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

Percentage Accurate: 89.8% → 97.1%

Time: 4.0s

Alternatives: 18

Speedup: 0.3×

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: 89.8% 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: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;1 + \frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{x + \frac{\mathsf{fma}\left(z, y, -x\right)}{t\_1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-\frac{\left(-y\right) - \frac{-x}{z}}{t}\right) + x}{x + 1}\\ \end{array} \end{array} \]

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 (- INFINITY))
     (+ 1.0 (/ (/ y t) (+ x 1.0)))
     (if (<= t_2 5e+278)
       (/ (+ x (/ (fma z y (- x)) t_1)) (+ x 1.0))
       (/ (+ (- (/ (- (- y) (/ (- x) z)) 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 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_2 <= 5e+278) {
		tmp = (x + (fma(z, y, -x) / t_1)) / (x + 1.0);
	} else {
		tmp = (-((-y - (-x / z)) / 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(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(1.0 + Float64(Float64(y / t) / Float64(x + 1.0)));
	elseif (t_2 <= 5e+278)
		tmp = Float64(Float64(x + Float64(fma(z, y, Float64(-x)) / t_1)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(-Float64(Float64(Float64(-y) - Float64(Float64(-x) / z)) / t)) + x) / Float64(x + 1.0));
	end
	return 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, (-Infinity)], N[(1.0 + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+278], N[(N[(x + N[(N[(z * y + (-x)), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[((-N[(N[((-y) - N[((-x) / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 45.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 75.7

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

   4. Applied rewrites 75.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 75.7

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

   6. Applied rewrites 75.7%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 75.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000029e278

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 99.0

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

   4. Applied rewrites 99.0%

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

   if 5.00000000000000029e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 27.0%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r/ N/A

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

      10. mul-1-neg N/A

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

      11. lower-/.f64 N/A

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

      12. lower-neg.f64 84.7

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

   4. Applied rewrites 84.7%

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

Alternative 2: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;1 + \frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-\frac{\left(-y\right) - \frac{-x}{z}}{t}\right) + x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 (- INFINITY))
     (+ 1.0 (/ (/ y t) (+ x 1.0)))
     (if (<= t_1 5e+278)
       t_1
       (/ (+ (- (/ (- (- y) (/ (- x) z)) 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 <= -((double) INFINITY)) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_1 <= 5e+278) {
		tmp = t_1;
	} else {
		tmp = (-((-y - (-x / z)) / t) + x) / (x + 1.0);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_1 <= 5e+278) {
		tmp = t_1;
	} else {
		tmp = (-((-y - (-x / z)) / 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 <= -math.inf:
		tmp = 1.0 + ((y / t) / (x + 1.0))
	elif t_1 <= 5e+278:
		tmp = t_1
	else:
		tmp = (-((-y - (-x / z)) / 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 <= Float64(-Inf))
		tmp = Float64(1.0 + Float64(Float64(y / t) / Float64(x + 1.0)));
	elseif (t_1 <= 5e+278)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-Float64(Float64(Float64(-y) - Float64(Float64(-x) / z)) / 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 <= -Inf)
		tmp = 1.0 + ((y / t) / (x + 1.0));
	elseif (t_1 <= 5e+278)
		tmp = t_1;
	else
		tmp = (-((-y - (-x / z)) / 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, (-Infinity)], N[(1.0 + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+278], t$95$1, N[(N[((-N[(N[((-y) - N[((-x) / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 45.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 75.7

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

   4. Applied rewrites 75.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 75.7

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

   6. Applied rewrites 75.7%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 75.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000029e278

   1. Initial program 99.0%

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

   if 5.00000000000000029e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 27.0%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r/ N/A

