Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.3% → 95.9%

Time: 5.6s

Alternatives: 20

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

C

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

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 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

C

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

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 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{y \cdot \frac{z}{t\_1}}{x + 1}\\ t_3 := x + \frac{y \cdot z - x}{t\_1}\\ t_4 := \frac{t\_3}{x + 1}\\ \mathbf{if}\;t\_4 \leq -60000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;\frac{t\_3}{1}\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (/ (* y (/ z t_1)) (+ x 1.0)))
        (t_3 (+ x (/ (- (* y z) x) t_1)))
        (t_4 (/ t_3 (+ x 1.0))))
   (if (<= t_4 -60000000.0)
     t_2
     (if (<= t_4 4e-19)
       (/ t_3 1.0)
       (if (<= t_4 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_4 INFINITY)
           t_2
           (+ (/ x (+ x 1.0)) (/ (/ y t) (+ x 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = x + (((y * z) - x) / t_1);
	double t_4 = t_3 / (x + 1.0);
	double tmp;
	if (t_4 <= -60000000.0) {
		tmp = t_2;
	} else if (t_4 <= 4e-19) {
		tmp = t_3 / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = x + (((y * z) - x) / t_1);
	double t_4 = t_3 / (x + 1.0);
	double tmp;
	if (t_4 <= -60000000.0) {
		tmp = t_2;
	} else if (t_4 <= 4e-19) {
		tmp = t_3 / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (y * (z / t_1)) / (x + 1.0)
	t_3 = x + (((y * z) - x) / t_1)
	t_4 = t_3 / (x + 1.0)
	tmp = 0
	if t_4 <= -60000000.0:
		tmp = t_2
	elif t_4 <= 4e-19:
		tmp = t_3 / 1.0
	elif t_4 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_2
	else:
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(y * Float64(z / t_1)) / Float64(x + 1.0))
	t_3 = Float64(x + Float64(Float64(Float64(y * z) - x) / t_1))
	t_4 = Float64(t_3 / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -60000000.0)
		tmp = t_2;
	elseif (t_4 <= 4e-19)
		tmp = Float64(t_3 / 1.0);
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(y / t) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (y * (z / t_1)) / (x + 1.0);
	t_3 = x + (((y * z) - x) / t_1);
	t_4 = t_3 / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -60000000.0)
		tmp = t_2;
	elseif (t_4 <= 4e-19)
		tmp = t_3 / 1.0;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_2;
	else
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -60000000.0], t$95$2, If[LessEqual[t$95$4, 4e-19], N[(t$95$3 / 1.0), $MachinePrecision], If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$2, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -6e7 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 79.2%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if -6e7 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 94.6%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 98.6

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

   4. Applied rewrites 98.6%

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

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

   1. Initial program 79.2%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 61.5

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

   4. Applied rewrites 61.5%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 61.5

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

   6. Applied rewrites 61.5%

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

Alternative 2: 95.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := t \cdot z - x\\ t_3 := \frac{y \cdot \frac{z}{t\_2}}{x + 1}\\ t_4 := \frac{x + \frac{t\_1}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -1000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;\frac{x + \frac{t\_1}{t \cdot z}}{1}\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x))
        (t_2 (- (* t z) x))
        (t_3 (/ (* y (/ z t_2)) (+ x 1.0)))
        (t_4 (/ (+ x (/ t_1 t_2)) (+ x 1.0))))
   (if (<= t_4 -1000.0)
     t_3
     (if (<= t_4 4e-19)
       (/ (+ x (/ t_1 (* t z))) 1.0)
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_4 INFINITY)
           t_3
           (+ (/ x (+ x 1.0)) (/ (/ y t) (+ x 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (t * z) - x;
	double t_3 = (y * (z / t_2)) / (x + 1.0);
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 4e-19) {
		tmp = (x + (t_1 / (t * z))) / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (t * z) - x;
	double t_3 = (y * (z / t_2)) / (x + 1.0);
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 4e-19) {
		tmp = (x + (t_1 / (t * z))) / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - x
	t_2 = (t * z) - x
	t_3 = (y * (z / t_2)) / (x + 1.0)
	t_4 = (x + (t_1 / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -1000.0:
		tmp = t_3
	elif t_4 <= 4e-19:
		tmp = (x + (t_1 / (t * z))) / 1.0
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(y * Float64(z / t_2)) / Float64(x + 1.0))
	t_4 = Float64(Float64(x + Float64(t_1 / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 4e-19)
		tmp = Float64(Float64(x + Float64(t_1 / Float64(t * z))) / 1.0);
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(y / t) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - x;
	t_2 = (t * z) - x;
	t_3 = (y * (z / t_2)) / (x + 1.0);
	t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 4e-19)
		tmp = (x + (t_1 / (t * z))) / 1.0;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1000.0], t$95$3, If[LessEqual[t$95$4, 4e-19], N[(N[(x + N[(t$95$1 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1e3 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 79.4%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 90.9

