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

Percentage Accurate: 89.1% → 96.7%

Time: 11.7s

Alternatives: 10

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: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+277}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} + \frac{x}{z \cdot \left(-1 - x\right)}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- x (* y z)) (- x (* z t)))) (+ x 1.0))))
   (if (<= t_1 -5e+90)
     (/ (/ y (- -1.0 x)) (- (/ x z) t))
     (if (<= t_1 5e+277)
       t_1
       (+ (/ x (+ x 1.0)) (/ (+ (/ y (+ x 1.0)) (/ x (* z (- -1.0 x)))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+90) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t_1 <= 5e+277) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) + (x / (z * (-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 - (y * z)) / (x - (z * t)))) / (x + 1.0d0)
    if (t_1 <= (-5d+90)) then
        tmp = (y / ((-1.0d0) - x)) / ((x / z) - t)
    else if (t_1 <= 5d+277) then
        tmp = t_1
    else
        tmp = (x / (x + 1.0d0)) + (((y / (x + 1.0d0)) + (x / (z * ((-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 - (y * z)) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+90) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t_1 <= 5e+277) {
		tmp = t_1;
	} else {
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) + (x / (z * (-1.0 - x)))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0)
	tmp = 0
	if t_1 <= -5e+90:
		tmp = (y / (-1.0 - x)) / ((x / z) - t)
	elif t_1 <= 5e+277:
		tmp = t_1
	else:
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) + (x / (z * (-1.0 - x)))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / Float64(x - Float64(z * t)))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -5e+90)
		tmp = Float64(Float64(y / Float64(-1.0 - x)) / Float64(Float64(x / z) - t));
	elseif (t_1 <= 5e+277)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(Float64(y / Float64(x + 1.0)) + Float64(x / Float64(z * Float64(-1.0 - x)))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -5e+90)
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	elseif (t_1 <= 5e+277)
		tmp = t_1;
	else
		tmp = (x / (x + 1.0)) + (((y / (x + 1.0)) + (x / (z * (-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[(y * z), $MachinePrecision]), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+90], N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(N[(x / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+277], t$95$1, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(z * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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))) < -5.0000000000000004e90

   1. Initial program 66.9%

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

      1. *-commutative 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in z around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. unsub-neg 66.9%

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

   7. Simplified 66.9%

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

   8. Taylor expanded in y around inf 94.9%

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

      1. associate-/r* 95.1%

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

      2. +-commutative 95.1%

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

   10. Simplified 95.1%

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

   if -5.0000000000000004e90 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999982e277

   1. Initial program 98.9%

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

   if 4.99999999999999982e277 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 15.5%

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

      1. *-commutative 15.5%

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

   3. Simplified 15.5%

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

   5. Taylor expanded in t around -inf 86.9%

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

      1. +-commutative 86.9%

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

      2. mul-1-neg 86.9%

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

      3. unsub-neg 86.9%

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

      4. +-commutative 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq -5 \cdot 10^{+90}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq 5 \cdot 10^{+277}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} + \frac{x}{z \cdot \left(-1 - x\right)}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+90}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+277}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- x (* y z)) (- x (* z t)))) (+ x 1.0))))
   (if (<= t_1 -5e+90)
     (/ (/ y (- -1.0 x)) (- (/ x z) t))
     (if (<= t_1 5e+277) t_1 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+90) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t_1 <= 5e+277) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 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) :: t_1
    real(8) :: tmp
    t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0d0)
    if (t_1 <= (-5d+90)) then
        tmp = (y / ((-1.0d0) - x)) / ((x / z) - t)
    else if (t_1 <= 5d+277) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0);
	double tmp;
	if (t_1 <= -5e+90) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t_1 <= 5e+277) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0)
	tmp = 0
	if t_1 <= -5e+90:
		tmp = (y / (-1.0 - x)) / ((x / z) - t)
	elif t_1 <= 5e+277:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / Float64(x - Float64(z * t)))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -5e+90)
		tmp = Float64(Float64(y / Float64(-1.0 - x)) / Float64(Float64(x / z) - t));
	elseif (t_1 <= 5e+277)
		tmp = t_1;
	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 = (x + ((x - (y * z)) / (x - (z * t)))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -5e+90)
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	elseif (t_1 <= 5e+277)
		tmp = t_1;
	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[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+90], N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(N[(x / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+277], t$95$1, 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))) < -5.0000000000000004e90