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

      10. mul-1-neg N/A

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

      11. lower-/.f64 N/A

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

      12. lower-neg.f64 84.7

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

   4. Applied rewrites 84.7%

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

Alternative 3: 96.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{y \cdot \frac{z}{t\_1}}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -5000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0.995:\\ \;\;\;\;\frac{\left(-\frac{\left(-y\right) - \frac{-x}{z}}{t}\right) + x}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (/ (* y (/ z t_1)) (+ x 1.0)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -5000.0)
     t_2
     (if (<= t_3 0.995)
       (/ (+ (- (/ (- (- y) (/ (- x) z)) t)) x) (+ x 1.0))
       (if (<= t_3 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_3 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5000.0) {
		tmp = t_2;
	} else if (t_3 <= 0.995) {
		tmp = (-((-y - (-x / z)) / t) + x) / (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 = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5000.0) {
		tmp = t_2;
	} else if (t_3 <= 0.995) {
		tmp = (-((-y - (-x / z)) / t) + x) / (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 = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (y * (z / t_1)) / (x + 1.0)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -5000.0:
		tmp = t_2
	elif t_3 <= 0.995:
		tmp = (-((-y - (-x / z)) / t) + x) / (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 = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(y * Float64(z / t_1)) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -5000.0)
		tmp = t_2;
	elseif (t_3 <= 0.995)
		tmp = Float64(Float64(Float64(-Float64(Float64(Float64(-y) - Float64(Float64(-x) / z)) / t)) + x) / 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(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (y * (z / t_1)) / (x + 1.0);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -5000.0)
		tmp = t_2;
	elseif (t_3 <= 0.995)
		tmp = (-((-y - (-x / z)) / t) + x) / (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 = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5000.0], t$95$2, If[LessEqual[t$95$3, 0.995], N[(N[((-N[(N[((-y) - N[((-x) / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $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[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e3 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 79.4%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 91.3

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

   4. Applied rewrites 91.3%

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

   if -5e3 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.994999999999999996

   1. Initial program 96.4%

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

   2. Taylor expanded in t around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r/ N/A

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

      10. mul-1-neg N/A

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

      11. lower-/.f64 N/A

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

      12. lower-neg.f64 98.5

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

   4. Applied rewrites 98.5%

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

   if 0.994999999999999996 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 99.5

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

   4. 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 79.4%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 62.6

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

   4. Applied rewrites 62.6%

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

Alternative 4: 95.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{y \cdot \frac{z}{t\_1}}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0.9:\\ \;\;\;\;\frac{x + \frac{\mathsf{fma}\left(z, y, -x\right)}{t\_1}}{1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (/ (* y (/ z t_1)) (+ x 1.0)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -4e+65)
     t_2
     (if (<= t_3 0.9)
       (/ (+ x (/ (fma z y (- x)) t_1)) 1.0)
       (if (<= t_3 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_3 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -4e+65) {
		tmp = t_2;
	} else if (t_3 <= 0.9) {
		tmp = (x + (fma(z, y, -x) / t_1)) / 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 + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(y * Float64(z / t_1)) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -4e+65)
		tmp = t_2;
	elseif (t_3 <= 0.9)
		tmp = Float64(Float64(x + Float64(fma(z, y, Float64(-x)) / t_1)) / 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(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -4e+65], t$95$2, If[LessEqual[t$95$3, 0.9], N[(N[(x + N[(N[(z * y + (-x)), $MachinePrecision] / t$95$1), $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[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4e65 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 77.2%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 90.9

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

   4. Applied rewrites 90.9%

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

   if -4e65 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.900000000000000022

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 96.7

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

   4. Applied rewrites 96.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 92.7%

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

   if 0.900000000000000022 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 99.4

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

   4. Applied rewrites 99.4%

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

   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 77.2%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 63.6

