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

Percentage Accurate: 89.1% → 96.5%

Time: 9.6s

Alternatives: 12

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

real(8) function code(x, y, z, t)
    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: 89.1% 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

real(8) function code(x, y, z, t)
    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: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x - \frac{x - z \cdot y}{t\_1}}{1 + x}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 10^{+233}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)) (t_2 (/ (- x (/ (- x (* z y)) t_1)) (+ 1.0 x))))
   (if (<= t_2 (- INFINITY))
     (* (/ z (+ 1.0 x)) (/ y t_1))
     (if (<= t_2 1e+233) t_2 (/ (+ (/ y t) x) (+ 1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (z / (1.0 + x)) * (y / t_1);
	} else if (t_2 <= 1e+233) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (1.0 + x);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (z / (1.0 + x)) * (y / t_1);
	} else if (t_2 <= 1e+233) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (1.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (x - ((x - (z * y)) / t_1)) / (1.0 + x)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (z / (1.0 + x)) * (y / t_1)
	elif t_2 <= 1e+233:
		tmp = t_2
	else:
		tmp = ((y / t) + x) / (1.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_1)) / Float64(1.0 + x))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(z / Float64(1.0 + x)) * Float64(y / t_1));
	elseif (t_2 <= 1e+233)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(1.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (z / (1.0 + x)) * (y / t_1);
	elseif (t_2 <= 1e+233)
		tmp = t_2;
	else
		tmp = ((y / t) + x) / (1.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+233], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + x), $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 41.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 84.8

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

   5. Applied rewrites 84.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.99999999999999974e232

   1. Initial program 98.5%

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

   if 9.99999999999999974e232 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 44.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 91.6

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

   5. Applied rewrites 91.6%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq -\infty:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t \cdot z - x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{+233}:\\ \;\;\;\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{z}{1 + x} \cdot \frac{y}{t\_1}\\ t_3 := \frac{x - \frac{x - z \cdot y}{t\_1}}{1 + x}\\ \mathbf{if}\;t\_3 \leq -0.1:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-12}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{1 + x}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{1 + x}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (* (/ z (+ 1.0 x)) (/ y t_1)))
