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

Percentage Accurate: 89.5% → 92.8%

Time: 2.9s

Alternatives: 14

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: 89.5% 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: 92.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := x + \frac{y \cdot z - x}{t\_1}\\ t_3 := \frac{t\_2}{x + 1}\\ \mathbf{if}\;t\_3 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{t\_2}{1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;\frac{y}{1 + x} \cdot \frac{z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + x} + \frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (+ x (/ (- (* y z) x) t_1)))
        (t_3 (/ t_2 (+ x 1.0))))
   (if (<= t_3 2e-37)
     (/ t_2 1.0)
     (if (<= t_3 2.0)
       (/ (- x (/ x t_1)) (+ x 1.0))
       (if (<= t_3 INFINITY)
         (* (/ y (+ 1.0 x)) (/ z t_1))
         (+ (/ x (+ 1.0 x)) (/ y (* t (+ 1.0 x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = x + (((y * z) - x) / t_1);
	double t_3 = t_2 / (x + 1.0);
	double tmp;
	if (t_3 <= 2e-37) {
		tmp = t_2 / 1.0;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = (y / (1.0 + x)) * (z / t_1);
	} else {
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = x + (((y * z) - x) / t_1);
	double t_3 = t_2 / (x + 1.0);
	double tmp;
	if (t_3 <= 2e-37) {
		tmp = t_2 / 1.0;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = (y / (1.0 + x)) * (z / t_1);
	} else {
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = x + (((y * z) - x) / t_1)
	t_3 = t_2 / (x + 1.0)
	tmp = 0
	if t_3 <= 2e-37:
		tmp = t_2 / 1.0
	elif t_3 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_3 <= math.inf:
		tmp = (y / (1.0 + x)) * (z / t_1)
	else:
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(x + Float64(Float64(Float64(y * z) - x) / t_1))
	t_3 = Float64(t_2 / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= 2e-37)
		tmp = Float64(t_2 / 1.0);
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (t_3 <= Inf)
		tmp = Float64(Float64(y / Float64(1.0 + x)) * Float64(z / t_1));
	else
		tmp = Float64(Float64(x / Float64(1.0 + x)) + Float64(y / Float64(t * Float64(1.0 + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = x + (((y * z) - x) / t_1);
	t_3 = t_2 / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= 2e-37)
		tmp = t_2 / 1.0;
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_3 <= Inf)
		tmp = (y / (1.0 + x)) * (z / t_1);
	else
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 2e-37], N[(t$95$2 / 1.0), $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], N[(N[(y / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $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))) < 2.00000000000000013e-37

   1. Initial program 90.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 88.1%

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

   if 2.00000000000000013e-37 < (/.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. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x - \frac{x}{t \cdot z - x}}}{x + 1} \]
   4. 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

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

      4. lift--.f64 100.0

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

   5. Applied rewrites 100.0%

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

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

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. times-frac N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   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 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 100.0

