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

Percentage Accurate: 89.3% → 97.6%

Time: 17.7s

Alternatives: 11

Speedup: 0.2×

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: 89.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{y \cdot \left(\left(\frac{x}{y} + \frac{z}{t\_1}\right) + \frac{x}{y \cdot \left(x - z \cdot t\right)}\right)}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{-297}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2
         (/
          (* y (+ (+ (/ x y) (/ z t_1)) (/ x (* y (- x (* z t))))))
          (+ x 1.0)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -2e-297)
     t_2
     (if (<= t_3 2.0)
       t_3
       (if (<= t_3 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * (((x / y) + (z / t_1)) + (x / (y * (x - (z * t)))))) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -2e-297) {
		tmp = t_2;
	} else if (t_3 <= 2.0) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * (((x / y) + (z / t_1)) + (x / (y * (x - (z * t)))))) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -2e-297) {
		tmp = t_2;
	} else if (t_3 <= 2.0) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (y * (((x / y) + (z / t_1)) + (x / (y * (x - (z * t)))))) / (x + 1.0)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -2e-297:
		tmp = t_2
	elif t_3 <= 2.0:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(y * Float64(Float64(Float64(x / y) + Float64(z / t_1)) + Float64(x / Float64(y * Float64(x - Float64(z * t)))))) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -2e-297)
		tmp = t_2;
	elseif (t_3 <= 2.0)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (y * (((x / y) + (z / t_1)) + (x / (y * (x - (z * t)))))) / (x + 1.0);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -2e-297)
		tmp = t_2;
	elseif (t_3 <= 2.0)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(N[(x / y), $MachinePrecision] + N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y * N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-297], t$95$2, If[LessEqual[t$95$3, 2.0], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -2.00000000000000008e-297 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 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 y around inf 97.7%

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

   if -2.00000000000000008e-297 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 99.9%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -2 \cdot 10^{-297}:\\ \;\;\;\;\frac{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z \cdot t - x}\right) + \frac{x}{y \cdot \left(x - z \cdot t\right)}\right)}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y \cdot \left(\left(\frac{x}{y} + \frac{z}{z \cdot t - x}\right) + \frac{x}{y \cdot \left(x - z \cdot t\right)}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + y \cdot \frac{z}{t\_1}}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (+ x (* y (/ z t_1))) (+ x 1.0)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 4e+60)
       t_3
       (if (<= t_3 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (y * (z / t_1))) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= 4e+60) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (y * (z / t_1))) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= 4e+60) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (y * (z / t_1))) / (x + 1.0)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= 4e+60:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t_1))) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= 4e+60)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (y * (z / t_1))) / (x + 1.0);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= 4e+60)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, 4e+60], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -inf.0 or 3.9999999999999998e60 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

      1. div-inv 63.1%

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

      2. fma-neg 63.1%

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

   6. Applied egg-rr 63.1%

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

   7. Taylor expanded in y around inf 63.1%

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

      1. associate-/l* 97.5%

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

   9. Simplified 97.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 3.9999999999999998e60

   1. Initial program 99.5%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-21} \lor \neg \left(y \leq 8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7e-21) (not (<= y 8e-63)))
   (/ (+ x (* y (/ z (- (* z t) x)))) (+ x 1.0))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e-21) || !(y <= 8e-63)) {
		tmp = (x + (y * (z / ((z * t) - x)))) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * 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) :: tmp
    if ((y <= (-7d-21)) .or. (.not. (y <= 8d-63))) then
        tmp = (x + (y * (z / ((z * t) - x)))) / (x + 1.0d0)
    else
        tmp = (x + (x / (x - (z * t)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e-21) || !(y <= 8e-63)) {
		tmp = (x + (y * (z / ((z * t) - x)))) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7e-21) or not (y <= 8e-63):
		tmp = (x + (y * (z / ((z * t) - x)))) / (x + 1.0)
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7e-21) || !(y <= 8e-63))
		tmp = Float64(Float64(x + Float64(y * Float64(z / Float64(Float64(z * t) - x)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7e-21) || ~((y <= 8e-63)))
		tmp = (x + (y * (z / ((z * t) - x)))) / (x + 1.0);
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7e-21], N[Not[LessEqual[y, 8e-63]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000007e-21 or 8.00000000000000053e-63 < y