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

   4. Applied rewrites 90.9%

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

   if -1e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 94.7%

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

   5. Taylor expanded in x around 0

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

      1. lift-*.f64 93.9

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

   7. Applied rewrites 93.9%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 98.6

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

   4. Applied rewrites 98.6%

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

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

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 61.5

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

   4. Applied rewrites 61.5%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 61.5

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

   6. Applied rewrites 61.5%

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

Alternative 3: 95.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := t \cdot z - x\\ t_3 := \frac{y \cdot \frac{z}{t\_2}}{x + 1}\\ t_4 := \frac{x + \frac{t\_1}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -1000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;\frac{x + \frac{t\_1}{t \cdot z}}{1}\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x))
        (t_2 (- (* t z) x))
        (t_3 (/ (* y (/ z t_2)) (+ x 1.0)))
        (t_4 (/ (+ x (/ t_1 t_2)) (+ x 1.0))))
   (if (<= t_4 -1000.0)
     t_3
     (if (<= t_4 4e-19)
       (/ (+ x (/ t_1 (* t z))) 1.0)
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_4 INFINITY) t_3 (/ (+ x (/ y t)) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (t * z) - x;
	double t_3 = (y * (z / t_2)) / (x + 1.0);
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 4e-19) {
		tmp = (x + (t_1 / (t * z))) / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (t * z) - x;
	double t_3 = (y * (z / t_2)) / (x + 1.0);
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 4e-19) {
		tmp = (x + (t_1 / (t * z))) / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - x
	t_2 = (t * z) - x
	t_3 = (y * (z / t_2)) / (x + 1.0)
	t_4 = (x + (t_1 / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -1000.0:
		tmp = t_3
	elif t_4 <= 4e-19:
		tmp = (x + (t_1 / (t * z))) / 1.0
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(y * Float64(z / t_2)) / Float64(x + 1.0))
	t_4 = Float64(Float64(x + Float64(t_1 / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 4e-19)
		tmp = Float64(Float64(x + Float64(t_1 / Float64(t * z))) / 1.0);
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - x;
	t_2 = (t * z) - x;
	t_3 = (y * (z / t_2)) / (x + 1.0);
	t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 4e-19)
		tmp = (x + (t_1 / (t * z))) / 1.0;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1000.0], t$95$3, If[LessEqual[t$95$4, 4e-19], N[(N[(x + N[(t$95$1 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1e3 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 79.4%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 90.9

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

   4. Applied rewrites 90.9%

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

   if -1e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 94.7%

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

   5. Taylor expanded in x around 0

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

      1. lift-*.f64 93.9

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

   7. Applied rewrites 93.9%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 98.6

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

   4. Applied rewrites 98.6%

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

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

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 61.5

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

   4. Applied rewrites 61.5%

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

Alternative 4: 95.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{y \cdot \frac{z}{t\_1}}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -1000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(1 + x\right)}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (/ (* y (/ z t_1)) (+ x 1.0)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -1000.0)
     t_2
     (if (<= t_3 4e-19)
       (+ (/ x (+ x 1.0)) (/ y (* t (+ 1.0 x))))
       (if (<= t_3 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_3 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -1000.0) {
		tmp = t_2;
	} else if (t_3 <= 4e-19) {
		tmp = (x / (x + 1.0)) + (y / (t * (1.0 + x)));
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -1000.0) {
		tmp = t_2;
	} else if (t_3 <= 4e-19) {
		tmp = (x / (x + 1.0)) + (y / (t * (1.0 + x)));
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (y * (z / t_1)) / (x + 1.0)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -1000.0:
		tmp = t_2
	elif t_3 <= 4e-19:
		tmp = (x / (x + 1.0)) + (y / (t * (1.0 + x)))
	elif t_3 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(y * Float64(z / t_1)) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -1000.0)
		tmp = t_2;
	elseif (t_3 <= 4e-19)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(1.0 + x))));
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (y * (z / t_1)) / (x + 1.0);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -1000.0)
		tmp = t_2;
	elseif (t_3 <= 4e-19)
		tmp = (x / (x + 1.0)) + (y / (t * (1.0 + x)));
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1000.0], t$95$2, If[LessEqual[t$95$3, 4e-19], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1e3 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 79.4%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 90.9

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

   4. Applied rewrites 90.9%

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

   if -1e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 84.8

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

   4. Applied rewrites 84.8%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 84.8

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

   6. Applied rewrites 84.8%

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

   7. Taylor expanded in z around inf

      \[\leadsto \frac{x}{x + 1} + \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 84.8