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

   7. Applied rewrites 100.0%

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

Alternative 2: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ t_3 := \frac{z}{t\_1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot t\_3}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{y}{1 + x} \cdot t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + x} + \frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0)))
        (t_3 (/ z t_1)))
   (if (<= t_2 -1e-11)
     (/ (* y t_3) (+ x 1.0))
     (if (<= t_2 2e-37)
       (/ (+ x (/ y t)) 1.0)
       (if (<= t_2 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_2 INFINITY)
           (* (/ y (+ 1.0 x)) t_3)
           (+ (/ x (+ 1.0 x)) (/ y (* t (+ 1.0 x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double t_3 = z / t_1;
	double tmp;
	if (t_2 <= -1e-11) {
		tmp = (y * t_3) / (x + 1.0);
	} else if (t_2 <= 2e-37) {
		tmp = (x + (y / t)) / 1.0;
	} else if (t_2 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (y / (1.0 + x)) * t_3;
	} else {
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double t_3 = z / t_1;
	double tmp;
	if (t_2 <= -1e-11) {
		tmp = (y * t_3) / (x + 1.0);
	} else if (t_2 <= 2e-37) {
		tmp = (x + (y / t)) / 1.0;
	} else if (t_2 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (y / (1.0 + x)) * t_3;
	} else {
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	t_3 = z / t_1
	tmp = 0
	if t_2 <= -1e-11:
		tmp = (y * t_3) / (x + 1.0)
	elif t_2 <= 2e-37:
		tmp = (x + (y / t)) / 1.0
	elif t_2 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_2 <= math.inf:
		tmp = (y / (1.0 + x)) * t_3
	else:
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	t_3 = Float64(z / t_1)
	tmp = 0.0
	if (t_2 <= -1e-11)
		tmp = Float64(Float64(y * t_3) / Float64(x + 1.0));
	elseif (t_2 <= 2e-37)
		tmp = Float64(Float64(x + Float64(y / t)) / 1.0);
	elseif (t_2 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(y / Float64(1.0 + x)) * t_3);
	else
		tmp = Float64(Float64(x / Float64(1.0 + x)) + Float64(y / Float64(t * Float64(1.0 + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	t_3 = z / t_1;
	tmp = 0.0;
	if (t_2 <= -1e-11)
		tmp = (y * t_3) / (x + 1.0);
	elseif (t_2 <= 2e-37)
		tmp = (x + (y / t)) / 1.0;
	elseif (t_2 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_2 <= Inf)
		tmp = (y / (1.0 + x)) * t_3;
	else
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-11], N[(N[(y * t$95$3), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e-37], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$2, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(y / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] * t$95$3), $MachinePrecision], N[(N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -9.99999999999999939e-12

   1. Initial program 85.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{t \cdot z - x}}}{x + 1} \]
   4. 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

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

      5. lift--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   if -9.99999999999999939e-12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000013e-37

   1. Initial program 92.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 88.6

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

   5. Applied rewrites 88.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 88.6%

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

   if 2.00000000000000013e-37 < (/.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. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x - \frac{x}{t \cdot z - x}}}{x + 1} \]
   4. 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

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

      4. lift--.f64 100.0

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

   5. Applied rewrites 100.0%

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

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

   1. Initial program 76.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. times-frac N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   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 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 100.0

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

   7. Applied rewrites 100.0%

      \[\leadsto \frac{x}{1 + x} + \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 94.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{y}{1 + x} \cdot \frac{z}{t\_1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + x} + \frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (* (/ y (+ 1.0 x)) (/ z t_1)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -1e-11)
     t_2
     (if (<= t_3 2e-37)
       (/ (+ x (/ y t)) 1.0)
       (if (<= t_3 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_3 INFINITY)
           t_2
           (+ (/ x (+ 1.0 x)) (/ y (* t (+ 1.0 x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y / (1.0 + x)) * (z / t_1);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -1e-11) {
		tmp = t_2;
	} else if (t_3 <= 2e-37) {
		tmp = (x + (y / t)) / 1.0;
	} 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 / (1.0 + x)) + (y / (t * (1.0 + x)));
	}
	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 / (1.0 + x)) * (z / t_1);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -1e-11) {
		tmp = t_2;
	} else if (t_3 <= 2e-37) {
		tmp = (x + (y / t)) / 1.0;
	} 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 / (1.0 + x)) + (y / (t * (1.0 + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (y / (1.0 + x)) * (z / t_1)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -1e-11:
		tmp = t_2
	elif t_3 <= 2e-37:
		tmp = (x + (y / t)) / 1.0
	elif t_3 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(y / Float64(1.0 + x)) * Float64(z / t_1))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -1e-11)
		tmp = t_2;
	elseif (t_3 <= 2e-37)
		tmp = Float64(Float64(x + Float64(y / t)) / 1.0);
	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(1.0 + x)) + Float64(y / Float64(t * Float64(1.0 + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (y / (1.0 + x)) * (z / t_1);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -1e-11)
		tmp = t_2;
	elseif (t_3 <= 2e-37)
		tmp = (x + (y / t)) / 1.0;
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	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[(1.0 + x), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $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, -1e-11], t$95$2, If[LessEqual[t$95$3, 2e-37], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / 1.0), $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[(1.0 + x), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $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))) < -9.99999999999999939e-12 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 80.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. times-frac N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -9.99999999999999939e-12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000013e-37