        (t_3 (/ (- x (/ (- x (* z y)) t_1)) (+ 1.0 x))))
   (if (<= t_3 -0.1)
     t_2
     (if (<= t_3 1e-12)
       (/ (- x (/ (- (/ x z) y) t)) (+ 1.0 x))
       (if (<= t_3 2.0)
         (/ (- x (/ x t_1)) (+ 1.0 x))
         (if (<= t_3 5e+124) t_2 (/ (+ (/ y t) x) (+ 1.0 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (z / (1.0 + x)) * (y / t_1);
	double t_3 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	double tmp;
	if (t_3 <= -0.1) {
		tmp = t_2;
	} else if (t_3 <= 1e-12) {
		tmp = (x - (((x / z) - y) / t)) / (1.0 + x);
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (1.0 + x);
	} else if (t_3 <= 5e+124) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (1.0 + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t * z) - x
    t_2 = (z / (1.0d0 + x)) * (y / t_1)
    t_3 = (x - ((x - (z * y)) / t_1)) / (1.0d0 + x)
    if (t_3 <= (-0.1d0)) then
        tmp = t_2
    else if (t_3 <= 1d-12) then
        tmp = (x - (((x / z) - y) / t)) / (1.0d0 + x)
    else if (t_3 <= 2.0d0) then
        tmp = (x - (x / t_1)) / (1.0d0 + x)
    else if (t_3 <= 5d+124) then
        tmp = t_2
    else
        tmp = ((y / t) + x) / (1.0d0 + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (z / (1.0 + x)) * (y / t_1);
	double t_3 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	double tmp;
	if (t_3 <= -0.1) {
		tmp = t_2;
	} else if (t_3 <= 1e-12) {
		tmp = (x - (((x / z) - y) / t)) / (1.0 + x);
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (1.0 + x);
	} else if (t_3 <= 5e+124) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (1.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (z / (1.0 + x)) * (y / t_1)
	t_3 = (x - ((x - (z * y)) / t_1)) / (1.0 + x)
	tmp = 0
	if t_3 <= -0.1:
		tmp = t_2
	elif t_3 <= 1e-12:
		tmp = (x - (((x / z) - y) / t)) / (1.0 + x)
	elif t_3 <= 2.0:
		tmp = (x - (x / t_1)) / (1.0 + x)
	elif t_3 <= 5e+124:
		tmp = t_2
	else:
		tmp = ((y / t) + x) / (1.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(z / Float64(1.0 + x)) * Float64(y / t_1))
	t_3 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_1)) / Float64(1.0 + x))
	tmp = 0.0
	if (t_3 <= -0.1)
		tmp = t_2;
	elseif (t_3 <= 1e-12)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(1.0 + x));
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(1.0 + x));
	elseif (t_3 <= 5e+124)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(1.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (z / (1.0 + x)) * (y / t_1);
	t_3 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	tmp = 0.0;
	if (t_3 <= -0.1)
		tmp = t_2;
	elseif (t_3 <= 1e-12)
		tmp = (x - (((x / z) - y) / t)) / (1.0 + x);
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_1)) / (1.0 + x);
	elseif (t_3 <= 5e+124)
		tmp = t_2;
	else
		tmp = ((y / t) + x) / (1.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -0.1], t$95$2, If[LessEqual[t$95$3, 1e-12], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+124], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -0.10000000000000001 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999996e124