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

   9. Applied rewrites 84.8%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 98.6

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

   4. Applied rewrites 98.6%

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

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

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 61.5

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

   4. Applied rewrites 61.5%

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

Alternative 5: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-\frac{\frac{-y}{1 + x} - \frac{-x}{\left(1 + x\right) \cdot z}}{t}\right) + \frac{x}{1 + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 5e+301)
     t_1
     (+
      (- (/ (- (/ (- y) (+ 1.0 x)) (/ (- x) (* (+ 1.0 x) z))) t))
      (/ x (+ 1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = -(((-y / (1.0 + x)) - (-x / ((1.0 + x) * z))) / t) + (x / (1.0 + 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, 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 * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= 5d+301) then
        tmp = t_1
    else
        tmp = -(((-y / (1.0d0 + x)) - (-x / ((1.0d0 + x) * z))) / t) + (x / (1.0d0 + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = -(((-y / (1.0 + x)) - (-x / ((1.0 + x) * z))) / t) + (x / (1.0 + x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 5e+301:
		tmp = t_1
	else:
		tmp = -(((-y / (1.0 + x)) - (-x / ((1.0 + x) * z))) / t) + (x / (1.0 + x))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 5e+301)
		tmp = t_1;
	else
		tmp = Float64(Float64(-Float64(Float64(Float64(Float64(-y) / Float64(1.0 + x)) - Float64(Float64(-x) / Float64(Float64(1.0 + x) * z))) / t)) + Float64(x / Float64(1.0 + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 5e+301)
		tmp = t_1;
	else
		tmp = -(((-y / (1.0 + x)) - (-x / ((1.0 + x) * z))) / t) + (x / (1.0 + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+301], t$95$1, N[((-N[(N[(N[((-y) / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] - N[((-x) / N[(N[(1.0 + x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e301

   1. Initial program 96.0%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 24.9%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{y}{1 + x} - -1 \cdot \frac{x}{z \cdot \left(1 + x\right)}}{t} + \frac{x}{1 + x}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

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

   4. Applied rewrites 85.3%

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

Alternative 6: 94.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 5e+301) t_1 (+ (/ x (+ x 1.0)) (/ (/ y t) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= 5d+301) then
        tmp = t_1
    else
        tmp = (x / (x + 1.0d0)) + ((y / t) / (x + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 5e+301:
		tmp = t_1
	else:
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 5e+301)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(y / t) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 5e+301)
		tmp = t_1;
	else
		tmp = (x / (x + 1.0)) + ((y / t) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+301], t$95$1, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e301

   1. Initial program 96.0%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 24.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 84.5

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

   4. Applied rewrites 84.5%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 84.4

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

   6. Applied rewrites 84.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1} + \frac{\frac{y}{t}}{x + 1}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 92.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1} + \frac{y}{t \cdot \left(1 + x\right)}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -1000:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t\_2}\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{z \cdot y}{\left(1 + x\right) \cdot t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x (+ x 1.0)) (/ y (* t (+ 1.0 x)))))
        (t_2 (- (* t z) x))
        (t_3 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_3 -1000.0)
     (* (/ z (+ 1.0 x)) (/ y t_2))
     (if (<= t_3 4e-19)
       t_1
       (if (<= t_3 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_3 5e+301) (/ (* z y) (* (+ 1.0 x) t_2)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / (x + 1.0)) + (y / (t * (1.0 + x)));
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= -1000.0) {
		tmp = (z / (1.0 + x)) * (y / t_2);
	} else if (t_3 <= 4e-19) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_3 <= 5e+301) {
		tmp = (z * y) / ((1.0 + x) * t_2);
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x / (x + 1.0d0)) + (y / (t * (1.0d0 + x)))
    t_2 = (t * z) - x
    t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0d0)
    if (t_3 <= (-1000.0d0)) then
        tmp = (z / (1.0d0 + x)) * (y / t_2)
    else if (t_3 <= 4d-19) then
        tmp = t_1
    else if (t_3 <= 2.0d0) then
        tmp = (x - (x / t_2)) / (x + 1.0d0)
    else if (t_3 <= 5d+301) then
        tmp = (z * y) / ((1.0d0 + x) * t_2)
    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 / (x + 1.0)) + (y / (t * (1.0 + x)));
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= -1000.0) {
		tmp = (z / (1.0 + x)) * (y / t_2);
	} else if (t_3 <= 4e-19) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_3 <= 5e+301) {
		tmp = (z * y) / ((1.0 + x) * t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / (x + 1.0)) + (y / (t * (1.0 + x)))
	t_2 = (t * z) - x
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_3 <= -1000.0:
		tmp = (z / (1.0 + x)) * (y / t_2)
	elif t_3 <= 4e-19:
		tmp = t_1
	elif t_3 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_3 <= 5e+301:
		tmp = (z * y) / ((1.0 + x) * t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(1.0 + x))))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -1000.0)
		tmp = Float64(Float64(z / Float64(1.0 + x)) * Float64(y / t_2));
	elseif (t_3 <= 4e-19)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_3 <= 5e+301)
		tmp = Float64(Float64(z * y) / Float64(Float64(1.0 + x) * t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / (x + 1.0)) + (y / (t * (1.0 + x)));
	t_2 = (t * z) - x;
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -1000.0)
		tmp = (z / (1.0 + x)) * (y / t_2);
	elseif (t_3 <= 4e-19)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_3 <= 5e+301)
		tmp = (z * y) / ((1.0 + x) * t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1000.0], N[(N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e-19], t$95$1, If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+301], N[(N[(z * y), $MachinePrecision] / N[(N[(1.0 + x), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1e3