   1. Initial program 66.9%

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

      1. *-commutative 66.9%

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

   3. Simplified 66.9%

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

   5. Taylor expanded in z around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. unsub-neg 66.9%

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

   7. Simplified 66.9%

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

   8. Taylor expanded in y around inf 94.9%

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

      1. associate-/r* 95.1%

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

      2. +-commutative 95.1%

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

   10. Simplified 95.1%

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

   if -5.0000000000000004e90 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999982e277

   1. Initial program 98.9%

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

   if 4.99999999999999982e277 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 15.5%

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

      1. *-commutative 15.5%

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

   3. Simplified 15.5%

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

   5. Taylor expanded in z around inf 86.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq -5 \cdot 10^{+90}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1} \leq 5 \cdot 10^{+277}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-252}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;t \leq 7800000:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -2.4e-5)
     t_1
     (if (<= t 9.8e-252)
       (+ 1.0 (* (/ y x) (/ z (- -1.0 x))))
       (if (<= t 5.4e-128)
         (/ (/ y (- -1.0 x)) (- (/ x z) t))
         (if (<= t 7800000.0) (/ (+ x (/ x (- x (* z t)))) (+ x 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 tmp;
	if (t <= -2.4e-5) {
		tmp = t_1;
	} else if (t <= 9.8e-252) {
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	} else if (t <= 5.4e-128) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t <= 7800000.0) {
		tmp = (x + (x / (x - (z * t)))) / (x + 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) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-2.4d-5)) then
        tmp = t_1
    else if (t <= 9.8d-252) then
        tmp = 1.0d0 + ((y / x) * (z / ((-1.0d0) - x)))
    else if (t <= 5.4d-128) then
        tmp = (y / ((-1.0d0) - x)) / ((x / z) - t)
    else if (t <= 7800000.0d0) then
        tmp = (x + (x / (x - (z * t)))) / (x + 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 tmp;
	if (t <= -2.4e-5) {
		tmp = t_1;
	} else if (t <= 9.8e-252) {
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	} else if (t <= 5.4e-128) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t <= 7800000.0) {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -2.4e-5:
		tmp = t_1
	elif t <= 9.8e-252:
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)))
	elif t <= 5.4e-128:
		tmp = (y / (-1.0 - x)) / ((x / z) - t)
	elif t <= 7800000.0:
		tmp = (x + (x / (x - (z * t)))) / (x + 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))
	tmp = 0.0
	if (t <= -2.4e-5)
		tmp = t_1;
	elseif (t <= 9.8e-252)
		tmp = Float64(1.0 + Float64(Float64(y / x) * Float64(z / Float64(-1.0 - x))));
	elseif (t <= 5.4e-128)
		tmp = Float64(Float64(y / Float64(-1.0 - x)) / Float64(Float64(x / z) - t));
	elseif (t <= 7800000.0)
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 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);
	tmp = 0.0;
	if (t <= -2.4e-5)
		tmp = t_1;
	elseif (t <= 9.8e-252)
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	elseif (t <= 5.4e-128)
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	elseif (t <= 7800000.0)
		tmp = (x + (x / (x - (z * t)))) / (x + 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]}, If[LessEqual[t, -2.4e-5], t$95$1, If[LessEqual[t, 9.8e-252], N[(1.0 + N[(N[(y / x), $MachinePrecision] * N[(z / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-128], N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(N[(x / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7800000.0], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.4000000000000001e-5 or 7.8e6 < t

