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

Percentage Accurate: 89.0% → 96.4%

Time: 10.8s

Alternatives: 9

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: 89.0% 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: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+238}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -5e+141)
     (* y (/ (/ z (+ x 1.0)) t_1))
     (if (<= t_2 5e+238) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+141) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else if (t_2 <= 5e+238) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-5d+141)) then
        tmp = y * ((z / (x + 1.0d0)) / t_1)
    else if (t_2 <= 5d+238) then
        tmp = t_2
    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 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+141) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else if (t_2 <= 5e+238) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -5e+141:
		tmp = y * ((z / (x + 1.0)) / t_1)
	elif t_2 <= 5e+238:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+141)
		tmp = Float64(y * Float64(Float64(z / Float64(x + 1.0)) / t_1));
	elseif (t_2 <= 5e+238)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -5e+141)
		tmp = y * ((z / (x + 1.0)) / t_1);
	elseif (t_2 <= 5e+238)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+141], N[(y * N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+238], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5.00000000000000025e141

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in y around inf 62.9%

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

      1. associate-/l* 85.8%

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

      2. associate-/r* 95.2%

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

      3. +-commutative 95.2%

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

   7. Simplified 95.2%

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

   if -5.00000000000000025e141 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999995e238

   1. Initial program 99.0%

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

   if 4.99999999999999995e238 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 38.7%

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

      1. *-commutative 38.7%

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

   3. Simplified 38.7%

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

   5. Taylor expanded in z around inf 93.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+141}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+238}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;1 + \frac{z \cdot t}{x \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-259}:\\ \;\;\;\;\frac{y \cdot z}{x \cdot \left(-1 - x\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-145}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -2.4e-136)
     t_1
     (if (<= t -8.5e-229)
       (+ 1.0 (/ (* z t) (* x (+ x 1.0))))
       (if (<= t -3.8e-259)
         (/ (* y z) (* x (- -1.0 x)))
         (if (<= t 2e-145) 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-136) {
		tmp = t_1;
	} else if (t <= -8.5e-229) {
		tmp = 1.0 + ((z * t) / (x * (x + 1.0)));
	} else if (t <= -3.8e-259) {
		tmp = (y * z) / (x * (-1.0 - x));
	} else if (t <= 2e-145) {
		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) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-2.4d-136)) then
        tmp = t_1
    else if (t <= (-8.5d-229)) then
        tmp = 1.0d0 + ((z * t) / (x * (x + 1.0d0)))
    else if (t <= (-3.8d-259)) then
        tmp = (y * z) / (x * ((-1.0d0) - x))
    else if (t <= 2d-145) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -2.4e-136) {
		tmp = t_1;
	} else if (t <= -8.5e-229) {
		tmp = 1.0 + ((z * t) / (x * (x + 1.0)));
	} else if (t <= -3.8e-259) {
		tmp = (y * z) / (x * (-1.0 - x));
	} else if (t <= 2e-145) {
		tmp = 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-136:
		tmp = t_1
	elif t <= -8.5e-229:
		tmp = 1.0 + ((z * t) / (x * (x + 1.0)))
	elif t <= -3.8e-259:
		tmp = (y * z) / (x * (-1.0 - x))
	elif t <= 2e-145:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -2.4e-136)
		tmp = t_1;
	elseif (t <= -8.5e-229)
		tmp = Float64(1.0 + Float64(Float64(z * t) / Float64(x * Float64(x + 1.0))));
	elseif (t <= -3.8e-259)
		tmp = Float64(Float64(y * z) / Float64(x * Float64(-1.0 - x)));
	elseif (t <= 2e-145)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -2.4e-136)
		tmp = t_1;
	elseif (t <= -8.5e-229)
		tmp = 1.0 + ((z * t) / (x * (x + 1.0)));
	elseif (t <= -3.8e-259)
		tmp = (y * z) / (x * (-1.0 - x));
	elseif (t <= 2e-145)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e-136], t$95$1, If[LessEqual[t, -8.5e-229], N[(1.0 + N[(N[(z * t), $MachinePrecision] / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-259], N[(N[(y * z), $MachinePrecision] / N[(x * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-145], 1.0, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.3999999999999999e-136 or 1.99999999999999983e-145 < t

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in z around inf 81.7%

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

   if -2.3999999999999999e-136 < t < -8.49999999999999977e-229

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 74.4%

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

      1. +-commutative 74.4%

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

   7. Simplified 74.4%

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

   8. Taylor expanded in t around 0 74.4%

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

   if -8.49999999999999977e-229 < t < -3.8e-259

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 89.0%

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

      1. associate-/l* 89.0%

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

      2. associate-/r* 89.0%

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

      3. +-commutative 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in z around 0 78.0%

