ 2.0 t) (if (<= t_2 INFINITY) t_1 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t_2 <= -1e+287) {
		tmp = t_1;
	} else if (t_2 <= -1e+141) {
		tmp = 2.0 / t;
	} else if (t_2 <= -1e+78) {
		tmp = t_1;
	} else if (t_2 <= 10000000000.0) {
		tmp = t_3;
	} else if (t_2 <= 1e+240) {
		tmp = 2.0 / t;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t_2 <= -1e+287) {
		tmp = t_1;
	} else if (t_2 <= -1e+141) {
		tmp = 2.0 / t;
	} else if (t_2 <= -1e+78) {
		tmp = t_1;
	} else if (t_2 <= 10000000000.0) {
		tmp = t_3;
	} else if (t_2 <= 1e+240) {
		tmp = 2.0 / t;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_3 = (x / y) - 2.0
	tmp = 0
	if t_2 <= -1e+287:
		tmp = t_1
	elif t_2 <= -1e+141:
		tmp = 2.0 / t
	elif t_2 <= -1e+78:
		tmp = t_1
	elif t_2 <= 10000000000.0:
		tmp = t_3
	elif t_2 <= 1e+240:
		tmp = 2.0 / t
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_3 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t_2 <= -1e+287)
		tmp = t_1;
	elseif (t_2 <= -1e+141)
		tmp = Float64(2.0 / t);
	elseif (t_2 <= -1e+78)
		tmp = t_1;
	elseif (t_2 <= 10000000000.0)
		tmp = t_3;
	elseif (t_2 <= 1e+240)
		tmp = Float64(2.0 / t);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_3 = (x / y) - 2.0;
	tmp = 0.0;
	if (t_2 <= -1e+287)
		tmp = t_1;
	elseif (t_2 <= -1e+141)
		tmp = 2.0 / t;
	elseif (t_2 <= -1e+78)
		tmp = t_1;
	elseif (t_2 <= 10000000000.0)
		tmp = t_3;
	elseif (t_2 <= 1e+240)
		tmp = 2.0 / t;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+287], t$95$1, If[LessEqual[t$95$2, -1e+141], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$2, -1e+78], t$95$1, If[LessEqual[t$95$2, 10000000000.0], t$95$3, If[LessEqual[t$95$2, 1e+240], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.0000000000000001e287 or -1.00000000000000002e141 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000001e78 or 1.00000000000000001e240 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 86.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   4. Applied rewrites 31.3%

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   if -1.0000000000000001e287 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.00000000000000002e141 or 1e10 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.00000000000000001e240

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \frac{2}{\color{blue}{t}} \]

   7. Applied rewrites 18.6%

      \[\leadsto \frac{2}{\color{blue}{t}} \]

   if -1.00000000000000001e78 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1e10 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 86.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   4. Applied rewrites 54.3%

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

Alternative 13: 59.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -6.6e-59) t_1 (if (<= t 7.5e-10) (/ 2.0 t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -6.6e-59) {
		tmp = t_1;
	} else if (t <= 7.5e-10) {
		tmp = 2.0 / 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 = (x / y) - 2.0d0
    if (t <= (-6.6d-59)) then
        tmp = t_1
    else if (t <= 7.5d-10) then
        tmp = 2.0d0 / 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 = (x / y) - 2.0;
	double tmp;
	if (t <= -6.6e-59) {
		tmp = t_1;
	} else if (t <= 7.5e-10) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -6.6e-59:
		tmp = t_1
	elif t <= 7.5e-10:
		tmp = 2.0 / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -6.6e-59)
		tmp = t_1;
	elseif (t <= 7.5e-10)
		tmp = Float64(2.0 / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -6.6e-59)
		tmp = t_1;
	elseif (t <= 7.5e-10)
		tmp = 2.0 / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -6.6e-59], t$95$1, If[LessEqual[t, 7.5e-10], N[(2.0 / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999964e-59 or 7.49999999999999995e-10 < t

   1. Initial program 86.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   4. Applied rewrites 54.3%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -6.59999999999999964e-59 < t < 7.49999999999999995e-10

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \frac{2}{\color{blue}{t}} \]

   7. Applied rewrites 18.6%

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

Alternative 14: 36.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e-8) -2.0 (if (<= t 1.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-8) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	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, 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 <= (-6.5d-8)) then
        tmp = -2.0d0
    else if (t <= 1.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-8) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e-8:
		tmp = -2.0
	elif t <= 1.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.5e-8)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.5e-8)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.5e-8], -2.0, If[LessEqual[t, 1.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -6.49999999999999997e-8 or 1 < t

   1. Initial program 86.4%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   4. Applied rewrites 54.3%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   5. Taylor expanded in x around 0

      \[\leadsto -2 \]

   7. Applied rewrites 20.7%

      \[\leadsto -2 \]

   if -6.49999999999999997e-8 < t < 1

   1. Initial program 86.4%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   4. Applied rewrites 47.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \frac{2}{\color{blue}{t}} \]

   7. Applied rewrites 18.6%

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

Alternative 15: 20.7% accurate, 24.7× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 -2.0)

C

double code(double x, double y, double z, double t) {
	return -2.0;
}

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 = -2.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return -2.0;
}

Python

def code(x, y, z, t):
	return -2.0

Julia

function code(x, y, z, t)
	return -2.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = -2.0;
end

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 86.4%

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

2. Taylor expanded in t around inf

   \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

4. Applied rewrites 54.3%

   \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

5. Taylor expanded in x around 0

   \[\leadsto -2 \]

7. Applied rewrites 20.7%

   \[\leadsto -2 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025161 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64
  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))