   1. Initial program 78.7%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 77.6

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

   4. Applied rewrites 77.6%

      \[\leadsto \color{blue}{\frac{z \cdot y}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. times-frac N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 83.1

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

   6. Applied rewrites 83.1%

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

   if -1e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19 or 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 84.7

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

   4. Applied rewrites 84.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 84.7

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

   6. Applied rewrites 84.7%

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

   7. Taylor expanded in z around inf

      \[\leadsto \frac{x}{x + 1} + \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 84.9

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

   9. Applied rewrites 84.9%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 98.6

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

   4. Applied rewrites 98.6%

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

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e301

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 96.5

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

   4. Applied rewrites 96.5%

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

Alternative 8: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1} + \frac{y}{t \cdot \left(1 + x\right)}\\ t_2 := t \cdot z - x\\ t_3 := \frac{z \cdot y}{\left(1 + x\right) \cdot t\_2}\\ t_4 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -1000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x (+ x 1.0)) (/ y (* t (+ 1.0 x)))))
        (t_2 (- (* t z) x))
        (t_3 (/ (* z y) (* (+ 1.0 x) t_2)))
        (t_4 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_4 -1000.0)
     t_3
     (if (<= t_4 4e-19)
       t_1
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_4 5e+301) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / (x + 1.0)) + (y / (t * (1.0 + x)));
	double t_2 = (t * z) - x;
	double t_3 = (z * y) / ((1.0 + x) * t_2);
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 4e-19) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= 5e+301) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x / (x + 1.0d0)) + (y / (t * (1.0d0 + x)))
    t_2 = (t * z) - x
    t_3 = (z * y) / ((1.0d0 + x) * t_2)
    t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0d0)
    if (t_4 <= (-1000.0d0)) then
        tmp = t_3
    else if (t_4 <= 4d-19) then
        tmp = t_1
    else if (t_4 <= 2.0d0) then
        tmp = (x - (x / t_2)) / (x + 1.0d0)
    else if (t_4 <= 5d+301) then
        tmp = t_3
    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 / (x + 1.0)) + (y / (t * (1.0 + x)));
	double t_2 = (t * z) - x;
	double t_3 = (z * y) / ((1.0 + x) * t_2);
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 4e-19) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= 5e+301) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / (x + 1.0)) + (y / (t * (1.0 + x)))
	t_2 = (t * z) - x
	t_3 = (z * y) / ((1.0 + x) * t_2)
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -1000.0:
		tmp = t_3
	elif t_4 <= 4e-19:
		tmp = t_1
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_4 <= 5e+301:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(1.0 + x))))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(z * y) / Float64(Float64(1.0 + x) * t_2))
	t_4 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 4e-19)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_4 <= 5e+301)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / (x + 1.0)) + (y / (t * (1.0 + x)));
	t_2 = (t * z) - x;
	t_3 = (z * y) / ((1.0 + x) * t_2);
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 4e-19)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_4 <= 5e+301)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * y), $MachinePrecision] / N[(N[(1.0 + x), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1000.0], t$95$3, If[LessEqual[t$95$4, 4e-19], t$95$1, If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+301], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1e3 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e301

   1. Initial program 87.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 85.2

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

   4. Applied rewrites 85.2%

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

   if -1e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19 or 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 84.7

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

   4. Applied rewrites 84.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 84.7

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

   6. Applied rewrites 84.7%

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

   7. Taylor expanded in z around inf

      \[\leadsto \frac{x}{x + 1} + \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 84.9

