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

Percentage Accurate: 89.3% → 97.4%

Time: 8.5s

Alternatives: 11

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{\frac{z}{1 + x}}{t\_1} \cdot y\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -500000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (* (/ (/ z (+ 1.0 x)) t_1) y))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -500000000.0)
     t_2
     (if (<= t_3 5e-20)
       (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
       (if (<= t_3 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_3 INFINITY) t_2 (/ (+ (/ y t) x) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = ((z / (1.0 + x)) / t_1) * y;
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -500000000.0) {
		tmp = t_2;
	} else if (t_3 <= 5e-20) {
		tmp = (x - (((x / z) - y) / t)) / (x + 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 = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = ((z / (1.0 + x)) / t_1) * y;
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -500000000.0) {
		tmp = t_2;
	} else if (t_3 <= 5e-20) {
		tmp = (x - (((x / z) - y) / t)) / (x + 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 = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = ((z / (1.0 + x)) / t_1) * y
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -500000000.0:
		tmp = t_2
	elif t_3 <= 5e-20:
		tmp = (x - (((x / z) - y) / t)) / (x + 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 = ((y / t) + x) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(Float64(z / Float64(1.0 + x)) / t_1) * y)
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -500000000.0)
		tmp = t_2;
	elseif (t_3 <= 5e-20)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 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(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = ((z / (1.0 + x)) / t_1) * y;
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -500000000.0)
		tmp = t_2;
	elseif (t_3 <= 5e-20)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = ((y / t) + x) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] * y), $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, -500000000.0], t$95$2, If[LessEqual[t$95$3, 5e-20], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e8 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 83.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 93.6%

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

   if -5e8 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999999e-20

   1. Initial program 98.4%

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

   3. Taylor expanded in t around -inf

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. fp-cancel-sub-sign-inv N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. lower-/.f64 N/A

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

      9. +-commutative N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if 4.9999999999999999e-20 < (/.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

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 99.5

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

   5. Applied rewrites 99.5%

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

   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. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 2: 94.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{\frac{z}{1 + x}}{t\_2} \cdot y\\ t_4 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -500000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (* (/ (/ z (+ 1.0 x)) t_2) y))
        (t_4 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_4 -500000000.0)
     t_3
     (if (<= t_4 1e-46)
       t_1
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ x 1.0))
         (if (<= t_4 INFINITY) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = ((z / (1.0 + x)) / t_2) * y;
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -500000000.0) {
		tmp = t_3;
	} else if (t_4 <= 1e-46) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = ((z / (1.0 + x)) / t_2) * y;
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -500000000.0) {
		tmp = t_3;
	} else if (t_4 <= 1e-46) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = ((z / (1.0 + x)) / t_2) * y
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -500000000.0:
		tmp = t_3
	elif t_4 <= 1e-46:
		tmp = t_1
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(Float64(z / Float64(1.0 + x)) / t_2) * y)
	t_4 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -500000000.0)
		tmp = t_3;
	elseif (t_4 <= 1e-46)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) + x) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = ((z / (1.0 + x)) / t_2) * y;
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -500000000.0)
		tmp = t_3;
	elseif (t_4 <= 1e-46)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -500000000.0], t$95$3, If[LessEqual[t$95$4, 1e-46], t$95$1, If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e8 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 83.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 92.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 93.6%

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

   if -5e8 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000002e-46 or +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 85.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 89.4

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

   5. Applied rewrites 89.4%

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

   if 1.00000000000000002e-46 < (/.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

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.8

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

   5. Applied rewrites 98.8%

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

Alternative 3: 73.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999996843258:\\ \;\;\;\;\frac{x}{1 + x}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+64}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{-y}{\mathsf{fma}\left(x, x, x\right)}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2e-91)
     (/ y t)
     (if (<= t_1 0.9999999996843258)
       (/ x (+ 1.0 x))
       (if (<= t_1 4e+64) (fma z (/ (- y) (fma x x x)) 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 <= -2e-91) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999996843258) {
		tmp = x / (1.0 + x);
	} else if (t_1 <= 4e+64) {
		tmp = fma(z, (-y / fma(x, x, x)), 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 <= -2e-91)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999996843258)
		tmp = Float64(x / Float64(1.0 + x));
	elseif (t_1 <= 4e+64)
		tmp = fma(z, Float64(Float64(-y) / fma(x, x, x)), 1.0);
	else
		tmp = Float64(y / t);
	end
	return 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-91], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999996843258], N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+64], N[(z * N[((-y) / N[(x * x + x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], 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))) < -2.00000000000000004e-91 or 4.00000000000000009e64 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 56.9

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

   5. Applied rewrites 56.9%

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

   if -2.00000000000000004e-91 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999999968432585

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if 0.99999999968432585 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.00000000000000009e64