   1. Initial program 92.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 88.6

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

   5. Applied rewrites 88.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 88.6%

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

   if 2.00000000000000013e-37 < (/.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. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x - \frac{x}{t \cdot z - x}}}{x + 1} \]
   4. 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

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

      4. lift--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   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 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 100.0

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

   7. Applied rewrites 100.0%

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

Alternative 4: 87.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t\_1}}{1}\\ \mathbf{elif}\;t\_2 \leq 0.9999999999999999 \lor \neg \left(t\_2 \leq 1.000000001\right):\\ \;\;\;\;\frac{x}{1 + x} + \frac{y}{t \cdot \left(1 + x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -1e-11)
     (/ (* y (/ z t_1)) 1.0)
     (if (or (<= t_2 0.9999999999999999) (not (<= t_2 1.000000001)))
       (+ (/ x (+ 1.0 x)) (/ y (* t (+ 1.0 x))))
       1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e-11) {
		tmp = (y * (z / t_1)) / 1.0;
	} else if ((t_2 <= 0.9999999999999999) || !(t_2 <= 1.000000001)) {
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (t * z) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-1d-11)) then
        tmp = (y * (z / t_1)) / 1.0d0
    else if ((t_2 <= 0.9999999999999999d0) .or. (.not. (t_2 <= 1.000000001d0))) then
        tmp = (x / (1.0d0 + x)) + (y / (t * (1.0d0 + x)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e-11) {
		tmp = (y * (z / t_1)) / 1.0;
	} else if ((t_2 <= 0.9999999999999999) || !(t_2 <= 1.000000001)) {
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e-11:
		tmp = (y * (z / t_1)) / 1.0
	elif (t_2 <= 0.9999999999999999) or not (t_2 <= 1.000000001):
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e-11)
		tmp = Float64(Float64(y * Float64(z / t_1)) / 1.0);
	elseif ((t_2 <= 0.9999999999999999) || !(t_2 <= 1.000000001))
		tmp = Float64(Float64(x / Float64(1.0 + x)) + Float64(y / Float64(t * Float64(1.0 + x))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e-11)
		tmp = (y * (z / t_1)) / 1.0;
	elseif ((t_2 <= 0.9999999999999999) || ~((t_2 <= 1.000000001)))
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	else
		tmp = 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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-11], N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[Or[LessEqual[t$95$2, 0.9999999999999999], N[Not[LessEqual[t$95$2, 1.000000001]], $MachinePrecision]], N[(N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

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))) < -9.99999999999999939e-12

   1. Initial program 85.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{t \cdot z - x}}}{x + 1} \]
   4. 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

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

      5. lift--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 81.9%

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

   if -9.99999999999999939e-12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999999999889 or 1.0000000010000001 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 81.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 79.2

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

   7. Applied rewrites 79.2%

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

   if 0.999999999999999889 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.0000000010000001