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

   9. Applied rewrites 84.9%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 98.6

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

   4. Applied rewrites 98.6%

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

Alternative 9: 91.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{z \cdot y}{\left(1 + x\right) \cdot t\_2}\\ t_4 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -1000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (* z y) (* (+ 1.0 x) t_2)))
        (t_4 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_4 -1000.0)
     t_3
     (if (<= t_4 4e-19)
       t_1
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_4 5e+301) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (z * y) / ((1.0 + x) * t_2);
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 4e-19) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= 5e+301) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = (t * z) - x
    t_3 = (z * y) / ((1.0d0 + x) * t_2)
    t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0d0)
    if (t_4 <= (-1000.0d0)) then
        tmp = t_3
    else if (t_4 <= 4d-19) then
        tmp = t_1
    else if (t_4 <= 2.0d0) then
        tmp = (x - (x / t_2)) / (x + 1.0d0)
    else if (t_4 <= 5d+301) then
        tmp = t_3
    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 / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (z * y) / ((1.0 + x) * t_2);
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 4e-19) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= 5e+301) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (z * y) / ((1.0 + x) * t_2)
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -1000.0:
		tmp = t_3
	elif t_4 <= 4e-19:
		tmp = t_1
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_4 <= 5e+301:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(z * y) / Float64(Float64(1.0 + x) * t_2))
	t_4 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 4e-19)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_4 <= 5e+301)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (z * y) / ((1.0 + x) * t_2);
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 4e-19)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_4 <= 5e+301)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * y), $MachinePrecision] / N[(N[(1.0 + x), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1000.0], t$95$3, If[LessEqual[t$95$4, 4e-19], t$95$1, If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+301], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1e3 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e301

   1. Initial program 87.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 85.2

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

   4. Applied rewrites 85.2%

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

   if -1e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19 or 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 84.7

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

   4. Applied rewrites 84.7%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 98.6

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

   4. Applied rewrites 98.6%

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

Alternative 10: 91.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{z \cdot y}{\left(1 + x\right) \cdot t\_2}\\ t_4 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -1000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 0.9999999999825053:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (* z y) (* (+ 1.0 x) t_2)))
        (t_4 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_4 -1000.0)
     t_3
     (if (<= t_4 0.9999999999825053)
       t_1
       (if (<= t_4 2.0) 1.0 (if (<= t_4 5e+301) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (z * y) / ((1.0 + x) * t_2);
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 0.9999999999825053) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = 1.0;
	} else if (t_4 <= 5e+301) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = (t * z) - x
    t_3 = (z * y) / ((1.0d0 + x) * t_2)
    t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0d0)
    if (t_4 <= (-1000.0d0)) then
        tmp = t_3
    else if (t_4 <= 0.9999999999825053d0) then
        tmp = t_1
    else if (t_4 <= 2.0d0) then
        tmp = 1.0d0
    else if (t_4 <= 5d+301) then
        tmp = t_3
    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 / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (z * y) / ((1.0 + x) * t_2);
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -1000.0) {
		tmp = t_3;
	} else if (t_4 <= 0.9999999999825053) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = 1.0;
	} else if (t_4 <= 5e+301) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (z * y) / ((1.0 + x) * t_2)
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -1000.0:
		tmp = t_3
	elif t_4 <= 0.9999999999825053:
		tmp = t_1
	elif t_4 <= 2.0:
		tmp = 1.0
	elif t_4 <= 5e+301:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(z * y) / Float64(Float64(1.0 + x) * t_2))
	t_4 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 0.9999999999825053)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = 1.0;
	elseif (t_4 <= 5e+301)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (z * y) / ((1.0 + x) * t_2);
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -1000.0)
		tmp = t_3;
	elseif (t_4 <= 0.9999999999825053)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = 1.0;
	elseif (t_4 <= 5e+301)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * y), $MachinePrecision] / N[(N[(1.0 + x), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -1000.0], t$95$3, If[LessEqual[t$95$4, 0.9999999999825053], t$95$1, If[LessEqual[t$95$4, 2.0], 1.0, If[LessEqual[t$95$4, 5e+301], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1e3 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e301

   1. Initial program 87.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 85.2

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

   4. Applied rewrites 85.2%

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

   if -1e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999999998250533 or 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 73.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 83.7

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

   4. Applied rewrites 83.7%

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

   if 0.99999999998250533 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 99.1%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_3 \leq 0.9999999999825053:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{z \cdot y}{1 \cdot t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_3 0.9999999999825053)
     t_1
     (if (<= t_3 2.0) 1.0 (if (<= t_3 5e+301) (/ (* z y) (* 1.0 t_2)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= 0.9999999999825053) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+301) {
		tmp = (z * y) / (1.0 * t_2);
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = (t * z) - x
    t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0d0)
    if (t_3 <= 0.9999999999825053d0) then
        tmp = t_1
    else if (t_3 <= 2.0d0) then
        tmp = 1.0d0
    else if (t_3 <= 5d+301) then
        tmp = (z * y) / (1.0d0 * t_2)
    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 / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= 0.9999999999825053) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+301) {
		tmp = (z * y) / (1.0 * t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_3 <= 0.9999999999825053:
		tmp = t_1
	elif t_3 <= 2.0:
		tmp = 1.0
	elif t_3 <= 5e+301:
		tmp = (z * y) / (1.0 * t_2)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= 0.9999999999825053)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+301)
		tmp = Float64(Float64(z * y) / Float64(1.0 * t_2));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= 0.9999999999825053)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+301)
		tmp = (z * y) / (1.0 * t_2);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 0.9999999999825053], t$95$1, If[LessEqual[t$95$3, 2.0], 1.0, If[LessEqual[t$95$3, 5e+301], N[(N[(z * y), $MachinePrecision] / N[(1.0 * t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999999998250533 or 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 75.2%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 77.1