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

   4. Applied rewrites 63.6%

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

Alternative 5: 95.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{y \cdot \frac{z}{t\_1}}{x + 1}\\ t_3 := x + \frac{y \cdot z - x}{t\_1}\\ t_4 := \frac{t\_3}{x + 1}\\ \mathbf{if}\;t\_4 \leq -4 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 0.9:\\ \;\;\;\;\frac{t\_3}{1}\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (/ (* y (/ z t_1)) (+ x 1.0)))
        (t_3 (+ x (/ (- (* y z) x) t_1)))
        (t_4 (/ t_3 (+ x 1.0))))
   (if (<= t_4 -4e+65)
     t_2
     (if (<= t_4 0.9)
       (/ t_3 1.0)
       (if (<= t_4 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_4 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = x + (((y * z) - x) / t_1);
	double t_4 = t_3 / (x + 1.0);
	double tmp;
	if (t_4 <= -4e+65) {
		tmp = t_2;
	} else if (t_4 <= 0.9) {
		tmp = t_3 / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = x + (((y * z) - x) / t_1);
	double t_4 = t_3 / (x + 1.0);
	double tmp;
	if (t_4 <= -4e+65) {
		tmp = t_2;
	} else if (t_4 <= 0.9) {
		tmp = t_3 / 1.0;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (y * (z / t_1)) / (x + 1.0)
	t_3 = x + (((y * z) - x) / t_1)
	t_4 = t_3 / (x + 1.0)
	tmp = 0
	if t_4 <= -4e+65:
		tmp = t_2
	elif t_4 <= 0.9:
		tmp = t_3 / 1.0
	elif t_4 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(y * Float64(z / t_1)) / Float64(x + 1.0))
	t_3 = Float64(x + Float64(Float64(Float64(y * z) - x) / t_1))
	t_4 = Float64(t_3 / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -4e+65)
		tmp = t_2;
	elseif (t_4 <= 0.9)
		tmp = Float64(t_3 / 1.0);
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (y * (z / t_1)) / (x + 1.0);
	t_3 = x + (((y * z) - x) / t_1);
	t_4 = t_3 / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -4e+65)
		tmp = t_2;
	elseif (t_4 <= 0.9)
		tmp = t_3 / 1.0;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -4e+65], t$95$2, If[LessEqual[t$95$4, 0.9], N[(t$95$3 / 1.0), $MachinePrecision], If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4e65 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 77.2%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 90.9

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

   4. Applied rewrites 90.9%

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

   if -4e65 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.900000000000000022

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 92.7%

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

   if 0.900000000000000022 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 99.4

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

   4. Applied rewrites 99.4%

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

   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 77.2%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 63.6

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

   4. Applied rewrites 63.6%

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

Alternative 6: 92.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ t_3 := \frac{z \cdot y}{\left(1 + x\right) \cdot t\_1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;1 + \frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-8}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0)))
        (t_3 (/ (* z y) (* (+ 1.0 x) t_1))))
   (if (<= t_2 (- INFINITY))
     (+ 1.0 (/ (/ y t) (+ x 1.0)))
     (if (<= t_2 -4e-8)
       t_3
       (if (<= t_2 2.0)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= t_2 5e+278) t_3 (/ (+ x (/ y t)) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double t_3 = (z * y) / ((1.0 + x) * t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_2 <= -4e-8) {
		tmp = t_3;
	} else if (t_2 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_2 <= 5e+278) {
		tmp = t_3;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double t_3 = (z * y) / ((1.0 + x) * t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_2 <= -4e-8) {
		tmp = t_3;
	} else if (t_2 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_2 <= 5e+278) {
		tmp = t_3;
	} else {
		tmp = (x + (y / t)) / (x + 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)
	t_3 = (z * y) / ((1.0 + x) * t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 1.0 + ((y / t) / (x + 1.0))
	elif t_2 <= -4e-8:
		tmp = t_3
	elif t_2 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_2 <= 5e+278:
		tmp = t_3
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	t_3 = Float64(Float64(z * y) / Float64(Float64(1.0 + x) * t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(1.0 + Float64(Float64(y / t) / Float64(x + 1.0)));
	elseif (t_2 <= -4e-8)
		tmp = t_3;
	elseif (t_2 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (t_2 <= 5e+278)
		tmp = t_3;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	t_3 = (z * y) / ((1.0 + x) * t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 1.0 + ((y / t) / (x + 1.0));
	elseif (t_2 <= -4e-8)
		tmp = t_3;
	elseif (t_2 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_2 <= 5e+278)
		tmp = t_3;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(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[(N[(z * y), $MachinePrecision] / N[(N[(1.0 + x), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(1.0 + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -4e-8], t$95$3, 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, 5e+278], t$95$3, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 45.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 75.7