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t \cdot z - x}}{1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 0.9999999999999999 \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 1.000000001\right):\\ \;\;\;\;\frac{x}{1 + x} + \frac{y}{t \cdot \left(1 + x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t\_1}}{1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1}\\ \mathbf{elif}\;t\_2 \leq 1.002:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + x} + \frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -1e-11)
     (/ (* y (/ z t_1)) 1.0)
     (if (<= t_2 2e-37)
       (/ (+ x (/ y t)) 1.0)
       (if (<= t_2 1.002)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (+ (/ x (+ 1.0 x)) (/ y (* t (+ 1.0 x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e-11) {
		tmp = (y * (z / t_1)) / 1.0;
	} else if (t_2 <= 2e-37) {
		tmp = (x + (y / t)) / 1.0;
	} else if (t_2 <= 1.002) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else {
		tmp = (x / (1.0 + x)) + (y / (t * (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) :: t_2
    real(8) :: tmp
    t_1 = (t * z) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-1d-11)) then
        tmp = (y * (z / t_1)) / 1.0d0
    else if (t_2 <= 2d-37) then
        tmp = (x + (y / t)) / 1.0d0
    else if (t_2 <= 1.002d0) then
        tmp = (x - (x / t_1)) / (x + 1.0d0)
    else
        tmp = (x / (1.0d0 + x)) + (y / (t * (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 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e-11) {
		tmp = (y * (z / t_1)) / 1.0;
	} else if (t_2 <= 2e-37) {
		tmp = (x + (y / t)) / 1.0;
	} else if (t_2 <= 1.002) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else {
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e-11:
		tmp = (y * (z / t_1)) / 1.0
	elif t_2 <= 2e-37:
		tmp = (x + (y / t)) / 1.0
	elif t_2 <= 1.002:
		tmp = (x - (x / t_1)) / (x + 1.0)
	else:
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e-11)
		tmp = Float64(Float64(y * Float64(z / t_1)) / 1.0);
	elseif (t_2 <= 2e-37)
		tmp = Float64(Float64(x + Float64(y / t)) / 1.0);
	elseif (t_2 <= 1.002)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(1.0 + x)) + Float64(y / Float64(t * Float64(1.0 + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e-11)
		tmp = (y * (z / t_1)) / 1.0;
	elseif (t_2 <= 2e-37)
		tmp = (x + (y / t)) / 1.0;
	elseif (t_2 <= 1.002)
		tmp = (x - (x / t_1)) / (x + 1.0);
	else
		tmp = (x / (1.0 + x)) + (y / (t * (1.0 + x)));
	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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-11], N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$2, 2e-37], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$2, 1.002], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $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))) < -9.99999999999999939e-12

   1. Initial program 85.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{t \cdot z - x}}}{x + 1} \]
   4. 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

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

      5. lift--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 81.9%

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

   if -9.99999999999999939e-12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000013e-37

   1. Initial program 92.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 88.6

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

   5. Applied rewrites 88.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 88.6%

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

   if 2.00000000000000013e-37 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.002

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x - \frac{x}{t \cdot z - x}}}{x + 1} \]
   4. 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

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

      4. lift--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if 1.002 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 63.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 63.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 68.3

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

   7. Applied rewrites 68.3%

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

Alternative 6: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t\_1}}{1}\\ \mathbf{elif}\;t\_2 \leq 0.9999999999999999 \lor \neg \left(t\_2 \leq 1.000000001\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -1e-11)
     (/ (* y (/ z t_1)) 1.0)
     (if (or (<= t_2 0.9999999999999999) (not (<= t_2 1.000000001)))
       (/ (+ x (/ y t)) (+ x 1.0))
       1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e-11) {
		tmp = (y * (z / t_1)) / 1.0;
	} else if ((t_2 <= 0.9999999999999999) || !(t_2 <= 1.000000001)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (t * z) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-1d-11)) then
        tmp = (y * (z / t_1)) / 1.0d0
    else if ((t_2 <= 0.9999999999999999d0) .or. (.not. (t_2 <= 1.000000001d0))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e-11) {
		tmp = (y * (z / t_1)) / 1.0;
	} else if ((t_2 <= 0.9999999999999999) || !(t_2 <= 1.000000001)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e-11:
		tmp = (y * (z / t_1)) / 1.0
	elif (t_2 <= 0.9999999999999999) or not (t_2 <= 1.000000001):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e-11)
		tmp = Float64(Float64(y * Float64(z / t_1)) / 1.0);
	elseif ((t_2 <= 0.9999999999999999) || !(t_2 <= 1.000000001))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e-11)
		tmp = (y * (z / t_1)) / 1.0;
	elseif ((t_2 <= 0.9999999999999999) || ~((t_2 <= 1.000000001)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-11], N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[Or[LessEqual[t$95$2, 0.9999999999999999], N[Not[LessEqual[t$95$2, 1.000000001]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]]