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

   3. Simplified 83.6%

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

      1. div-inv 83.5%

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

      2. fma-neg 83.6%

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

   6. Applied egg-rr 83.6%

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

   7. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 89.8%

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

   9. Simplified 89.8%

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

   if -7.0000000000000007e-21 < y < 8.00000000000000053e-63

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 93.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-21} \lor \neg \left(y \leq 8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-149} \lor \neg \left(t \leq 3.7 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{\frac{y}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-149) (not (<= t 3.7e-101)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* z (/ (/ y x) (- -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-149) || !(t <= 3.7e-101)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (z * ((y / 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 <= (-6.2d-149)) .or. (.not. (t <= 3.7d-101))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + (z * ((y / 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 <= -6.2e-149) || !(t <= 3.7e-101)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-149) or not (t <= 3.7e-101):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-149) || !(t <= 3.7e-101))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(z * Float64(Float64(y / x) / Float64(-1.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.2e-149) || ~((t <= 3.7e-101)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.2e-149], N[Not[LessEqual[t, 3.7e-101]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(N[(y / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.19999999999999974e-149 or 3.70000000000000005e-101 < t

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around inf 85.5%

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

   if -6.19999999999999974e-149 < t < 3.70000000000000005e-101

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in z around 0 80.9%

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

   6. Taylor expanded in y around inf 81.0%

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

      1. associate-*r/ 81.0%

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

      2. +-commutative 81.0%

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

      3. associate-/r* 85.5%

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

      4. mul-1-neg 85.5%

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

   8. Simplified 85.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-149} \lor \neg \left(t \leq 3.7 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{\frac{y}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-150} \lor \neg \left(t \leq 5.5 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.5e-150) (not (<= t 5.5e-101)))
   (/ (+ 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 <= -6.5e-150) || !(t <= 5.5e-101)) {
		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 <= (-6.5d-150)) .or. (.not. (t <= 5.5d-101))) 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 <= -6.5e-150) || !(t <= 5.5e-101)) {
		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 <= -6.5e-150) or not (t <= 5.5e-101):
		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 <= -6.5e-150) || !(t <= 5.5e-101))
		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 <= -6.5e-150) || ~((t <= 5.5e-101)))
		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, -6.5e-150], N[Not[LessEqual[t, 5.5e-101]], $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 < -6.49999999999999997e-150 or 5.49999999999999973e-101 < t

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around inf 85.5%

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

   if -6.49999999999999997e-150 < t < 5.49999999999999973e-101

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in t around 0 76.4%

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

      1. associate-+r+ 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

      4. +-commutative 76.4%

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

      5. associate-/l* 85.5%

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

      6. +-commutative 85.5%

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

   7. Simplified 85.5%

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

      1. div-sub 85.5%

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

      2. pow1 85.5%

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

      3. pow1 85.5%

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

      4. pow-div 85.5%

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

      5. metadata-eval 85.5%

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

      6. metadata-eval 85.5%

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

   9. Applied egg-rr 85.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-150} \lor \neg \left(t \leq 5.5 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \frac{z}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-52}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-73}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e-52)
   1.0
   (if (<= x 1.6e-73) (/ y t) (if (<= x 1.3e-5) (* x (- 1.0 x)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e-52) {
		tmp = 1.0;
	} else if (x <= 1.6e-73) {
		tmp = y / t;
	} else if (x <= 1.3e-5) {
		tmp = x * (1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-5.8d-52)) then
        tmp = 1.0d0
    else if (x <= 1.6d-73) then
        tmp = y / t
    else if (x <= 1.3d-5) then
        tmp = x * (1.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e-52) {
		tmp = 1.0;
	} else if (x <= 1.6e-73) {
		tmp = y / t;
	} else if (x <= 1.3e-5) {
		tmp = x * (1.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.8e-52:
		tmp = 1.0
	elif x <= 1.6e-73:
		tmp = y / t
	elif x <= 1.3e-5:
		tmp = x * (1.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.8e-52)
		tmp = 1.0;
	elseif (x <= 1.6e-73)
		tmp = Float64(y / t);
	elseif (x <= 1.3e-5)
		tmp = Float64(x * Float64(1.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.8e-52)
		tmp = 1.0;
	elseif (x <= 1.6e-73)
		tmp = y / t;
	elseif (x <= 1.3e-5)
		tmp = x * (1.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.8e-52], 1.0, If[LessEqual[x, 1.6e-73], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.3e-5], N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.8000000000000003e-52 or 1.29999999999999992e-5 < x