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

   4. Applied rewrites 75.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 75.7

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

   6. Applied rewrites 75.7%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 75.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.0000000000000001e-8 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000029e278

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 96.0

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

   4. Applied rewrites 96.0%

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

   if -4.0000000000000001e-8 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 89.3

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

   4. Applied rewrites 89.3%

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

   if 5.00000000000000029e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 55.8

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

   4. Applied rewrites 55.8%

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

Alternative 7: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ t_4 := \frac{z \cdot y}{\left(1 + x\right) \cdot t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;1 + \frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{-24}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 0.9999984407579054:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0)))
        (t_4 (/ (* z y) (* (+ 1.0 x) t_2))))
   (if (<= t_3 (- INFINITY))
     (+ 1.0 (/ (/ y t) (+ x 1.0)))
     (if (<= t_3 -5e-24)
       t_4
       (if (<= t_3 0.9999984407579054)
         t_1
         (if (<= t_3 2.0) 1.0 (if (<= t_3 5e+278) t_4 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double t_4 = (z * y) / ((1.0 + x) * t_2);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_3 <= -5e-24) {
		tmp = t_4;
	} else if (t_3 <= 0.9999984407579054) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+278) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double t_4 = (z * y) / ((1.0 + x) * t_2);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_3 <= -5e-24) {
		tmp = t_4;
	} else if (t_3 <= 0.9999984407579054) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+278) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	t_4 = (z * y) / ((1.0 + x) * t_2)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = 1.0 + ((y / t) / (x + 1.0))
	elif t_3 <= -5e-24:
		tmp = t_4
	elif t_3 <= 0.9999984407579054:
		tmp = t_1
	elif t_3 <= 2.0:
		tmp = 1.0
	elif t_3 <= 5e+278:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	t_4 = Float64(Float64(z * y) / Float64(Float64(1.0 + x) * t_2))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(1.0 + Float64(Float64(y / t) / Float64(x + 1.0)));
	elseif (t_3 <= -5e-24)
		tmp = t_4;
	elseif (t_3 <= 0.9999984407579054)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+278)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	t_4 = (z * y) / ((1.0 + x) * t_2);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = 1.0 + ((y / t) / (x + 1.0));
	elseif (t_3 <= -5e-24)
		tmp = t_4;
	elseif (t_3 <= 0.9999984407579054)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+278)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z * y), $MachinePrecision] / N[(N[(1.0 + x), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(1.0 + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e-24], t$95$4, If[LessEqual[t$95$3, 0.9999984407579054], t$95$1, If[LessEqual[t$95$3, 2.0], 1.0, If[LessEqual[t$95$3, 5e+278], t$95$4, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 45.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 75.7

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

   4. Applied rewrites 75.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 75.7

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

   6. Applied rewrites 75.7%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 75.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.9999999999999998e-24 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000029e278

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 93.6

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

   4. Applied rewrites 93.6%

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

   if -4.9999999999999998e-24 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999844075790545 or 5.00000000000000029e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 74.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 84.2

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

   4. Applied rewrites 84.2%

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

   if 0.99999844075790545 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 98.7%

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

Alternative 8: 89.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{y \cdot \frac{z}{t\_1}}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (/ (* y (/ z t_1)) (+ x 1.0)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -4e-8)
     t_2
     (if (<= t_3 2.0)
       (/ (- x (/ x t_1)) (+ x 1.0))
       (if (<= t_3 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -4e-8) {
		tmp = t_2;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (y * (z / t_1)) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -4e-8) {
		tmp = t_2;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (y * (z / t_1)) / (x + 1.0)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -4e-8:
		tmp = t_2
	elif t_3 <= 2.0:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(y * Float64(z / t_1)) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -4e-8)
		tmp = t_2;
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (y * (z / t_1)) / (x + 1.0);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -4e-8)
		tmp = t_2;
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -4e-8], t$95$2, If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.0000000000000001e-8 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 79.8%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 90.2