   1. Initial program 86.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if -0.10000000000000001 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999998e-13

   1. Initial program 94.4%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 99.0

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

   5. Applied rewrites 99.0%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.8

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

   5. Applied rewrites 98.8%

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

   if 4.9999999999999996e124 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 56.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 90.0

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

   5. Applied rewrites 90.0%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq -0.1:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t \cdot z - x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t \cdot z - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{z}{1 + x} \cdot \frac{y}{t\_1}\\ t_3 := \frac{x - \frac{x - z \cdot y}{t\_1}}{1 + x}\\ \mathbf{if}\;t\_3 \leq -0.1:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-12}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_1}}{1 + x}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x))
        (t_2 (* (/ z (+ 1.0 x)) (/ y t_1)))
        (t_3 (/ (- x (/ (- x (* z y)) t_1)) (+ 1.0 x))))
   (if (<= t_3 -0.1)
     t_2
     (if (<= t_3 1e-12)
       (/ (- x (/ (- (/ x z) y) t)) 1.0)
       (if (<= t_3 2.0)
         (/ (- x (/ x t_1)) (+ 1.0 x))
         (if (<= t_3 5e+124) t_2 (/ (+ (/ y t) x) (+ 1.0 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (z / (1.0 + x)) * (y / t_1);
	double t_3 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	double tmp;
	if (t_3 <= -0.1) {
		tmp = t_2;
	} else if (t_3 <= 1e-12) {
		tmp = (x - (((x / z) - y) / t)) / 1.0;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (1.0 + x);
	} else if (t_3 <= 5e+124) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (1.0 + x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t * z) - x
    t_2 = (z / (1.0d0 + x)) * (y / t_1)
    t_3 = (x - ((x - (z * y)) / t_1)) / (1.0d0 + x)
    if (t_3 <= (-0.1d0)) then
        tmp = t_2
    else if (t_3 <= 1d-12) then
        tmp = (x - (((x / z) - y) / t)) / 1.0d0
    else if (t_3 <= 2.0d0) then
        tmp = (x - (x / t_1)) / (1.0d0 + x)
    else if (t_3 <= 5d+124) then
        tmp = t_2
    else
        tmp = ((y / t) + x) / (1.0d0 + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = (z / (1.0 + x)) * (y / t_1);
	double t_3 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	double tmp;
	if (t_3 <= -0.1) {
		tmp = t_2;
	} else if (t_3 <= 1e-12) {
		tmp = (x - (((x / z) - y) / t)) / 1.0;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_1)) / (1.0 + x);
	} else if (t_3 <= 5e+124) {
		tmp = t_2;
	} else {
		tmp = ((y / t) + x) / (1.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = (z / (1.0 + x)) * (y / t_1)
	t_3 = (x - ((x - (z * y)) / t_1)) / (1.0 + x)
	tmp = 0
	if t_3 <= -0.1:
		tmp = t_2
	elif t_3 <= 1e-12:
		tmp = (x - (((x / z) - y) / t)) / 1.0
	elif t_3 <= 2.0:
		tmp = (x - (x / t_1)) / (1.0 + x)
	elif t_3 <= 5e+124:
		tmp = t_2
	else:
		tmp = ((y / t) + x) / (1.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(Float64(z / Float64(1.0 + x)) * Float64(y / t_1))
	t_3 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_1)) / Float64(1.0 + x))
	tmp = 0.0
	if (t_3 <= -0.1)
		tmp = t_2;
	elseif (t_3 <= 1e-12)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / 1.0);
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(1.0 + x));
	elseif (t_3 <= 5e+124)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(y / t) + x) / Float64(1.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = (z / (1.0 + x)) * (y / t_1);
	t_3 = (x - ((x - (z * y)) / t_1)) / (1.0 + x);
	tmp = 0.0;
	if (t_3 <= -0.1)
		tmp = t_2;
	elseif (t_3 <= 1e-12)
		tmp = (x - (((x / z) - y) / t)) / 1.0;
	elseif (t_3 <= 2.0)
		tmp = (x - (x / t_1)) / (1.0 + x);
	elseif (t_3 <= 5e+124)
		tmp = t_2;
	else
		tmp = ((y / t) + x) / (1.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -0.1], t$95$2, If[LessEqual[t$95$3, 1e-12], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+124], t$95$2, N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -0.10000000000000001 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999996e124