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around inf 91.2%

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

   if -2.4000000000000001e-5 < t < 9.7999999999999994e-252

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around 0 84.9%

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

      1. associate-+r+ 84.9%

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

      2. mul-1-neg 84.9%

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

      3. unsub-neg 84.9%

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

      4. +-commutative 84.9%

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

      5. associate-/l* 87.3%

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

      6. +-commutative 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in y around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. sub-neg 84.8%

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

      3. times-frac 87.4%

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

      4. +-commutative 87.4%

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

   10. Simplified 87.4%

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

   if 9.7999999999999994e-252 < t < 5.40000000000000011e-128

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in z around inf 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in y around inf 87.7%

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

      1. associate-/r* 87.8%

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

      2. +-commutative 87.8%

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

   10. Simplified 87.8%

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

   if 5.40000000000000011e-128 < t < 7.8e6

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around 0 68.8%

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

      1. +-commutative 68.8%

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

   7. Simplified 68.8%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-252}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;t \leq 7800000:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-252}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;t \leq 7800000:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -2.75e-5)
     t_1
     (if (<= t 9.8e-252)
       (+ 1.0 (* (/ y x) (/ z (- -1.0 x))))
       (if (<= t 3.5e-134)
         (/ (/ y (- -1.0 x)) (- (/ x z) t))
         (if (<= t 7800000.0)
           (/ (- (+ x 1.0) (* y (/ z x))) (+ x 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 tmp;
	if (t <= -2.75e-5) {
		tmp = t_1;
	} else if (t <= 9.8e-252) {
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	} else if (t <= 3.5e-134) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t <= 7800000.0) {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 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) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-2.75d-5)) then
        tmp = t_1
    else if (t <= 9.8d-252) then
        tmp = 1.0d0 + ((y / x) * (z / ((-1.0d0) - x)))
    else if (t <= 3.5d-134) then
        tmp = (y / ((-1.0d0) - x)) / ((x / z) - t)
    else if (t <= 7800000.0d0) then
        tmp = ((x + 1.0d0) - (y * (z / x))) / (x + 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 tmp;
	if (t <= -2.75e-5) {
		tmp = t_1;
	} else if (t <= 9.8e-252) {
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	} else if (t <= 3.5e-134) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t <= 7800000.0) {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -2.75e-5:
		tmp = t_1
	elif t <= 9.8e-252:
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)))
	elif t <= 3.5e-134:
		tmp = (y / (-1.0 - x)) / ((x / z) - t)
	elif t <= 7800000.0:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 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))
	tmp = 0.0
	if (t <= -2.75e-5)
		tmp = t_1;
	elseif (t <= 9.8e-252)
		tmp = Float64(1.0 + Float64(Float64(y / x) * Float64(z / Float64(-1.0 - x))));
	elseif (t <= 3.5e-134)
		tmp = Float64(Float64(y / Float64(-1.0 - x)) / Float64(Float64(x / z) - t));
	elseif (t <= 7800000.0)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 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);
	tmp = 0.0;
	if (t <= -2.75e-5)
		tmp = t_1;
	elseif (t <= 9.8e-252)
		tmp = 1.0 + ((y / x) * (z / (-1.0 - x)));
	elseif (t <= 3.5e-134)
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	elseif (t <= 7800000.0)
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 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]}, If[LessEqual[t, -2.75e-5], t$95$1, If[LessEqual[t, 9.8e-252], N[(1.0 + N[(N[(y / x), $MachinePrecision] * N[(z / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-134], N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(N[(x / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7800000.0], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.7500000000000001e-5 or 7.8e6 < t

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around inf 91.2%

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

   if -2.7500000000000001e-5 < t < 9.7999999999999994e-252

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around 0 84.9%

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

      1. associate-+r+ 84.9%

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

      2. mul-1-neg 84.9%

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

      3. unsub-neg 84.9%

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

      4. +-commutative 84.9%

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

      5. associate-/l* 87.3%

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

      6. +-commutative 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in y around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. sub-neg 84.8%