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

   4. Applied rewrites 90.2%

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

   if -4.0000000000000001e-8 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 89.3

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

   4. Applied rewrites 89.3%

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

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

   1. Initial program 79.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 62.7

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

   4. Applied rewrites 62.7%

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

Alternative 9: 89.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ t_4 := \frac{z \cdot y}{1 \cdot t\_2}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;1 + \frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq -4 \cdot 10^{-23}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 0.9999984407579054:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0)))
        (t_4 (/ (* z y) (* 1.0 t_2))))
   (if (<= t_3 (- INFINITY))
     (+ 1.0 (/ (/ y t) (+ x 1.0)))
     (if (<= t_3 -4e-23)
       t_4
       (if (<= t_3 0.9999984407579054)
         t_1
         (if (<= t_3 2.0) 1.0 (if (<= t_3 5e+278) t_4 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double t_4 = (z * y) / (1.0 * t_2);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_3 <= -4e-23) {
		tmp = t_4;
	} else if (t_3 <= 0.9999984407579054) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+278) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double t_4 = (z * y) / (1.0 * t_2);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 + ((y / t) / (x + 1.0));
	} else if (t_3 <= -4e-23) {
		tmp = t_4;
	} else if (t_3 <= 0.9999984407579054) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+278) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	t_4 = (z * y) / (1.0 * t_2)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = 1.0 + ((y / t) / (x + 1.0))
	elif t_3 <= -4e-23:
		tmp = t_4
	elif t_3 <= 0.9999984407579054:
		tmp = t_1
	elif t_3 <= 2.0:
		tmp = 1.0
	elif t_3 <= 5e+278:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	t_4 = Float64(Float64(z * y) / Float64(1.0 * t_2))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(1.0 + Float64(Float64(y / t) / Float64(x + 1.0)));
	elseif (t_3 <= -4e-23)
		tmp = t_4;
	elseif (t_3 <= 0.9999984407579054)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+278)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	t_4 = (z * y) / (1.0 * t_2);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = 1.0 + ((y / t) / (x + 1.0));
	elseif (t_3 <= -4e-23)
		tmp = t_4;
	elseif (t_3 <= 0.9999984407579054)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+278)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z * y), $MachinePrecision] / N[(1.0 * t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(1.0 + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -4e-23], t$95$4, If[LessEqual[t$95$3, 0.9999984407579054], t$95$1, If[LessEqual[t$95$3, 2.0], 1.0, If[LessEqual[t$95$3, 5e+278], t$95$4, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 45.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 75.7

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

   4. Applied rewrites 75.7%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 75.7

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

   6. Applied rewrites 75.7%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 75.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -3.99999999999999984e-23 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000029e278

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 93.8

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

   4. Applied rewrites 93.8%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 81.1%

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

   if -3.99999999999999984e-23 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999844075790545 or 5.00000000000000029e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 74.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 84.3

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

   4. Applied rewrites 84.3%

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

   if 0.99999844075790545 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 98.7%