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

   4. Applied rewrites 77.1%

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

   if 0.99999999998250533 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 99.1%

      \[\leadsto \color{blue}{1} \]

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e301

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 96.5

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

   4. Applied rewrites 96.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto \frac{z \cdot y}{1 \cdot \left(\color{blue}{t \cdot z} - x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 82.5%

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

Alternative 12: 85.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq 0.9999999999825053:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 0.9999999999825053) t_1 (if (<= t_2 1.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 0.9999999999825053) {
		tmp = t_1;
	} else if (t_2 <= 1.0) {
		tmp = 1.0;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= 0.9999999999825053d0) then
        tmp = t_1
    else if (t_2 <= 1.0d0) then
        tmp = 1.0d0
    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 / t)) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 0.9999999999825053) {
		tmp = t_1;
	} else if (t_2 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= 0.9999999999825053:
		tmp = t_1
	elif t_2 <= 1.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= 0.9999999999825053)
		tmp = t_1;
	elseif (t_2 <= 1.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 0.9999999999825053)
		tmp = t_1;
	elseif (t_2 <= 1.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.9999999999825053], t$95$1, If[LessEqual[t$95$2, 1.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999999998250533 or 1 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 79.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 73.1

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

   4. Applied rewrites 73.1%

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

   if 0.99999999998250533 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 99.9%

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

Alternative 13: 82.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t}}{x + 1}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;t\_2 \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ y t) (+ x 1.0)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 4e-19) (+ x t_1) (if (<= t_2 1.0) 1.0 (+ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / t) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 4e-19) {
		tmp = x + t_1;
	} else if (t_2 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + 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) :: t_2
    real(8) :: tmp
    t_1 = (y / t) / (x + 1.0d0)
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= 4d-19) then
        tmp = x + t_1
    else if (t_2 <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / t) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 4e-19) {
		tmp = x + t_1;
	} else if (t_2 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / t) / (x + 1.0)
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= 4e-19:
		tmp = x + t_1
	elif t_2 <= 1.0:
		tmp = 1.0
	else:
		tmp = 1.0 + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / t) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= 4e-19)
		tmp = Float64(x + t_1);
	elseif (t_2 <= 1.0)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / t) / (x + 1.0);
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 4e-19)
		tmp = x + t_1;
	elseif (t_2 <= 1.0)
		tmp = 1.0;
	else
		tmp = 1.0 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 4e-19], N[(x + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 1.0], 1.0, N[(1.0 + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19

   1. Initial program 88.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 75.4

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

   4. Applied rewrites 75.4%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 75.4

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

   6. Applied rewrites 75.4%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 73.4%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 97.1%

      \[\leadsto \color{blue}{1} \]

   if 1 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 62.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 69.5

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

   4. Applied rewrites 69.5%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 69.5

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

   6. Applied rewrites 69.5%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 61.5%

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

Alternative 14: 82.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{t \cdot \left(1 + x\right)}\\ \mathbf{elif}\;t\_1 \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 4e-19)
     (+ x (/ y (* t (+ 1.0 x))))
     (if (<= t_1 1.0) 1.0 (+ 1.0 (/ (/ y t) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 4e-19) {
		tmp = x + (y / (t * (1.0 + x)));
	} else if (t_1 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= 4d-19) then
        tmp = x + (y / (t * (1.0d0 + x)))
    else if (t_1 <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + ((y / t) / (x + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 4e-19) {
		tmp = x + (y / (t * (1.0 + x)));
	} else if (t_1 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 4e-19:
		tmp = x + (y / (t * (1.0 + x)))
	elif t_1 <= 1.0:
		tmp = 1.0
	else:
		tmp = 1.0 + ((y / t) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 4e-19)
		tmp = Float64(x + Float64(y / Float64(t * Float64(1.0 + x))));
	elseif (t_1 <= 1.0)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + Float64(Float64(y / t) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 4e-19)
		tmp = x + (y / (t * (1.0 + x)));
	elseif (t_1 <= 1.0)
		tmp = 1.0;
	else
		tmp = 1.0 + ((y / t) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-19], N[(x + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.0], 1.0, N[(1.0 + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19

   1. Initial program 88.8%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 75.4

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

   4. Applied rewrites 75.4%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 75.4

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

   6. Applied rewrites 75.4%

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

   7. Taylor expanded in z around inf

      \[\leadsto \frac{x}{x + 1} + \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 75.8

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

   9. Applied rewrites 75.8%

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

   10. Taylor expanded in x around 0

       \[\leadsto \color{blue}{x} + \frac{y}{t \cdot \left(1 + x\right)} \]
   11. Step-by-step derivation