   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 t around 0

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

      1. associate-+r+ N/A

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

      2. div-add N/A

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

      3. *-inverses N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac N/A

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

      6. associate-/r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. *-rgt-identity N/A

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

      20. lower-fma.f64 97.4

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

   5. Applied rewrites 97.4%

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

   7. Applied rewrites 97.4%

      \[\leadsto \mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, \color{blue}{-y}, 1\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 97.4%

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

Alternative 4: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999996843258:\\ \;\;\;\;\frac{x}{1 + x}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2e-91)
     (/ y t)
     (if (<= t_1 0.9999999996843258)
       (/ x (+ 1.0 x))
       (if (<= t_1 4e+64) 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 <= -2e-91) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999996843258) {
		tmp = x / (1.0 + x);
	} else if (t_1 <= 4e+64) {
		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 <= (-2d-91)) then
        tmp = y / t
    else if (t_1 <= 0.9999999996843258d0) then
        tmp = x / (1.0d0 + x)
    else if (t_1 <= 4d+64) 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 <= -2e-91) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999996843258) {
		tmp = x / (1.0 + x);
	} else if (t_1 <= 4e+64) {
		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 <= -2e-91:
		tmp = y / t
	elif t_1 <= 0.9999999996843258:
		tmp = x / (1.0 + x)
	elif t_1 <= 4e+64:
		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 <= -2e-91)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999996843258)
		tmp = Float64(x / Float64(1.0 + x));
	elseif (t_1 <= 4e+64)
		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 <= -2e-91)
		tmp = y / t;
	elseif (t_1 <= 0.9999999996843258)
		tmp = x / (1.0 + x);
	elseif (t_1 <= 4e+64)
		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, -2e-91], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999996843258], N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+64], 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))) < -2.00000000000000004e-91 or 4.00000000000000009e64 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 56.9

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

   5. Applied rewrites 56.9%

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

   if -2.00000000000000004e-91 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999999968432585

   1. Initial program 98.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 62.1

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

   5. Applied rewrites 62.1%

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

   if 0.99999999968432585 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.00000000000000009e64

   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 96.9%

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

Alternative 5: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-91}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(-1, x, 1\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -2e-91)
     (/ y t)
     (if (<= t_1 2e-42)
       (* (fma -1.0 x 1.0) x)
       (if (<= t_1 4e+64) 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 <= -2e-91) {
		tmp = y / t;
	} else if (t_1 <= 2e-42) {
		tmp = fma(-1.0, x, 1.0) * x;
	} else if (t_1 <= 4e+64) {
		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 <= -2e-91)
		tmp = Float64(y / t);
	elseif (t_1 <= 2e-42)
		tmp = Float64(fma(-1.0, x, 1.0) * x);
	elseif (t_1 <= 4e+64)
		tmp = 1.0;
	else
		tmp = Float64(y / t);
	end
	return 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-91], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 2e-42], N[(N[(-1.0 * x + 1.0), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 4e+64], 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))) < -2.00000000000000004e-91 or 4.00000000000000009e64 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 56.9

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

   5. Applied rewrites 56.9%

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

   if -2.00000000000000004e-91 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2.00000000000000008e-42

   1. Initial program 97.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 65.3

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

   5. Applied rewrites 65.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.3%

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

   if 2.00000000000000008e-42 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.00000000000000009e64

   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 94.8%

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

Alternative 6: 78.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-20} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{-y}{\mathsf{fma}\left(x, x, x\right)}, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (or (<= t_1 5e-20) (not (<= t_1 4e+64)))
     (/ (+ (/ y t) x) 1.0)
     (fma z (/ (- y) (fma x x x)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= 5e-20) || !(t_1 <= 4e+64)) {
		tmp = ((y / t) + x) / 1.0;
	} else {
		tmp = fma(z, (-y / fma(x, x, x)), 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if ((t_1 <= 5e-20) || !(t_1 <= 4e+64))
		tmp = Float64(Float64(Float64(y / t) + x) / 1.0);
	else
		tmp = fma(z, Float64(Float64(-y) / fma(x, x, x)), 1.0);
	end
	return 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, 5e-20], N[Not[LessEqual[t$95$1, 4e+64]], $MachinePrecision]], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / 1.0), $MachinePrecision], N[(z * N[((-y) / N[(x * x + x), $MachinePrecision]), $MachinePrecision] + 1.0), $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))) < 4.9999999999999999e-20 or 4.00000000000000009e64 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 84.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 78.0

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

   5. Applied rewrites 78.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 73.8%

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

   if 4.9999999999999999e-20 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.00000000000000009e64

   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 t around 0

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

      1. associate-+r+ N/A

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

      2. div-add N/A

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

      3. *-inverses N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac N/A

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

      6. associate-/r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. *-rgt-identity N/A