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

Alternative 10: 89.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := t \cdot z - x\\ t_3 := \frac{y \cdot \frac{z}{t\_2}}{1}\\ t_4 := \frac{x + \frac{y \cdot z - x}{t\_2}}{x + 1}\\ \mathbf{if}\;t\_4 \leq -4 \cdot 10^{-23}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 0.9999984407579054:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (- (* t z) x))
        (t_3 (/ (* y (/ z t_2)) 1.0))
        (t_4 (/ (+ x (/ (- (* y z) x) t_2)) (+ x 1.0))))
   (if (<= t_4 -4e-23)
     t_3
     (if (<= t_4 0.9999984407579054)
       t_1
       (if (<= t_4 2.0) 1.0 (if (<= t_4 5e+278) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (y * (z / t_2)) / 1.0;
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -4e-23) {
		tmp = t_3;
	} else if (t_4 <= 0.9999984407579054) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = 1.0;
	} else if (t_4 <= 5e+278) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = (t * z) - x
    t_3 = (y * (z / t_2)) / 1.0d0
    t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0d0)
    if (t_4 <= (-4d-23)) then
        tmp = t_3
    else if (t_4 <= 0.9999984407579054d0) then
        tmp = t_1
    else if (t_4 <= 2.0d0) then
        tmp = 1.0d0
    else if (t_4 <= 5d+278) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (t * z) - x;
	double t_3 = (y * (z / t_2)) / 1.0;
	double t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -4e-23) {
		tmp = t_3;
	} else if (t_4 <= 0.9999984407579054) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = 1.0;
	} else if (t_4 <= 5e+278) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (t * z) - x
	t_3 = (y * (z / t_2)) / 1.0
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -4e-23:
		tmp = t_3
	elif t_4 <= 0.9999984407579054:
		tmp = t_1
	elif t_4 <= 2.0:
		tmp = 1.0
	elif t_4 <= 5e+278:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(y * Float64(z / t_2)) / 1.0)
	t_4 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -4e-23)
		tmp = t_3;
	elseif (t_4 <= 0.9999984407579054)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = 1.0;
	elseif (t_4 <= 5e+278)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (t * z) - x;
	t_3 = (y * (z / t_2)) / 1.0;
	t_4 = (x + (((y * z) - x) / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -4e-23)
		tmp = t_3;
	elseif (t_4 <= 0.9999984407579054)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = 1.0;
	elseif (t_4 <= 5e+278)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(z / t$95$2), $MachinePrecision]), $MachinePrecision] / 1.0), $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, -4e-23], t$95$3, If[LessEqual[t$95$4, 0.9999984407579054], t$95$1, If[LessEqual[t$95$4, 2.0], 1.0, If[LessEqual[t$95$4, 5e+278], 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))) < -3.99999999999999984e-23 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000029e278

   1. Initial program 87.6%

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

   2. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 90.4

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

   4. Applied rewrites 90.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 77.4%

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

   if -3.99999999999999984e-23 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999844075790545 or 5.00000000000000029e278 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 74.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 84.3

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

   4. Applied rewrites 84.3%

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

   if 0.99999844075790545 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 98.7%

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

Alternative 11: 85.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq 0.9999984407579054:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 0.9999984407579054) t_1 (if (<= t_2 1.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 0.9999984407579054) {
		tmp = t_1;
	} else if (t_2 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= 0.9999984407579054d0) then
        tmp = t_1
    else if (t_2 <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 0.9999984407579054) {
		tmp = t_1;
	} else if (t_2 <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= 0.9999984407579054:
		tmp = t_1
	elif t_2 <= 1.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= 0.9999984407579054)
		tmp = t_1;
	elseif (t_2 <= 1.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 0.9999984407579054)
		tmp = t_1;
	elseif (t_2 <= 1.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.9999984407579054], t$95$1, If[LessEqual[t$95$2, 1.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.99999844075790545 or 1 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 80.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 73.3

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

   4. Applied rewrites 73.3%

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

   if 0.99999844075790545 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 99.6%