   12. Applied rewrites 73.6%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 97.1%

      \[\leadsto \color{blue}{1} \]

   if 1 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 62.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 69.5

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

   4. Applied rewrites 69.5%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 69.5

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

   6. Applied rewrites 69.5%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 61.5%

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

Alternative 15: 80.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{t \cdot \left(1 + x\right)}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ y (* t (+ 1.0 x)))))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 4e-19) t_1 (if (<= t_2 5e+61) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y / (t * (1.0 + x)));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 4e-19) {
		tmp = t_1;
	} else if (t_2 <= 5e+61) {
		tmp = 1.0;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (t * (1.0d0 + x)))
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= 4d-19) then
        tmp = t_1
    else if (t_2 <= 5d+61) then
        tmp = 1.0d0
    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 / (t * (1.0 + x)));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 4e-19) {
		tmp = t_1;
	} else if (t_2 <= 5e+61) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y / (t * (1.0 + x)))
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= 4e-19:
		tmp = t_1
	elif t_2 <= 5e+61:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y / Float64(t * Float64(1.0 + x))))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= 4e-19)
		tmp = t_1;
	elseif (t_2 <= 5e+61)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y / (t * (1.0 + x)));
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 4e-19)
		tmp = t_1;
	elseif (t_2 <= 5e+61)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 4e-19], t$95$1, If[LessEqual[t$95$2, 5e+61], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19 or 5.00000000000000018e61 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 77.2%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 74.7

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

   4. Applied rewrites 74.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 74.7

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

   6. Applied rewrites 74.7%

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

   7. Taylor expanded in z around inf

      \[\leadsto \frac{x}{x + 1} + \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 75.1

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

   9. Applied rewrites 75.1%

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

   10. Taylor expanded in x around 0

       \[\leadsto \color{blue}{x} + \frac{y}{t \cdot \left(1 + x\right)} \]
   11. Step-by-step derivation

   12. Applied rewrites 68.3%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000018e61

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 91.8%

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

Alternative 16: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -0.5:\\ \;\;\;\;\frac{y}{t \cdot \left(1 + x\right)}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999825053:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -0.5)
     (/ y (* t (+ 1.0 x)))
     (if (<= t_1 0.9999999999825053)
       (/ x (+ x 1.0))
       (if (<= t_1 5e+61) 1.0 (/ (/ y t) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -0.5) {
		tmp = y / (t * (1.0 + x));
	} else if (t_1 <= 0.9999999999825053) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 5e+61) {
		tmp = 1.0;
	} else {
		tmp = (y / t) / (x + 1.0);
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= (-0.5d0)) then
        tmp = y / (t * (1.0d0 + x))
    else if (t_1 <= 0.9999999999825053d0) then
        tmp = x / (x + 1.0d0)
    else if (t_1 <= 5d+61) then
        tmp = 1.0d0
    else
        tmp = (y / t) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -0.5) {
		tmp = y / (t * (1.0 + x));
	} else if (t_1 <= 0.9999999999825053) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 5e+61) {
		tmp = 1.0;
	} else {
		tmp = (y / t) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -0.5:
		tmp = y / (t * (1.0 + x))
	elif t_1 <= 0.9999999999825053:
		tmp = x / (x + 1.0)
	elif t_1 <= 5e+61:
		tmp = 1.0
	else:
		tmp = (y / t) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -0.5)
		tmp = Float64(y / Float64(t * Float64(1.0 + x)));
	elseif (t_1 <= 0.9999999999825053)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_1 <= 5e+61)
		tmp = 1.0;
	else
		tmp = Float64(Float64(y / t) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -0.5)
		tmp = y / (t * (1.0 + x));
	elseif (t_1 <= 0.9999999999825053)
		tmp = x / (x + 1.0);
	elseif (t_1 <= 5e+61)
		tmp = 1.0;
	else
		tmp = (y / t) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.5], N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999825053], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+61], 1.0, N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -0.5

   1. Initial program 79.0%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 77.2

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

   4. Applied rewrites 77.2%

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

   5. Taylor expanded in z around inf

      \[\leadsto \frac{y}{\color{blue}{t \cdot \left(1 + x\right)}} \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 60.2

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

   7. Applied rewrites 60.2%

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

   if -0.5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999999998250533

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{x + 1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.8%

      \[\leadsto \frac{\color{blue}{x}}{x + 1} \]

   if 0.99999999998250533 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000018e61

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 94.2%

      \[\leadsto \color{blue}{1} \]

   if 5.00000000000000018e61 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 53.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\frac{y}{t}}}{x + 1} \]
   3. Step-by-step derivation