   1. Initial program 86.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 88.5

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

   5. Applied rewrites 88.5%

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

   if -0.10000000000000001 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999998e-13

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 86.8

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

   5. Applied rewrites 86.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 86.7%

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

   9. Taylor expanded in t around -inf

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

       1. mul-1-neg N/A

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

       2. unsub-neg N/A

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

       3. lower--.f64 N/A

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

       4. lower-/.f64 N/A

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

       5. sub-neg N/A

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

       6. mul-1-neg N/A

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

       7. remove-double-neg N/A

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

       8. +-commutative N/A

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

       9. mul-1-neg N/A

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

       10. sub-neg N/A

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

       11. lower--.f64 N/A

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

       12. lower-/.f64 98.9

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

   11. Applied rewrites 98.9%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.8

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

   5. Applied rewrites 98.8%

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

   if 4.9999999999999996e124 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 56.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 90.0

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

   5. Applied rewrites 90.0%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq -0.1:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t \cdot z - x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t \cdot z - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{1 + x}\\ t_2 := t \cdot z - x\\ t_3 := \frac{z}{1 + x} \cdot \frac{y}{t\_2}\\ t_4 := \frac{x - \frac{x - z \cdot y}{t\_2}}{1 + x}\\ \mathbf{if}\;t\_4 \leq -4 \cdot 10^{-7}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{1 + x}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+124}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ 1.0 x)))
        (t_2 (- (* t z) x))
        (t_3 (* (/ z (+ 1.0 x)) (/ y t_2)))
        (t_4 (/ (- x (/ (- x (* z y)) t_2)) (+ 1.0 x))))
   (if (<= t_4 -4e-7)
     t_3
     (if (<= t_4 1e-12)
       t_1
       (if (<= t_4 2.0)
         (/ (- x (/ x t_2)) (+ 1.0 x))
         (if (<= t_4 5e+124) t_3 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (1.0 + x);
	double t_2 = (t * z) - x;
	double t_3 = (z / (1.0 + x)) * (y / t_2);
	double t_4 = (x - ((x - (z * y)) / t_2)) / (1.0 + x);
	double tmp;
	if (t_4 <= -4e-7) {
		tmp = t_3;
	} else if (t_4 <= 1e-12) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (1.0 + x);
	} else if (t_4 <= 5e+124) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    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 = ((y / t) + x) / (1.0d0 + x)
    t_2 = (t * z) - x
    t_3 = (z / (1.0d0 + x)) * (y / t_2)
    t_4 = (x - ((x - (z * y)) / t_2)) / (1.0d0 + x)
    if (t_4 <= (-4d-7)) then
        tmp = t_3
    else if (t_4 <= 1d-12) then
        tmp = t_1
    else if (t_4 <= 2.0d0) then
        tmp = (x - (x / t_2)) / (1.0d0 + x)
    else if (t_4 <= 5d+124) 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 = ((y / t) + x) / (1.0 + x);
	double t_2 = (t * z) - x;
	double t_3 = (z / (1.0 + x)) * (y / t_2);
	double t_4 = (x - ((x - (z * y)) / t_2)) / (1.0 + x);
	double tmp;
	if (t_4 <= -4e-7) {
		tmp = t_3;
	} else if (t_4 <= 1e-12) {
		tmp = t_1;
	} else if (t_4 <= 2.0) {
		tmp = (x - (x / t_2)) / (1.0 + x);
	} else if (t_4 <= 5e+124) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y / t) + x) / (1.0 + x)
	t_2 = (t * z) - x
	t_3 = (z / (1.0 + x)) * (y / t_2)
	t_4 = (x - ((x - (z * y)) / t_2)) / (1.0 + x)
	tmp = 0
	if t_4 <= -4e-7:
		tmp = t_3
	elif t_4 <= 1e-12:
		tmp = t_1
	elif t_4 <= 2.0:
		tmp = (x - (x / t_2)) / (1.0 + x)
	elif t_4 <= 5e+124:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(1.0 + x))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(z / Float64(1.0 + x)) * Float64(y / t_2))
	t_4 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_2)) / Float64(1.0 + x))
	tmp = 0.0
	if (t_4 <= -4e-7)
		tmp = t_3;
	elseif (t_4 <= 1e-12)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(1.0 + x));
	elseif (t_4 <= 5e+124)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y / t) + x) / (1.0 + x);
	t_2 = (t * z) - x;
	t_3 = (z / (1.0 + x)) * (y / t_2);
	t_4 = (x - ((x - (z * y)) / t_2)) / (1.0 + x);
	tmp = 0.0;
	if (t_4 <= -4e-7)
		tmp = t_3;
	elseif (t_4 <= 1e-12)
		tmp = t_1;
	elseif (t_4 <= 2.0)
		tmp = (x - (x / t_2)) / (1.0 + x);
	elseif (t_4 <= 5e+124)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -4e-7], t$95$3, If[LessEqual[t$95$4, 1e-12], t$95$1, If[LessEqual[t$95$4, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+124], 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))) < -3.9999999999999998e-7 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999996e124

   1. Initial program 86.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 87.1

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

   5. Applied rewrites 87.1%

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

   if -3.9999999999999998e-7 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999998e-13 or 4.9999999999999996e124 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 82.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 88.8