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

      3. times-frac 87.4%

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

      4. +-commutative 87.4%

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

   10. Simplified 87.4%

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

   if 9.7999999999999994e-252 < t < 3.4999999999999998e-134

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in z around inf 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in y around inf 86.9%

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

      1. associate-/r* 87.0%

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

      2. +-commutative 87.0%

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

   10. Simplified 87.0%

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

   if 3.4999999999999998e-134 < t < 7.8e6

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around 0 74.1%

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

      1. associate-+r+ 74.1%

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

      2. mul-1-neg 74.1%

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

      3. unsub-neg 74.1%

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

      4. +-commutative 74.1%

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

      5. associate-/l* 76.9%

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

      6. +-commutative 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-252}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;t \leq 7800000:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -0.0038:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (* (/ y x) (/ z (- -1.0 x)))))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -0.0038)
     t_2
     (if (<= t 1.16e-229)
       t_1
       (if (<= t 1.4e-162)
         (/ y (* t (+ x 1.0)))
         (if (<= t 3.15e-56) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((y / x) * (z / (-1.0 - x)));
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -0.0038) {
		tmp = t_2;
	} else if (t <= 1.16e-229) {
		tmp = t_1;
	} else if (t <= 1.4e-162) {
		tmp = y / (t * (x + 1.0));
	} else if (t <= 3.15e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = 1.0d0 + ((y / x) * (z / ((-1.0d0) - x)))
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-0.0038d0)) then
        tmp = t_2
    else if (t <= 1.16d-229) then
        tmp = t_1
    else if (t <= 1.4d-162) then
        tmp = y / (t * (x + 1.0d0))
    else if (t <= 3.15d-56) then
        tmp = t_1
    else
        tmp = t_2
    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 / x) * (z / (-1.0 - x)));
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -0.0038) {
		tmp = t_2;
	} else if (t <= 1.16e-229) {
		tmp = t_1;
	} else if (t <= 1.4e-162) {
		tmp = y / (t * (x + 1.0));
	} else if (t <= 3.15e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + ((y / x) * (z / (-1.0 - x)))
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -0.0038:
		tmp = t_2
	elif t <= 1.16e-229:
		tmp = t_1
	elif t <= 1.4e-162:
		tmp = y / (t * (x + 1.0))
	elif t <= 3.15e-56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(y / x) * Float64(z / Float64(-1.0 - x))))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -0.0038)
		tmp = t_2;
	elseif (t <= 1.16e-229)
		tmp = t_1;
	elseif (t <= 1.4e-162)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (t <= 3.15e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((y / x) * (z / (-1.0 - x)));
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -0.0038)
		tmp = t_2;
	elseif (t <= 1.16e-229)
		tmp = t_1;
	elseif (t <= 1.4e-162)
		tmp = y / (t * (x + 1.0));
	elseif (t <= 3.15e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(y / x), $MachinePrecision] * N[(z / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.0038], t$95$2, If[LessEqual[t, 1.16e-229], t$95$1, If[LessEqual[t, 1.4e-162], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.15e-56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.00379999999999999999 or 3.1499999999999999e-56 < t

   1. Initial program 83.7%

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

      1. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in z around inf 87.6%

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

   if -0.00379999999999999999 < t < 1.16000000000000002e-229 or 1.40000000000000011e-162 < t < 3.1499999999999999e-56

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around 0 81.8%

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

      1. associate-+r+ 81.8%

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

      2. mul-1-neg 81.8%

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

      3. unsub-neg 81.8%

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

      4. +-commutative 81.8%

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

      5. associate-/l* 85.6%

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

      6. +-commutative 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in y around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. sub-neg 81.8%