      1. lower-/.f64 56.6

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

   4. Applied rewrites 56.6%

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

Alternative 17: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t \cdot \left(1 + x\right)}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.9999999999825053:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* t (+ 1.0 x))))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 -0.5)
     t_1
     (if (<= t_2 0.9999999999825053)
       (/ x (+ x 1.0))
       (if (<= t_2 5e+61) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t * (1.0 + x));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -0.5) {
		tmp = t_1;
	} else if (t_2 <= 0.9999999999825053) {
		tmp = x / (x + 1.0);
	} else if (t_2 <= 5e+61) {
		tmp = 1.0;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y / (t * (1.0d0 + x))
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= (-0.5d0)) then
        tmp = t_1
    else if (t_2 <= 0.9999999999825053d0) then
        tmp = x / (x + 1.0d0)
    else if (t_2 <= 5d+61) then
        tmp = 1.0d0
    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 = y / (t * (1.0 + x));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -0.5) {
		tmp = t_1;
	} else if (t_2 <= 0.9999999999825053) {
		tmp = x / (x + 1.0);
	} else if (t_2 <= 5e+61) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t * (1.0 + x))
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= -0.5:
		tmp = t_1
	elif t_2 <= 0.9999999999825053:
		tmp = x / (x + 1.0)
	elif t_2 <= 5e+61:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t * Float64(1.0 + x)))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -0.5)
		tmp = t_1;
	elseif (t_2 <= 0.9999999999825053)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_2 <= 5e+61)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t * (1.0 + x));
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -0.5)
		tmp = t_1;
	elseif (t_2 <= 0.9999999999825053)
		tmp = x / (x + 1.0);
	elseif (t_2 <= 5e+61)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -0.5], t$95$1, If[LessEqual[t$95$2, 0.9999999999825053], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+61], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -0.5 or 5.00000000000000018e61 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 65.2%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{y \cdot z}{\left(1 + x\right) \cdot \left(t \cdot z - x\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 64.2

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

   4. Applied rewrites 64.2%

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

   5. Taylor expanded in z around inf

      \[\leadsto \frac{y}{\color{blue}{t \cdot \left(1 + x\right)}} \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 58.5

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

   7. Applied rewrites 58.5%

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

   if -0.5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999999998250533

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{x + 1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.8%

      \[\leadsto \frac{\color{blue}{x}}{x + 1} \]

   if 0.99999999998250533 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000018e61

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 94.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 18: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -0.5:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999825053:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -0.5)
     (/ y t)
     (if (<= t_1 0.9999999999825053)
       (/ x (+ x 1.0))
       (if (<= t_1 5e+61) 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -0.5) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999825053) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 5e+61) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= (-0.5d0)) then
        tmp = y / t
    else if (t_1 <= 0.9999999999825053d0) then
        tmp = x / (x + 1.0d0)
    else if (t_1 <= 5d+61) then
        tmp = 1.0d0
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -0.5) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999825053) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 5e+61) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -0.5:
		tmp = y / t
	elif t_1 <= 0.9999999999825053:
		tmp = x / (x + 1.0)
	elif t_1 <= 5e+61:
		tmp = 1.0
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -0.5)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999999825053)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_1 <= 5e+61)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -0.5)
		tmp = y / t;
	elseif (t_1 <= 0.9999999999825053)
		tmp = x / (x + 1.0);
	elseif (t_1 <= 5e+61)
		tmp = 1.0;
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.5], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999825053], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+61], 1.0, N[(y / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -0.5 or 5.00000000000000018e61 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 65.2%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 52.2

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

   4. Applied rewrites 52.2%

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

   if -0.5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999999998250533

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{\color{blue}{x}}{x + 1} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.8%

      \[\leadsto \frac{\color{blue}{x}}{x + 1} \]

   if 0.99999999998250533 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000018e61

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 94.2%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 4e-19) (/ y t) (if (<= t_1 5e+61) 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 4e-19) {
		tmp = y / t;
	} else if (t_1 <= 5e+61) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= 4d-19) then
        tmp = y / t
    else if (t_1 <= 5d+61) then
        tmp = 1.0d0
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 4e-19) {
		tmp = y / t;
	} else if (t_1 <= 5e+61) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 4e-19:
		tmp = y / t
	elif t_1 <= 5e+61:
		tmp = 1.0
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 4e-19)
		tmp = Float64(y / t);
	elseif (t_1 <= 5e+61)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 4e-19)
		tmp = y / t;
	elseif (t_1 <= 5e+61)
		tmp = 1.0;
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-19], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 5e+61], 1.0, N[(y / t), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999999e-19 or 5.00000000000000018e61 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 77.2%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 45.9

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

   4. Applied rewrites 45.9%

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

   if 3.9999999999999999e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000018e61

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   3. Step-by-step derivation

   4. Applied rewrites 91.8%

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

Alternative 20: 53.5% accurate, 24.3× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

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

C

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

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 = 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 89.3%

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

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
3. Step-by-step derivation

4. Applied rewrites 53.5%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025124 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))