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

   9. Taylor expanded in y around 0 78.0%

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

       1. associate-*r/ 78.0%

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

       2. mul-1-neg 78.0%

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

       3. distribute-rgt-neg-out 78.0%

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

       4. +-commutative 78.0%

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

   11. Simplified 78.0%

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

   if -3.8e-259 < t < 1.99999999999999983e-145

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in y around 0 68.5%

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

      1. +-commutative 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in x around inf 68.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-136}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;1 + \frac{z \cdot t}{x \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-259}:\\ \;\;\;\;\frac{y \cdot z}{x \cdot \left(-1 - x\right)}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-145}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.12 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-259}:\\ \;\;\;\;\frac{y \cdot z}{x \cdot \left(-1 - x\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-146}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.12e-138)
     t_1
     (if (<= t -8.5e-229)
       1.0
       (if (<= t -4e-259)
         (/ (* y z) (* x (- -1.0 x)))
         (if (<= t 4.6e-146) 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 <= -1.12e-138) {
		tmp = t_1;
	} else if (t <= -8.5e-229) {
		tmp = 1.0;
	} else if (t <= -4e-259) {
		tmp = (y * z) / (x * (-1.0 - x));
	} else if (t <= 4.6e-146) {
		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) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.12d-138)) then
        tmp = t_1
    else if (t <= (-8.5d-229)) then
        tmp = 1.0d0
    else if (t <= (-4d-259)) then
        tmp = (y * z) / (x * ((-1.0d0) - x))
    else if (t <= 4.6d-146) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.12e-138) {
		tmp = t_1;
	} else if (t <= -8.5e-229) {
		tmp = 1.0;
	} else if (t <= -4e-259) {
		tmp = (y * z) / (x * (-1.0 - x));
	} else if (t <= 4.6e-146) {
		tmp = 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 <= -1.12e-138:
		tmp = t_1
	elif t <= -8.5e-229:
		tmp = 1.0
	elif t <= -4e-259:
		tmp = (y * z) / (x * (-1.0 - x))
	elif t <= 4.6e-146:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.12e-138)
		tmp = t_1;
	elseif (t <= -8.5e-229)
		tmp = 1.0;
	elseif (t <= -4e-259)
		tmp = Float64(Float64(y * z) / Float64(x * Float64(-1.0 - x)));
	elseif (t <= 4.6e-146)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.12e-138)
		tmp = t_1;
	elseif (t <= -8.5e-229)
		tmp = 1.0;
	elseif (t <= -4e-259)
		tmp = (y * z) / (x * (-1.0 - x));
	elseif (t <= 4.6e-146)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.12e-138], t$95$1, If[LessEqual[t, -8.5e-229], 1.0, If[LessEqual[t, -4e-259], N[(N[(y * z), $MachinePrecision] / N[(x * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-146], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1199999999999999e-138 or 4.6000000000000001e-146 < t

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in z around inf 81.7%

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

   if -1.1199999999999999e-138 < t < -8.49999999999999977e-229 or -4.0000000000000003e-259 < t < 4.6000000000000001e-146

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. +-commutative 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in x around inf 70.4%

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

   if -8.49999999999999977e-229 < t < -4.0000000000000003e-259

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 89.0%

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

      1. associate-/l* 89.0%

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

      2. associate-/r* 89.0%

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

      3. +-commutative 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in z around 0 78.0%