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

   5. Applied rewrites 88.8%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.8

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

   5. Applied rewrites 98.8%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t \cdot z - x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\frac{z}{1 + x} \cdot \frac{y}{t \cdot z - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\left(1 + x\right) \cdot t}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-268}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;t\_2 \leq 10^{-12}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* (+ 1.0 x) t)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (+ 1.0 x))))
   (if (<= t_2 -5e-31)
     t_1
     (if (<= t_2 2e-268)
       (* (- 1.0 x) x)
       (if (<= t_2 1e-12) (/ y t) (if (<= t_2 2.0) 1.0 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / ((1.0 + x) * t);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	double tmp;
	if (t_2 <= -5e-31) {
		tmp = t_1;
	} else if (t_2 <= 2e-268) {
		tmp = (1.0 - x) * x;
	} else if (t_2 <= 1e-12) {
		tmp = y / t;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    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 / ((1.0d0 + x) * t)
    t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0d0 + x)
    if (t_2 <= (-5d-31)) then
        tmp = t_1
    else if (t_2 <= 2d-268) then
        tmp = (1.0d0 - x) * x
    else if (t_2 <= 1d-12) then
        tmp = y / t
    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 / ((1.0 + x) * t);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	double tmp;
	if (t_2 <= -5e-31) {
		tmp = t_1;
	} else if (t_2 <= 2e-268) {
		tmp = (1.0 - x) * x;
	} else if (t_2 <= 1e-12) {
		tmp = y / t;
	} 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 / ((1.0 + x) * t)
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x)
	tmp = 0
	if t_2 <= -5e-31:
		tmp = t_1
	elif t_2 <= 2e-268:
		tmp = (1.0 - x) * x
	elif t_2 <= 1e-12:
		tmp = y / t
	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(Float64(1.0 + x) * t))
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(1.0 + x))
	tmp = 0.0
	if (t_2 <= -5e-31)
		tmp = t_1;
	elseif (t_2 <= 2e-268)
		tmp = Float64(Float64(1.0 - x) * x);
	elseif (t_2 <= 1e-12)
		tmp = Float64(y / t);
	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 / ((1.0 + x) * t);
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	tmp = 0.0;
	if (t_2 <= -5e-31)
		tmp = t_1;
	elseif (t_2 <= 2e-268)
		tmp = (1.0 - x) * x;
	elseif (t_2 <= 1e-12)
		tmp = y / t;
	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[(N[(1.0 + x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-31], t$95$1, If[LessEqual[t$95$2, 2e-268], N[(N[(1.0 - x), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$2, 1e-12], N[(y / t), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, 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))) < -5e-31 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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 81.8

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 61.3%

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

   if -5e-31 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999992e-268

   1. Initial program 90.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 62.3

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 62.3%

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

   if 1.99999999999999992e-268 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999998e-13

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 60.2

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

   5. Applied rewrites 60.2%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{\left(1 + x\right) \cdot t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2 \cdot 10^{-268}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(1 + x\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-268}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;t\_1 \leq 10^{-12}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (+ 1.0 x))))
   (if (<= t_1 -5e-31)
     (/ y t)
     (if (<= t_1 2e-268)
       (* (- 1.0 x) x)
       (if (<= t_1 1e-12) (/ 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 - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	double tmp;
	if (t_1 <= -5e-31) {
		tmp = y / t;
	} else if (t_1 <= 2e-268) {
		tmp = (1.0 - x) * x;
	} else if (t_1 <= 1e-12) {
		tmp = y / t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    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 - ((x - (z * y)) / ((t * z) - x))) / (1.0d0 + x)
    if (t_1 <= (-5d-31)) then
        tmp = y / t
    else if (t_1 <= 2d-268) then
        tmp = (1.0d0 - x) * x
    else if (t_1 <= 1d-12) 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 - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	double tmp;
	if (t_1 <= -5e-31) {
		tmp = y / t;
	} else if (t_1 <= 2e-268) {
		tmp = (1.0 - x) * x;
	} else if (t_1 <= 1e-12) {
		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 - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x)
	tmp = 0
	if t_1 <= -5e-31:
		tmp = y / t
	elif t_1 <= 2e-268:
		tmp = (1.0 - x) * x
	elif t_1 <= 1e-12:
		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(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(1.0 + x))
	tmp = 0.0
	if (t_1 <= -5e-31)
		tmp = Float64(y / t);
	elseif (t_1 <= 2e-268)
		tmp = Float64(Float64(1.0 - x) * x);
	elseif (t_1 <= 1e-12)
		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 - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	tmp = 0.0;
	if (t_1 <= -5e-31)
		tmp = y / t;
	elseif (t_1 <= 2e-268)
		tmp = (1.0 - x) * x;
	elseif (t_1 <= 1e-12)
		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[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-31], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 2e-268], N[(N[(1.0 - x), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 1e-12], N[(y / t), $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))) < -5e-31 or 1.99999999999999992e-268 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999998e-13 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 82.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 54.7