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))) < -9.99999999999999939e-12

   1. Initial program 85.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{\frac{y \cdot z}{t \cdot z - x}}}{x + 1} \]
   4. 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

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

      5. lift--.f64 86.5

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 81.9%

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

   if -9.99999999999999939e-12 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999999999889 or 1.0000000010000001 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 81.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 79.2

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

   5. Applied rewrites 79.2%

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

   if 0.999999999999999889 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.0000000010000001

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\frac{y \cdot \frac{z}{t \cdot z - x}}{1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 0.9999999999999999 \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 1.000000001\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999999999:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

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-51)
     (/ y t)
     (if (<= t_1 0.9999999999999999)
       (/ x (+ x 1.0))
       (if (<= t_1 1.0) 1.0 (+ 1.0 (/ y (* t (+ 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-51) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999999999) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (y / (t * (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-51)) then
        tmp = y / t
    else if (t_1 <= 0.9999999999999999d0) then
        tmp = x / (x + 1.0d0)
    else if (t_1 <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + (y / (t * (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-51) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999999999) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (y / (t * (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-51:
		tmp = y / t
	elif t_1 <= 0.9999999999999999:
		tmp = x / (x + 1.0)
	elif t_1 <= 1.0:
		tmp = 1.0
	else:
		tmp = 1.0 + (y / (t * (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-51)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999999999999)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_1 <= 1.0)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + Float64(y / Float64(t * 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-51)
		tmp = y / t;
	elseif (t_1 <= 0.9999999999999999)
		tmp = x / (x + 1.0);
	elseif (t_1 <= 1.0)
		tmp = 1.0;
	else
		tmp = 1.0 + (y / (t * (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-51], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999999999], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.0], 1.0, N[(1.0 + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $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))) < -5.00000000000000004e-51

   1. Initial program 89.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 50.7

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

   5. Applied rewrites 50.7%

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

   if -5.00000000000000004e-51 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999999999889

   1. Initial program 92.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 56.6%

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

   if 0.999999999999999889 < (/.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 100.0%

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

   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 65.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 65.9%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 59.0%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 15.9%

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

   11. Taylor expanded in z around inf

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-+.f64 60.9

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

   13. Applied rewrites 60.9%

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

Alternative 8: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-51}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999999999:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 1000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -5e-51)
     (/ y t)
     (if (<= t_1 0.9999999999999999)
       (/ x (+ x 1.0))
       (if (<= t_1 1000.0) 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 <= -5e-51) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999999999) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 1000.0) {
		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 <= (-5d-51)) then
        tmp = y / t
    else if (t_1 <= 0.9999999999999999d0) then
        tmp = x / (x + 1.0d0)
    else if (t_1 <= 1000.0d0) 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 <= -5e-51) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999999999999) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 1000.0) {
		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 <= -5e-51:
		tmp = y / t
	elif t_1 <= 0.9999999999999999:
		tmp = x / (x + 1.0)
	elif t_1 <= 1000.0:
		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 <= -5e-51)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999999999999)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_1 <= 1000.0)
		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 <= -5e-51)
		tmp = y / t;
	elseif (t_1 <= 0.9999999999999999)
		tmp = x / (x + 1.0);
	elseif (t_1 <= 1000.0)
		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, -5e-51], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999999999], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000.0], 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))) < -5.00000000000000004e-51 or 1e3 < (/.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. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 52.6

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

   5. Applied rewrites 52.6%

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

   if -5.00000000000000004e-51 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999999999999889