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

   9. Taylor expanded in y around 0 78.0%

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

       1. associate-*r/ 78.0%

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

       2. mul-1-neg 78.0%

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

       3. distribute-rgt-neg-out 78.0%

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

       4. +-commutative 78.0%

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

   11. Simplified 78.0%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-138}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-229}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-259}:\\ \;\;\;\;\frac{y \cdot z}{x \cdot \left(-1 - x\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-146}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-243}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-143}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.16e-132)
     t_1
     (if (<= t -9.2e-243)
       1.0
       (if (<= t -3.3e-260)
         (* y (/ z (- (* z t) x)))
         (if (<= t 7.8e-143) 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 <= -1.16e-132) {
		tmp = t_1;
	} else if (t <= -9.2e-243) {
		tmp = 1.0;
	} else if (t <= -3.3e-260) {
		tmp = y * (z / ((z * t) - x));
	} else if (t <= 7.8e-143) {
		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) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.16d-132)) then
        tmp = t_1
    else if (t <= (-9.2d-243)) then
        tmp = 1.0d0
    else if (t <= (-3.3d-260)) then
        tmp = y * (z / ((z * t) - x))
    else if (t <= 7.8d-143) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.16e-132) {
		tmp = t_1;
	} else if (t <= -9.2e-243) {
		tmp = 1.0;
	} else if (t <= -3.3e-260) {
		tmp = y * (z / ((z * t) - x));
	} else if (t <= 7.8e-143) {
		tmp = 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 <= -1.16e-132:
		tmp = t_1
	elif t <= -9.2e-243:
		tmp = 1.0
	elif t <= -3.3e-260:
		tmp = y * (z / ((z * t) - x))
	elif t <= 7.8e-143:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.16e-132)
		tmp = t_1;
	elseif (t <= -9.2e-243)
		tmp = 1.0;
	elseif (t <= -3.3e-260)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	elseif (t <= 7.8e-143)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.16e-132)
		tmp = t_1;
	elseif (t <= -9.2e-243)
		tmp = 1.0;
	elseif (t <= -3.3e-260)
		tmp = y * (z / ((z * t) - x));
	elseif (t <= 7.8e-143)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.16e-132], t$95$1, If[LessEqual[t, -9.2e-243], 1.0, If[LessEqual[t, -3.3e-260], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-143], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1599999999999999e-132 or 7.80000000000000007e-143 < t

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in z around inf 81.7%

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

   if -1.1599999999999999e-132 < t < -9.20000000000000001e-243 or -3.2999999999999997e-260 < t < 7.80000000000000007e-143

   1. Initial program 96.3%

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

      1. *-commutative 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around 0 69.4%

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

      1. +-commutative 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in x around inf 69.2%

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

   if -9.20000000000000001e-243 < t < -3.2999999999999997e-260

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. associate-/l* 87.6%

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

      2. associate-/r* 87.6%

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

      3. +-commutative 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around 0 76.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-132}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-243}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-143}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-243}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-24}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= t -4.2e+82)
     t_1
     (if (<= t -9e-243)
       1.0
       (if (<= t -3.8e-259)
         (* y (/ z (- (* z t) x)))
         (if (<= t 3.1e-24) 1.0 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (t <= -4.2e+82) {
		tmp = t_1;
	} else if (t <= -9e-243) {
		tmp = 1.0;
	} else if (t <= -3.8e-259) {
		tmp = y * (z / ((z * t) - x));
	} else if (t <= 3.1e-24) {
		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) :: tmp
    t_1 = x / (x + 1.0d0)
    if (t <= (-4.2d+82)) then
        tmp = t_1
    else if (t <= (-9d-243)) then
        tmp = 1.0d0
    else if (t <= (-3.8d-259)) then
        tmp = y * (z / ((z * t) - x))
    else if (t <= 3.1d-24) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (t <= -4.2e+82) {
		tmp = t_1;
	} else if (t <= -9e-243) {
		tmp = 1.0;
	} else if (t <= -3.8e-259) {
		tmp = y * (z / ((z * t) - x));
	} else if (t <= 3.1e-24) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if t <= -4.2e+82:
		tmp = t_1
	elif t <= -9e-243:
		tmp = 1.0
	elif t <= -3.8e-259:
		tmp = y * (z / ((z * t) - x))
	elif t <= 3.1e-24:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -4.2e+82)
		tmp = t_1;
	elseif (t <= -9e-243)
		tmp = 1.0;
	elseif (t <= -3.8e-259)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	elseif (t <= 3.1e-24)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (t <= -4.2e+82)
		tmp = t_1;
	elseif (t <= -9e-243)
		tmp = 1.0;
	elseif (t <= -3.8e-259)
		tmp = y * (z / ((z * t) - x));
	elseif (t <= 3.1e-24)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+82], t$95$1, If[LessEqual[t, -9e-243], 1.0, If[LessEqual[t, -3.8e-259], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-24], 1.0, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2e82 or 3.1e-24 < t

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in t around inf 77.2%

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

      1. +-commutative 77.2%

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

   7. Simplified 77.2%

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

   if -4.2e82 < t < -9.00000000000000035e-243 or -3.8e-259 < t < 3.1e-24

   1. Initial program 93.3%

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

      1. *-commutative 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around 0 58.7%