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

   5. Applied rewrites 54.7%

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

   if -5e-31 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999992e-268

   1. Initial program 90.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 62.3

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

   5. Applied rewrites 62.3%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 62.3%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.1%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq -5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2 \cdot 10^{-268}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{1 + x}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x - \frac{x - z \cdot y}{t\_2}}{1 + x}\\ \mathbf{if}\;t\_3 \leq 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t\_2}}{1 + x}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(-z, x, z\right) \cdot \frac{y}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ 1.0 x)))
        (t_2 (- (* t z) x))
        (t_3 (/ (- x (/ (- x (* z y)) t_2)) (+ 1.0 x))))
   (if (<= t_3 1e-12)
     t_1
     (if (<= t_3 2.0)
       (/ (- x (/ x t_2)) (+ 1.0 x))
       (if (<= t_3 5e+124) (* (fma (- z) x z) (/ y t_2)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (1.0 + x);
	double t_2 = (t * z) - x;
	double t_3 = (x - ((x - (z * y)) / t_2)) / (1.0 + x);
	double tmp;
	if (t_3 <= 1e-12) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = (x - (x / t_2)) / (1.0 + x);
	} else if (t_3 <= 5e+124) {
		tmp = fma(-z, x, z) * (y / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(1.0 + x))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_2)) / Float64(1.0 + x))
	tmp = 0.0
	if (t_3 <= 1e-12)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(1.0 + x));
	elseif (t_3 <= 5e+124)
		tmp = Float64(fma(Float64(-z), x, z) * Float64(y / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 1e-12], t$95$1, If[LessEqual[t$95$3, 2.0], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+124], N[(N[((-z) * x + z), $MachinePrecision] * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999998e-13 or 4.9999999999999996e124 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 81.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 78.6

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

   5. Applied rewrites 78.6%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 98.8

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

   5. Applied rewrites 98.8%

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

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999996e124

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 82.6%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(-z, x, z\right) \cdot \frac{y}{t \cdot z - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{1 + x}\\ t_2 := t \cdot z - x\\ t_3 := \frac{x - \frac{x - z \cdot y}{t\_2}}{1 + x}\\ \mathbf{if}\;t\_3 \leq 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(-z, x, z\right) \cdot \frac{y}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ 1.0 x)))
        (t_2 (- (* t z) x))
        (t_3 (/ (- x (/ (- x (* z y)) t_2)) (+ 1.0 x))))
   (if (<= t_3 1e-12)
     t_1
     (if (<= t_3 2.0)
       1.0
       (if (<= t_3 5e+124) (* (fma (- z) x z) (/ y t_2)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y / t) + x) / (1.0 + x);
	double t_2 = (t * z) - x;
	double t_3 = (x - ((x - (z * y)) / t_2)) / (1.0 + x);
	double tmp;
	if (t_3 <= 1e-12) {
		tmp = t_1;
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+124) {
		tmp = fma(-z, x, z) * (y / t_2);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(1.0 + x))
	t_2 = Float64(Float64(t * z) - x)
	t_3 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / t_2)) / Float64(1.0 + x))
	tmp = 0.0
	if (t_3 <= 1e-12)
		tmp = t_1;
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+124)
		tmp = Float64(fma(Float64(-z), x, z) * Float64(y / t_2));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 1e-12], t$95$1, If[LessEqual[t$95$3, 2.0], 1.0, If[LessEqual[t$95$3, 5e+124], N[(N[((-z) * x + z), $MachinePrecision] * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 9.9999999999999998e-13 or 4.9999999999999996e124 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 81.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 78.6

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

   5. Applied rewrites 78.6%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.1%

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

   if 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.9999999999999996e124

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 82.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(-z, x, z\right) \cdot \frac{y}{t \cdot z - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{t} + x}{1 + x}\\ t_2 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x}\\ \mathbf{if}\;t\_2 \leq 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (/ y t) x) (+ 1.0 x)))
        (t_2 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (+ 1.0 x))))
   (if (<= t_2 1e-12) t_1 (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) + x) / (1.0 + x);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	double tmp;
	if (t_2 <= 1e-12) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((y / t) + x) / (1.0d0 + x)
    t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0d0 + x)
    if (t_2 <= 1d-12) then
        tmp = t_1
    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) + x) / (1.0 + x);
	double t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	double tmp;
	if (t_2 <= 1e-12) {
		tmp = t_1;
	} 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) + x) / (1.0 + x)
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x)
	tmp = 0
	if t_2 <= 1e-12:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y / t) + x) / Float64(1.0 + x))
	t_2 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(1.0 + x))
	tmp = 0.0
	if (t_2 <= 1e-12)
		tmp = t_1;
	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) + x) / (1.0 + x);
	t_2 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	tmp = 0.0;
	if (t_2 <= 1e-12)
		tmp = t_1;
	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[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 1e-12], t$95$1, If[LessEqual[t$95$2, 2.0], 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))) < 9.9999999999999998e-13 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 84.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 75.0