   1. Initial program 92.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 56.6%

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

   if 0.999999999999999889 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1e3

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 97.8%

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

Alternative 9: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 0.9999999999999999 \lor \neg \left(t\_1 \leq 1.000000001\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (or (<= t_1 0.9999999999999999) (not (<= t_1 1.000000001)))
     (/ (+ x (/ y t)) (+ x 1.0))
     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 <= 0.9999999999999999) || !(t_1 <= 1.000000001)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 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 <= 0.9999999999999999d0) .or. (.not. (t_1 <= 1.000000001d0))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 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 <= 0.9999999999999999) || !(t_1 <= 1.000000001)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 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 <= 0.9999999999999999) or not (t_1 <= 1.000000001):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 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 <= 0.9999999999999999) || !(t_1 <= 1.000000001))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 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 <= 0.9999999999999999) || ~((t_1 <= 1.000000001)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 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[Or[LessEqual[t$95$1, 0.9999999999999999], N[Not[LessEqual[t$95$1, 1.000000001]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

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))) < 0.999999999999999889 or 1.0000000010000001 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 82.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 72.6

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

   5. Applied rewrites 72.6%

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

   if 0.999999999999999889 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.0000000010000001

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.8%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 0.9999999999999999 \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 1.000000001\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t \cdot \left(1 + x\right)}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq 0.0002:\\ \;\;\;\;x + t\_1\\ \mathbf{elif}\;t\_2 \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* t (+ 1.0 x))))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 0.0002) (+ 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 * (1.0 + x));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 0.0002) {
		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 * (1.0d0 + x))
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= 0.0002d0) 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 * (1.0 + x));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 0.0002) {
		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 * (1.0 + x))
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= 0.0002:
		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(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 <= 0.0002)
		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 * (1.0 + x));
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 0.0002)
		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[(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, 0.0002], 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))) < 2.0000000000000001e-4

   1. Initial program 90.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 90.7%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 74.8

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

   7. Applied rewrites 74.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 74.1%

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

   if 2.0000000000000001e-4 < (/.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 100.0%

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

   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 65.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 65.9%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 59.0%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 15.9%

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

   11. Taylor expanded in z around inf

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-+.f64 60.9

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

   13. Applied rewrites 60.9%

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

Alternative 11: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-37} \lor \neg \left(t\_1 \leq 1000\right):\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (or (<= t_1 2e-37) (not (<= t_1 1000.0))) (/ y t) 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 <= 2e-37) || !(t_1 <= 1000.0)) {
		tmp = y / t;
	} else {
		tmp = 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 <= 2d-37) .or. (.not. (t_1 <= 1000.0d0))) then
        tmp = y / t
    else
        tmp = 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 <= 2e-37) || !(t_1 <= 1000.0)) {
		tmp = y / t;
	} else {
		tmp = 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 <= 2e-37) or not (t_1 <= 1000.0):
		tmp = y / t
	else:
		tmp = 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 <= 2e-37) || !(t_1 <= 1000.0))
		tmp = Float64(y / t);
	else
		tmp = 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 <= 2e-37) || ~((t_1 <= 1000.0)))
		tmp = y / t;
	else
		tmp = 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[Or[LessEqual[t$95$1, 2e-37], N[Not[LessEqual[t$95$1, 1000.0]], $MachinePrecision]], N[(y / t), $MachinePrecision], 1.0]]

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))) < 2.00000000000000013e-37 or 1e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 81.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 47.4

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

   5. Applied rewrites 47.4%

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

   if 2.00000000000000013e-37 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1e3