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

Alternative 12: 84.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{\frac{y}{t}}{x + 1}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ (/ y t) (+ x 1.0))))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 -1e+73)
     t_1
     (if (<= t_2 2e-6) (/ (+ x (/ y t)) 1.0) (if (<= t_2 2.0) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((y / t) / (x + 1.0));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+73) {
		tmp = t_1;
	} else if (t_2 <= 2e-6) {
		tmp = (x + (y / t)) / 1.0;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 + ((y / t) / (x + 1.0d0))
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= (-1d+73)) then
        tmp = t_1
    else if (t_2 <= 2d-6) then
        tmp = (x + (y / t)) / 1.0d0
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((y / t) / (x + 1.0));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -1e+73) {
		tmp = t_1;
	} else if (t_2 <= 2e-6) {
		tmp = (x + (y / t)) / 1.0;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + ((y / t) / (x + 1.0))
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= -1e+73:
		tmp = t_1
	elif t_2 <= 2e-6:
		tmp = (x + (y / t)) / 1.0
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(y / t) / Float64(x + 1.0)))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -1e+73)
		tmp = t_1;
	elseif (t_2 <= 2e-6)
		tmp = Float64(Float64(x + Float64(y / t)) / 1.0);
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((y / t) / (x + 1.0));
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -1e+73)
		tmp = t_1;
	elseif (t_2 <= 2e-6)
		tmp = (x + (y / t)) / 1.0;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $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, -1e+73], t$95$1, If[LessEqual[t$95$2, 2e-6], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -9.99999999999999983e72 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 66.0%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 68.8

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

   4. Applied rewrites 68.8%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. div-add N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift-+.f64 68.8

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

   6. Applied rewrites 68.8%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 65.1%

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

   if -9.99999999999999983e72 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999991e-6

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 80.3

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

   4. Applied rewrites 80.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 78.6%

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

   if 1.99999999999999991e-6 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 97.9%

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

Alternative 13: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

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-6)
     (/ (+ x (/ y t)) 1.0)
     (if (<= t_1 2.0) 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 <= 2e-6) {
		tmp = (x + (y / t)) / 1.0;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = 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-6) then
        tmp = (x + (y / t)) / 1.0d0
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = 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-6) {
		tmp = (x + (y / t)) / 1.0;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = 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-6:
		tmp = (x + (y / t)) / 1.0
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = 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-6)
		tmp = Float64(Float64(x + Float64(y / t)) / 1.0);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = 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-6)
		tmp = (x + (y / t)) / 1.0;
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = 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-6], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999991e-6

   1. Initial program 89.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 75.4

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

   4. Applied rewrites 75.4%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 71.5%

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

   if 1.99999999999999991e-6 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 97.9%

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

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

   1. Initial program 61.3%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 60.3

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 59.0

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

   7. Applied rewrites 59.0%

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

Alternative 14: 76.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-32}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 0.995:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(1 + x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -4e-32)
     (/ (/ y t) (+ x 1.0))
     (if (<= t_1 0.995)
       (/ x (+ x 1.0))
       (if (<= t_1 2.0) 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 <= -4e-32) {
		tmp = (y / t) / (x + 1.0);
	} else if (t_1 <= 0.995) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = 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 <= (-4d-32)) then
        tmp = (y / t) / (x + 1.0d0)
    else if (t_1 <= 0.995d0) then
        tmp = x / (x + 1.0d0)
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = 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 <= -4e-32) {
		tmp = (y / t) / (x + 1.0);
	} else if (t_1 <= 0.995) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = 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 <= -4e-32:
		tmp = (y / t) / (x + 1.0)
	elif t_1 <= 0.995:
		tmp = x / (x + 1.0)
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = 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 <= -4e-32)
		tmp = Float64(Float64(y / t) / Float64(x + 1.0));
	elseif (t_1 <= 0.995)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = 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 <= -4e-32)
		tmp = (y / t) / (x + 1.0);
	elseif (t_1 <= 0.995)
		tmp = x / (x + 1.0);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = 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, -4e-32], N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.995], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / N[(t * N[(1.0 + x), $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))) < -4.00000000000000022e-32

   1. Initial program 81.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 57.3

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

   4. Applied rewrites 57.3%

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

   if -4.00000000000000022e-32 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.994999999999999996

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.9%

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

   if 0.994999999999999996 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 98.5%