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

   5. Applied rewrites 75.0%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.1%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1 + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x}\\ \mathbf{if}\;t\_1 \leq 10^{-12}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(1 + x\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ (- x (* z y)) (- (* t z) x))) (+ 1.0 x))))
   (if (<= t_1 1e-12)
     (/ (+ (/ y t) x) 1.0)
     (if (<= t_1 2.0) 1.0 (/ y (* (+ 1.0 x) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	double tmp;
	if (t_1 <= 1e-12) {
		tmp = ((y / t) + x) / 1.0;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / ((1.0 + x) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    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 - ((x - (z * y)) / ((t * z) - x))) / (1.0d0 + x)
    if (t_1 <= 1d-12) then
        tmp = ((y / t) + x) / 1.0d0
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = y / ((1.0d0 + x) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	double tmp;
	if (t_1 <= 1e-12) {
		tmp = ((y / t) + x) / 1.0;
	} else if (t_1 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = y / ((1.0 + x) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x)
	tmp = 0
	if t_1 <= 1e-12:
		tmp = ((y / t) + x) / 1.0
	elif t_1 <= 2.0:
		tmp = 1.0
	else:
		tmp = y / ((1.0 + x) * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(1.0 + x))
	tmp = 0.0
	if (t_1 <= 1e-12)
		tmp = Float64(Float64(Float64(y / t) + x) / 1.0);
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(y / Float64(Float64(1.0 + x) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x);
	tmp = 0.0;
	if (t_1 <= 1e-12)
		tmp = ((y / t) + x) / 1.0;
	elseif (t_1 <= 2.0)
		tmp = 1.0;
	else
		tmp = y / ((1.0 + x) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-12], N[(N[(N[(y / t), $MachinePrecision] + x), $MachinePrecision] / 1.0), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 1.0, N[(y / N[(N[(1.0 + x), $MachinePrecision] * t), $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))) < 9.9999999999999998e-13

   1. Initial program 88.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 75.5

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

   5. Applied rewrites 75.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 71.7%

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

   if 9.9999999999999998e-13 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 98.1%

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

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

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 82.3

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 65.5%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 10^{-12}:\\ \;\;\;\;\frac{\frac{y}{t} + x}{1}\\ \mathbf{elif}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(1 + x\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- x (/ (- x (* z y)) (- (* t z) x))) (+ 1.0 x)) 5e-16)
   (* (- 1.0 x) x)
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x)) <= 5e-16) {
		tmp = (1.0 - x) * x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x - ((x - (z * y)) / ((t * z) - x))) / (1.0d0 + x)) <= 5d-16) then
        tmp = (1.0d0 - x) * x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x)) <= 5e-16) {
		tmp = (1.0 - x) * x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x)) <= 5e-16:
		tmp = (1.0 - x) * x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x - Float64(Float64(x - Float64(z * y)) / Float64(Float64(t * z) - x))) / Float64(1.0 + x)) <= 5e-16)
		tmp = Float64(Float64(1.0 - x) * x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x - ((x - (z * y)) / ((t * z) - x))) / (1.0 + x)) <= 5e-16)
		tmp = (1.0 - x) * x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x - N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], 5e-16], N[(N[(1.0 - x), $MachinePrecision] * x), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e-16

   1. Initial program 88.8%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 29.2

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

   5. Applied rewrites 29.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 27.6%

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

   if 5.0000000000000004e-16 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 74.9%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - \frac{x - z \cdot y}{t \cdot z - x}}{1 + x} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\left(1 - x\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.2% accurate, 45.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.2%

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

3. Taylor expanded in z around 0

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

5. Applied rewrites 48.7%

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

Developer Target 1: 99.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024268 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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