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

   3. Simplified 88.2%

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

      1. div-inv 88.2%

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

      2. fma-neg 88.2%

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

   6. Applied egg-rr 88.2%

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

   7. Taylor expanded in y around inf 81.0%

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

      1. associate-/l* 92.0%

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

   9. Simplified 92.0%

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

   10. Taylor expanded in x around inf 79.7%

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

   if -5.8000000000000003e-52 < x < 1.59999999999999993e-73

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around inf 75.1%

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

   6. Taylor expanded in x around 0 56.7%

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

   if 1.59999999999999993e-73 < x < 1.29999999999999992e-5

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around inf 58.7%

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

      1. +-commutative 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in x around 0 57.9%

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

      1. neg-mul-1 57.9%

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

      2. sub-neg 57.9%

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

   10. Simplified 57.9%

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

Alternative 7: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-104} \lor \neg \left(z \leq 1.02 \cdot 10^{-173}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{t - y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.3e-104) (not (<= z 1.02e-173)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* z (/ (- t y) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e-104) || !(z <= 1.02e-173)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (z * ((t - y) / 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 ((z <= (-5.3d-104)) .or. (.not. (z <= 1.02d-173))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + (z * ((t - y) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.3e-104) || !(z <= 1.02e-173)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (z * ((t - y) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.3e-104) or not (z <= 1.02e-173):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (z * ((t - y) / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.3e-104) || !(z <= 1.02e-173))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(z * Float64(Float64(t - y) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.3e-104) || ~((z <= 1.02e-173)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (z * ((t - y) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.3e-104], N[Not[LessEqual[z, 1.02e-173]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(N[(t - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.30000000000000018e-104 or 1.02000000000000006e-173 < z

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in z around inf 82.0%

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

   if -5.30000000000000018e-104 < z < 1.02000000000000006e-173

   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 z around 0 77.6%

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

   6. Taylor expanded in x around 0 79.9%

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

      1. associate-/l* 75.6%

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

      2. mul-1-neg 75.6%

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

      3. sub-neg 75.6%

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

   8. Simplified 75.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-104} \lor \neg \left(z \leq 1.02 \cdot 10^{-173}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{t - y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-54}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-54) 1.0 (if (<= x 3.4e-75) (/ y t) (if (<= x 3e-13) x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-54) {
		tmp = 1.0;
	} else if (x <= 3.4e-75) {
		tmp = y / t;
	} else if (x <= 3e-13) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.6d-54)) then
        tmp = 1.0d0
    else if (x <= 3.4d-75) then
        tmp = y / t
    else if (x <= 3d-13) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-54) {
		tmp = 1.0;
	} else if (x <= 3.4e-75) {
		tmp = y / t;
	} else if (x <= 3e-13) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-54:
		tmp = 1.0
	elif x <= 3.4e-75:
		tmp = y / t
	elif x <= 3e-13:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-54)
		tmp = 1.0;
	elseif (x <= 3.4e-75)
		tmp = Float64(y / t);
	elseif (x <= 3e-13)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e-54)
		tmp = 1.0;
	elseif (x <= 3.4e-75)
		tmp = y / t;
	elseif (x <= 3e-13)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-54], 1.0, If[LessEqual[x, 3.4e-75], N[(y / t), $MachinePrecision], If[LessEqual[x, 3e-13], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.60000000000000002e-54 or 2.99999999999999984e-13 < x

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

   3. Simplified 88.5%

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

      1. div-inv 88.4%

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

      2. fma-neg 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in y around inf 80.8%