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

      20. lower-fma.f64 96.5

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

   5. Applied rewrites 96.5%

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

   7. Applied rewrites 96.5%

      \[\leadsto \mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, \color{blue}{-y}, 1\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 96.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 5 \cdot 10^{-20} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 4 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{-y}{\mathsf{fma}\left(x, x, x\right)}, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+266}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 5e+266) t_1 (/ (+ (/ y t) x) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+266) {
		tmp = t_1;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_1 <= 5d+266) then
        tmp = t_1
    else
        tmp = ((y / t) + x) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+266) {
		tmp = t_1;
	} else {
		tmp = ((y / t) + x) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 5e+266:
		tmp = t_1
	else:
		tmp = ((y / t) + x) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 5e+266)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 5e+266)
		tmp = t_1;
	else
		tmp = ((y / t) + x) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+266], t$95$1, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $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))) < 4.9999999999999999e266

   1. Initial program 98.3%

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

   if 4.9999999999999999e266 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 26.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

Alternative 8: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \leq 2 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(-1, x, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) 2e-42)
   (* (fma -1.0 x 1.0) x)
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)) <= 2e-42) {
		tmp = fma(-1.0, x, 1.0) * x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0)) <= 2e-42)
		tmp = Float64(fma(-1.0, x, 1.0) * x);
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[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], 2e-42], N[(N[(-1.0 * x + 1.0), $MachinePrecision] * x), $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))) < 2.00000000000000008e-42

   1. Initial program 95.5%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 38.3

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

   5. Applied rewrites 38.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 37.4%

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

   if 2.00000000000000008e-42 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   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 78.9%

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

Alternative 9: 83.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-17} \lor \neg \left(t \leq 2.45 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{z}{1 + x}}{x}, -y, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-17) (not (<= t 2.45e-51)))
   (/ (+ (/ y t) x) (+ x 1.0))
   (fma (/ (/ z (+ 1.0 x)) x) (- y) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-17) || !(t <= 2.45e-51)) {
		tmp = ((y / t) + x) / (x + 1.0);
	} else {
		tmp = fma(((z / (1.0 + x)) / x), -y, 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e-17) || !(t <= 2.45e-51))
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	else
		tmp = fma(Float64(Float64(z / Float64(1.0 + x)) / x), Float64(-y), 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e-17], N[Not[LessEqual[t, 2.45e-51]], $MachinePrecision]], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] * (-y) + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000002e-17 or 2.44999999999999987e-51 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 91.5

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

   5. Applied rewrites 91.5%

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

   if -3.2000000000000002e-17 < t < 2.44999999999999987e-51

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. div-add N/A

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

      3. *-inverses N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac N/A

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

      6. associate-/r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. *-rgt-identity N/A

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

      20. lower-fma.f64 85.5

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

   5. Applied rewrites 85.5%

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

   7. Applied rewrites 85.5%

      \[\leadsto \mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, \color{blue}{-y}, 1\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 87.0%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-17} \lor \neg \left(t \leq 2.45 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{z}{1 + x}}{x}, -y, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-17} \lor \neg \left(t \leq 2.2 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-17) (not (<= t 2.2e-51)))
   (/ (+ (/ y t) x) (+ x 1.0))
   (fma (/ z (fma x x x)) (- y) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-17) || !(t <= 2.2e-51)) {
		tmp = ((y / t) + x) / (x + 1.0);
	} else {
		tmp = fma((z / fma(x, x, x)), -y, 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e-17) || !(t <= 2.2e-51))
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(x + 1.0));
	else
		tmp = fma(Float64(z / fma(x, x, x)), Float64(-y), 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e-17], N[Not[LessEqual[t, 2.2e-51]], $MachinePrecision]], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(x * x + x), $MachinePrecision]), $MachinePrecision] * (-y) + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000002e-17 or 2.2e-51 < t

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 91.5

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

   5. Applied rewrites 91.5%

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

   if -3.2000000000000002e-17 < t < 2.2e-51

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0

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

      1. associate-+r+ N/A

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

      2. div-add N/A

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

      3. *-inverses N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-frac N/A

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

      6. associate-/r* N/A

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

      7. mul-1-neg N/A

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

      8. lower-+.f64 N/A

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

      9. mul-1-neg N/A

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

      10. associate-/l* N/A

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

      11. distribute-lft-neg-in N/A

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

      12. mul-1-neg N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. +-commutative N/A

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

      18. distribute-lft-in N/A

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

      19. *-rgt-identity N/A

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

      20. lower-fma.f64 85.5

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

   5. Applied rewrites 85.5%

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

   7. Applied rewrites 85.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-17} \lor \neg \left(t \leq 2.2 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{\frac{y}{t} + x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\mathsf{fma}\left(x, x, x\right)}, -y, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.2% 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 92.7%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 53.1%

   \[\leadsto \color{blue}{1} \]
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 2024360 
(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)))