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

      3. times-frac 84.7%

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

      4. +-commutative 84.7%

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

   10. Simplified 84.7%

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

   if 1.16000000000000002e-229 < t < 1.40000000000000011e-162

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around inf 75.8%

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

      1. associate-/l* 87.1%

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

      2. +-commutative 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in z around inf 87.6%

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

      1. +-commutative 87.6%

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

   10. Simplified 87.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0038:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-229}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 3.15 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-144}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (* (/ y x) (/ z (- -1.0 x)))))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -2.5e-5)
     t_2
     (if (<= t 9.8e-252)
       t_1
       (if (<= t 1.9e-144)
         (/ (/ y (- -1.0 x)) (- (/ x z) t))
         (if (<= t 3.7e-56) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + ((y / x) * (z / (-1.0 - x)));
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -2.5e-5) {
		tmp = t_2;
	} else if (t <= 9.8e-252) {
		tmp = t_1;
	} else if (t <= 1.9e-144) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t <= 3.7e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = 1.0d0 + ((y / x) * (z / ((-1.0d0) - x)))
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-2.5d-5)) then
        tmp = t_2
    else if (t <= 9.8d-252) then
        tmp = t_1
    else if (t <= 1.9d-144) then
        tmp = (y / ((-1.0d0) - x)) / ((x / z) - t)
    else if (t <= 3.7d-56) then
        tmp = t_1
    else
        tmp = t_2
    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 / x) * (z / (-1.0 - x)));
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -2.5e-5) {
		tmp = t_2;
	} else if (t <= 9.8e-252) {
		tmp = t_1;
	} else if (t <= 1.9e-144) {
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	} else if (t <= 3.7e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + ((y / x) * (z / (-1.0 - x)))
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -2.5e-5:
		tmp = t_2
	elif t <= 9.8e-252:
		tmp = t_1
	elif t <= 1.9e-144:
		tmp = (y / (-1.0 - x)) / ((x / z) - t)
	elif t <= 3.7e-56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(Float64(y / x) * Float64(z / Float64(-1.0 - x))))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -2.5e-5)
		tmp = t_2;
	elseif (t <= 9.8e-252)
		tmp = t_1;
	elseif (t <= 1.9e-144)
		tmp = Float64(Float64(y / Float64(-1.0 - x)) / Float64(Float64(x / z) - t));
	elseif (t <= 3.7e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + ((y / x) * (z / (-1.0 - x)));
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -2.5e-5)
		tmp = t_2;
	elseif (t <= 9.8e-252)
		tmp = t_1;
	elseif (t <= 1.9e-144)
		tmp = (y / (-1.0 - x)) / ((x / z) - t);
	elseif (t <= 3.7e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(N[(y / x), $MachinePrecision] * N[(z / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e-5], t$95$2, If[LessEqual[t, 9.8e-252], t$95$1, If[LessEqual[t, 1.9e-144], N[(N[(y / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(N[(x / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.50000000000000012e-5 or 3.7000000000000002e-56 < t

   1. Initial program 83.7%

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

      1. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   5. Taylor expanded in z around inf 87.6%

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

   if -2.50000000000000012e-5 < t < 9.7999999999999994e-252 or 1.89999999999999996e-144 < t < 3.7000000000000002e-56

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around 0 83.0%

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

      1. associate-+r+ 83.0%

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

      2. mul-1-neg 83.0%

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

      3. unsub-neg 83.0%

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

      4. +-commutative 83.0%

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

      5. associate-/l* 86.9%

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

      6. +-commutative 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in y around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. sub-neg 82.9%

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

      3. times-frac 86.0%

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

      4. +-commutative 86.0%

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

   10. Simplified 86.0%

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

   if 9.7999999999999994e-252 < t < 1.89999999999999996e-144

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in z around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. unsub-neg 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in y around inf 84.9%