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

      1. associate-/l* 91.6%

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

   9. Simplified 91.6%

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

   10. Taylor expanded in x around inf 78.8%

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

   if -2.60000000000000002e-54 < x < 3.40000000000000015e-75

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around inf 75.1%

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

   6. Taylor expanded in x around 0 56.7%

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

   if 3.40000000000000015e-75 < x < 2.99999999999999984e-13

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around inf 57.2%

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

      1. +-commutative 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in x around 0 57.2%

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

      1. neg-mul-1 57.2%

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

      2. sub-neg 57.2%

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

   10. Simplified 57.2%

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

   11. Taylor expanded in x around 0 57.0%

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

Alternative 9: 68.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-54}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-77}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e-54) 1.0 (if (<= x 3.25e-77) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-54) {
		tmp = 1.0;
	} else if (x <= 3.25e-77) {
		tmp = y / t;
	} else {
		tmp = x / (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) :: tmp
    if (x <= (-8.5d-54)) then
        tmp = 1.0d0
    else if (x <= 3.25d-77) then
        tmp = y / t
    else
        tmp = x / (x + 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 <= -8.5e-54) {
		tmp = 1.0;
	} else if (x <= 3.25e-77) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e-54:
		tmp = 1.0
	elif x <= 3.25e-77:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e-54)
		tmp = 1.0;
	elseif (x <= 3.25e-77)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.5e-54)
		tmp = 1.0;
	elseif (x <= 3.25e-77)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e-54], 1.0, If[LessEqual[x, 3.25e-77], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.5e-54

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

   3. Simplified 85.1%

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

      1. div-inv 85.0%

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

      2. fma-neg 85.0%

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

   6. Applied egg-rr 85.0%

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

   7. Taylor expanded in y around inf 72.9%

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

      1. associate-/l* 86.5%

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

   9. Simplified 86.5%

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

   10. Taylor expanded in x around inf 78.2%

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

   if -8.5e-54 < x < 3.25e-77

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around inf 75.1%

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

   6. Taylor expanded in x around 0 56.7%

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

   if 3.25e-77 < x

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around inf 74.3%

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

      1. +-commutative 74.3%

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

   7. Simplified 74.3%

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

Alternative 10: 56.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-72}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.5e-72) 1.0 (if (<= x 6.6e-13) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-72) {
		tmp = 1.0;
	} else if (x <= 6.6e-13) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.5d-72)) then
        tmp = 1.0d0
    else if (x <= 6.6d-13) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-72) {
		tmp = 1.0;
	} else if (x <= 6.6e-13) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.5e-72:
		tmp = 1.0
	elif x <= 6.6e-13:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.5e-72)
		tmp = 1.0;
	elseif (x <= 6.6e-13)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.5e-72)
		tmp = 1.0;
	elseif (x <= 6.6e-13)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.5e-72], 1.0, If[LessEqual[x, 6.6e-13], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999998e-72 or 6.6000000000000001e-13 < x

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

      1. div-inv 89.0%

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

      2. fma-neg 89.0%

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

   6. Applied egg-rr 89.0%

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

   7. Taylor expanded in y around inf 79.7%

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

      1. associate-/l* 90.0%

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

   9. Simplified 90.0%

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

   10. Taylor expanded in x around inf 76.7%

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

   if -2.4999999999999998e-72 < x < 6.6000000000000001e-13

   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 t around inf 28.9%

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

      1. +-commutative 28.9%

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

   7. Simplified 28.9%

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

   8. Taylor expanded in x around 0 28.9%

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

      1. neg-mul-1 28.9%

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

      2. sub-neg 28.9%

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

   10. Simplified 28.9%

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

   11. Taylor expanded in x around 0 28.9%

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

Alternative 11: 53.3% 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 89.7%

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

   1. *-commutative 89.7%

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

3. Simplified 89.7%

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

   1. div-inv 89.7%

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

   2. fma-neg 89.7%

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

6. Applied egg-rr 89.7%

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

7. Taylor expanded in y around inf 78.7%

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

   1. associate-/l* 86.2%

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

9. Simplified 86.2%

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

10. Taylor expanded in x around inf 48.8%

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

Developer target: 99.4% 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 2024110 
(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)))