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

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

   1. Initial program 61.3%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 60.3

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

   4. Applied rewrites 60.3%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 59.0

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

   7. Applied rewrites 59.0%

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

Alternative 15: 76.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t \cdot \left(1 + x\right)}\\ t_2 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.995:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* t (+ 1.0 x))))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_2 -4e-32)
     t_1
     (if (<= t_2 0.995) (/ x (+ x 1.0)) (if (<= t_2 2.0) 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 <= -4e-32) {
		tmp = t_1;
	} else if (t_2 <= 0.995) {
		tmp = x / (x + 1.0);
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y / (t * (1.0d0 + x))
    t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    if (t_2 <= (-4d-32)) then
        tmp = t_1
    else if (t_2 <= 0.995d0) then
        tmp = x / (x + 1.0d0)
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (t * (1.0 + x));
	double t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e-32) {
		tmp = t_1;
	} else if (t_2 <= 0.995) {
		tmp = x / (x + 1.0);
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t * (1.0 + x))
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= -4e-32:
		tmp = t_1
	elif t_2 <= 0.995:
		tmp = x / (x + 1.0)
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t * Float64(1.0 + x)))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -4e-32)
		tmp = t_1;
	elseif (t_2 <= 0.995)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t * (1.0 + x));
	t_2 = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -4e-32)
		tmp = t_1;
	elseif (t_2 <= 0.995)
		tmp = x / (x + 1.0);
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-32], t$95$1, If[LessEqual[t$95$2, 0.995], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.00000000000000022e-32 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.0%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 66.8

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

   4. Applied rewrites 66.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lift-+.f64 58.5

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

   7. Applied rewrites 58.5%

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

   if -4.00000000000000022e-32 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.994999999999999996

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.9%

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

   if 0.994999999999999996 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 98.5%

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

Alternative 16: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-32}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.995:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 -4e-32)
     (/ y t)
     (if (<= t_1 0.995) (/ x (+ x 1.0)) (if (<= t_1 2.0) 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 <= -4e-32) {
		tmp = y / t;
	} else if (t_1 <= 0.995) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 2.0) {
		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 <= (-4d-32)) then
        tmp = y / t
    else if (t_1 <= 0.995d0) then
        tmp = x / (x + 1.0d0)
    else if (t_1 <= 2.0d0) 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 <= -4e-32) {
		tmp = y / t;
	} else if (t_1 <= 0.995) {
		tmp = x / (x + 1.0);
	} else if (t_1 <= 2.0) {
		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 <= -4e-32:
		tmp = y / t
	elif t_1 <= 0.995:
		tmp = x / (x + 1.0)
	elif t_1 <= 2.0:
		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 <= -4e-32)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.995)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_1 <= 2.0)
		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 <= -4e-32)
		tmp = y / t;
	elseif (t_1 <= 0.995)
		tmp = x / (x + 1.0);
	elseif (t_1 <= 2.0)
		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, -4e-32], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.995], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 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))) < -4.00000000000000022e-32 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 71.0%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 52.7

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

   4. Applied rewrites 52.7%

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

   if -4.00000000000000022e-32 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.994999999999999996

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.9%

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

   if 0.994999999999999996 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 98.5%

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

Alternative 17: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 10^{-101}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))
   (if (<= t_1 1e-101) (/ y t) (if (<= t_1 2.0) 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 <= 1e-101) {
		tmp = y / t;
	} else if (t_1 <= 2.0) {
		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 <= 1d-101) then
        tmp = y / t
    else if (t_1 <= 2.0d0) 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 <= 1e-101) {
		tmp = y / t;
	} else if (t_1 <= 2.0) {
		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 <= 1e-101:
		tmp = y / t
	elif t_1 <= 2.0:
		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 <= 1e-101)
		tmp = Float64(y / t);
	elseif (t_1 <= 2.0)
		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 <= 1e-101)
		tmp = y / t;
	elseif (t_1 <= 2.0)
		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, 1e-101], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / t), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.00000000000000005e-101 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 78.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 47.7

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

   4. Applied rewrites 47.7%

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

   if 1.00000000000000005e-101 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 89.9%

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

Alternative 18: 52.8% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 52.8%

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

Reproduce

herbie shell --seed 2025120 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))