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

      1. associate-/r* 85.0%

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

      2. +-commutative 85.0%

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

   10. Simplified 85.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-252}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-144}:\\ \;\;\;\;\frac{\frac{y}{-1 - x}}{\frac{x}{z} - t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-56}:\\ \;\;\;\;1 + \frac{y}{x} \cdot \frac{z}{-1 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.2e-21) 1.0 (if (<= x 5.5e-9) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.2e-21) {
		tmp = 1.0;
	} else if (x <= 5.5e-9) {
		tmp = (x + (y / t)) / (x + 1.0);
	} 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 <= (-3.2d-21)) then
        tmp = 1.0d0
    else if (x <= 5.5d-9) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.2e-21) {
		tmp = 1.0;
	} else if (x <= 5.5e-9) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.2e-21:
		tmp = 1.0
	elif x <= 5.5e-9:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.2e-21)
		tmp = 1.0;
	elseif (x <= 5.5e-9)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.2e-21)
		tmp = 1.0;
	elseif (x <= 5.5e-9)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.2e-21], 1.0, If[LessEqual[x, 5.5e-9], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2000000000000002e-21 or 5.4999999999999996e-9 < x

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around inf 70.0%

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

   6. Taylor expanded in x around inf 89.7%

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

   if -3.2000000000000002e-21 < x < 5.4999999999999996e-9

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in z around inf 64.4%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.6e-21) 1.0 (if (<= x 4.1e-13) (/ y (* t (+ x 1.0))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e-21) {
		tmp = 1.0;
	} else if (x <= 4.1e-13) {
		tmp = y / (t * (x + 1.0));
	} 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 <= (-1.6d-21)) then
        tmp = 1.0d0
    else if (x <= 4.1d-13) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e-21) {
		tmp = 1.0;
	} else if (x <= 4.1e-13) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.6e-21:
		tmp = 1.0
	elif x <= 4.1e-13:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.6e-21)
		tmp = 1.0;
	elseif (x <= 4.1e-13)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.6e-21)
		tmp = 1.0;
	elseif (x <= 4.1e-13)
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.6e-21], 1.0, If[LessEqual[x, 4.1e-13], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e-21 or 4.1000000000000002e-13 < x

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around inf 70.0%

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

   6. Taylor expanded in x around inf 89.7%

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

   if -1.6000000000000001e-21 < x < 4.1000000000000002e-13

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in y around inf 47.9%

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

      1. associate-/l* 53.3%

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

      2. +-commutative 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in z around inf 48.1%

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

      1. +-commutative 48.1%

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

   10. Simplified 48.1%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.6e-21) 1.0 (if (<= x 3.6e-12) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e-21) {
		tmp = 1.0;
	} else if (x <= 3.6e-12) {
		tmp = y / t;
	} 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 <= (-1.6d-21)) then
        tmp = 1.0d0
    else if (x <= 3.6d-12) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e-21) {
		tmp = 1.0;
	} else if (x <= 3.6e-12) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.6e-21:
		tmp = 1.0
	elif x <= 3.6e-12:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.6e-21)
		tmp = 1.0;
	elseif (x <= 3.6e-12)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.6e-21)
		tmp = 1.0;
	elseif (x <= 3.6e-12)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.6e-21], 1.0, If[LessEqual[x, 3.6e-12], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e-21 or 3.6e-12 < x

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around inf 70.0%

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

   6. Taylor expanded in x around inf 89.7%

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

   if -1.6000000000000001e-21 < x < 3.6e-12

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in z around inf 64.4%

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

   6. Taylor expanded in x around 0 48.1%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.5% accurate, 17.0× 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 87.3%

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

   1. *-commutative 87.3%

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

3. Simplified 87.3%

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

5. Taylor expanded in z around inf 67.2%

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

6. Taylor expanded in x around inf 53.2%

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

7. Final simplification 53.2%

   \[\leadsto 1 \]
8. Add Preprocessing

Developer target: 99.5% accurate, 0.8× 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 2024080 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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