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

      1. +-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in x around inf 56.3%

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

   if -9.00000000000000035e-243 < t < -3.8e-259

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 87.6%

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

      1. associate-/l* 87.6%

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

      2. associate-/r* 87.6%

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

      3. +-commutative 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around 0 76.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-243}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-24}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+57} \lor \neg \left(t \leq 1.05 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.65e+57) (not (<= t 1.05e-131)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (/ (* y (/ z x)) (- -1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.65e+57) || !(t <= 1.05e-131)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y * (z / 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) :: tmp
    if ((t <= (-2.65d+57)) .or. (.not. (t <= 1.05d-131))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((y * (z / x)) / ((-1.0d0) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.65e+57) || !(t <= 1.05e-131)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.65e+57) or not (t <= 1.05e-131):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.65e+57) || !(t <= 1.05e-131))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(y * Float64(z / x)) / Float64(-1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.65e+57) || ~((t <= 1.05e-131)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((y * (z / x)) / (-1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.65e+57], N[Not[LessEqual[t, 1.05e-131]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.64999999999999993e57 or 1.04999999999999999e-131 < t

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in z around inf 87.9%

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

   if -2.64999999999999993e57 < t < 1.04999999999999999e-131

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 79.2%

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

      1. associate-+r+ 79.2%

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

      2. mul-1-neg 79.2%

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

      3. unsub-neg 79.2%

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

      4. +-commutative 79.2%

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

      5. associate-/l* 82.2%

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

      6. +-commutative 82.2%

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

   7. Simplified 82.2%

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

      1. div-sub 82.2%

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

      2. pow1 82.2%

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

      3. pow1 82.2%

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

      4. pow-div 82.2%

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

      5. metadata-eval 82.2%

         \[\leadsto {\left(x + 1\right)}^{\color{blue}{0}} - \frac{y \cdot \frac{z}{x}}{x + 1} \]

      6. metadata-eval 82.2%

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

   9. Applied egg-rr 82.2%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+57} \lor \neg \left(t \leq 1.05 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+81} \lor \neg \left(t \leq 6.2 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e+81) (not (<= t 6.2e-25))) (/ x (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e+81) || !(t <= 6.2e-25)) {
		tmp = x / (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 ((t <= (-5.2d+81)) .or. (.not. (t <= 6.2d-25))) then
        tmp = x / (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 ((t <= -5.2e+81) || !(t <= 6.2e-25)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.2e+81) or not (t <= 6.2e-25):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.2e+81) || !(t <= 6.2e-25))
		tmp = Float64(x / 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 ((t <= -5.2e+81) || ~((t <= 6.2e-25)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.2e+81], N[Not[LessEqual[t, 6.2e-25]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999984e81 or 6.19999999999999989e-25 < t

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in t around inf 77.2%

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

      1. +-commutative 77.2%

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

   7. Simplified 77.2%

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

   if -5.19999999999999984e81 < t < 6.19999999999999989e-25

   1. Initial program 93.7%

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

      1. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in y around 0 55.8%

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

      1. +-commutative 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in x around inf 53.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+81} \lor \neg \left(t \leq 6.2 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-97}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-150}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.2e-97) 1.0 (if (<= x 1.15e-150) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.2e-97) {
		tmp = 1.0;
	} else if (x <= 1.15e-150) {
		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 <= (-5.2d-97)) then
        tmp = 1.0d0
    else if (x <= 1.15d-150) 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 <= -5.2e-97) {
		tmp = 1.0;
	} else if (x <= 1.15e-150) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.2e-97:
		tmp = 1.0
	elif x <= 1.15e-150:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.2e-97)
		tmp = 1.0;
	elseif (x <= 1.15e-150)
		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 <= -5.2e-97)
		tmp = 1.0;
	elseif (x <= 1.15e-150)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.2e-97], 1.0, If[LessEqual[x, 1.15e-150], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.20000000000000014e-97 or 1.15000000000000001e-150 < x

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in y around 0 82.8%

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

      1. +-commutative 82.8%

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

   7. Simplified 82.8%

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

   8. Taylor expanded in x around inf 73.3%

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

   if -5.20000000000000014e-97 < x < 1.15000000000000001e-150

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in x around 0 50.7%

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

Alternative 9: 53.1% 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 92.3%

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

   1. *-commutative 92.3%

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

3. Simplified 92.3%

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

5. Taylor expanded in y around 0 70.1%

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

   1. +-commutative 70.1%

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

7. Simplified 70.1%

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

8. Taylor expanded in x around inf 55.1%

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

Developer target: 99.6% 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 2024098 
(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)))