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 95.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-37} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 1000\right):\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + x}\\ t_2 := t \cdot z - x\\ \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1} \leq 2 \cdot 10^{+235}:\\ \;\;\;\;t\_1 + \frac{\frac{z \cdot y - x}{t\_2}}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 x))) (t_2 (- (* t z) x)))
   (if (<= (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0)) 2e+235)
     (+ t_1 (/ (/ (- (* z y) x) t_2) (+ 1.0 x)))
     (+ t_1 (/ y (* t (+ 1.0 x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (1.0 + x);
	double t_2 = (t * z) - x;
	double tmp;
	if (((x + (((y * z) - x) / t_2)) / (x + 1.0)) <= 2e+235) {
		tmp = t_1 + ((((z * y) - x) / t_2) / (1.0 + x));
	} else {
		tmp = t_1 + (y / (t * (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) :: t_2
    real(8) :: tmp
    t_1 = x / (1.0d0 + x)
    t_2 = (t * z) - x
    if (((x + (((y * z) - x) / t_2)) / (x + 1.0d0)) <= 2d+235) then
        tmp = t_1 + ((((z * y) - x) / t_2) / (1.0d0 + x))
    else
        tmp = t_1 + (y / (t * (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 / (1.0 + x);
	double t_2 = (t * z) - x;
	double tmp;
	if (((x + (((y * z) - x) / t_2)) / (x + 1.0)) <= 2e+235) {
		tmp = t_1 + ((((z * y) - x) / t_2) / (1.0 + x));
	} else {
		tmp = t_1 + (y / (t * (1.0 + x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (1.0 + x)
	t_2 = (t * z) - x
	tmp = 0
	if ((x + (((y * z) - x) / t_2)) / (x + 1.0)) <= 2e+235:
		tmp = t_1 + ((((z * y) - x) / t_2) / (1.0 + x))
	else:
		tmp = t_1 + (y / (t * (1.0 + x)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(1.0 + x))
	t_2 = Float64(Float64(t * z) - x)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0)) <= 2e+235)
		tmp = Float64(t_1 + Float64(Float64(Float64(Float64(z * y) - x) / t_2) / Float64(1.0 + x)));
	else
		tmp = Float64(t_1 + Float64(y / Float64(t * Float64(1.0 + x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (1.0 + x);
	t_2 = (t * z) - x;
	tmp = 0.0;
	if (((x + (((y * z) - x) / t_2)) / (x + 1.0)) <= 2e+235)
		tmp = t_1 + ((((z * y) - x) / t_2) / (1.0 + x));
	else
		tmp = t_1 + (y / (t * (1.0 + x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 2e+235], N[(t$95$1 + N[(N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $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))) < 2.0000000000000001e235

   1. Initial program 96.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 96.6%

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

   if 2.0000000000000001e235 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 33.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 33.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 73.8

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

   7. Applied rewrites 73.8%

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

Alternative 13: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+235}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + x} + \frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 2e+235) t_1 (+ (/ x (+ 1.0 x)) (/ y (* t (+ 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 <= 2e+235) {
		tmp = t_1;
	} else {
		tmp = (x / (1.0 + x)) + (y / (t * (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 <= 2d+235) then
        tmp = t_1
    else
        tmp = (x / (1.0d0 + x)) + (y / (t * (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 <= 2e+235) {
		tmp = t_1;
	} else {
		tmp = (x / (1.0 + x)) + (y / (t * (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 <= 2e+235:
		tmp = t_1
	else:
		tmp = (x / (1.0 + x)) + (y / (t * (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 <= 2e+235)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(1.0 + x)) + Float64(y / Float64(t * 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 <= 2e+235)
		tmp = t_1;
	else
		tmp = (x / (1.0 + x)) + (y / (t * (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, 2e+235], t$95$1, N[(N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $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))) < 2.0000000000000001e235

   1. Initial program 96.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 2.0000000000000001e235 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 33.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. div-add N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-+.f64 N/A

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

      14. +-commutative N/A

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

      15. lower-/.f64 N/A

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

   4. Applied rewrites 33.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 73.8

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

   7. Applied rewrites 73.8%

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

Alternative 14: 53.6% accurate, 45.0× 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 91.2%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Applied rewrites 55.2%

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

Developer Target 1: 99.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025080 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))