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

Percentage Accurate: 89.3% → 97.0%

Time: 11.8s

Alternatives: 13

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: 89.3% 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: 97.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := z \cdot t - x\\ t_3 := \frac{x + \frac{t_1}{t_2}}{x + 1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t_2}}{x + 1}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+254}:\\ \;\;\;\;\frac{x + \frac{t_1}{\mathsf{fma}\left(z, t, -x\right)}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x))
        (t_2 (- (* z t) x))
        (t_3 (/ (+ x (/ t_1 t_2)) (+ x 1.0))))
   (if (<= t_3 (- INFINITY))
     (/ (+ x (* z (/ y t_2))) (+ x 1.0))
     (if (<= t_3 2e+254)
       (/ (+ x (/ t_1 (fma z t (- x)))) (+ x 1.0))
       (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (z * t) - x;
	double t_3 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t_2))) / (x + 1.0);
	} else if (t_3 <= 2e+254) {
		tmp = (x + (t_1 / fma(z, t, -x))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	t_2 = Float64(Float64(z * t) - x)
	t_3 = Float64(Float64(x + Float64(t_1 / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t_2))) / Float64(x + 1.0));
	elseif (t_3 <= 2e+254)
		tmp = Float64(Float64(x + Float64(t_1 / fma(z, t, Float64(-x)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(x + N[(z * N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+254], N[(N[(x + N[(t$95$1 / N[(z * t + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 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 1)) < -inf.0

   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. Taylor expanded in y around inf 38.7%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/r/ 99.8%

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

      4. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.9999999999999999e254

   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. Step-by-step derivation

      1. fma-neg 99.8%

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

   5. Applied egg-rr 99.8%

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

   if 1.9999999999999999e254 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 27.8%

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

      1. *-commutative 27.8%

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

   3. Simplified 27.8%

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

   4. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+254}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{\mathsf{fma}\left(z, t, -x\right)}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t_1}}{x + 1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+254}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

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 (- INFINITY))
     (/ (+ x (* z (/ y t_1))) (+ x 1.0))
     (if (<= t_2 2e+254) 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 <= -((double) INFINITY)) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else if (t_2 <= 2e+254) {
		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) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else if (t_2 <= 2e+254) {
		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 <= -math.inf:
		tmp = (x + (z * (y / t_1))) / (x + 1.0)
	elif t_2 <= 2e+254:
		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 <= Float64(-Inf))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t_1))) / Float64(x + 1.0));
	elseif (t_2 <= 2e+254)
		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 <= -Inf)
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	elseif (t_2 <= 2e+254)
		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, (-Infinity)], N[(N[(x + N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+254], 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 1)) < -inf.0

   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. Taylor expanded in y around inf 38.7%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/r/ 99.8%

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

      4. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.9999999999999999e254

   1. Initial program 99.8%

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

   if 1.9999999999999999e254 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 27.8%

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

      1. *-commutative 27.8%

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

   3. Simplified 27.8%

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

   4. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+254}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 86.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-209} \lor \neg \left(z \leq 3.6 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.7e-209) (not (<= z 3.6e-126)))
   (/ (+ x (* z (/ y (- (* z t) x)))) (+ x 1.0))
   (/ (+ x (/ (- x (* y z)) x)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e-209) || !(z <= 3.6e-126)) {
		tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / 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 ((z <= (-2.7d-209)) .or. (.not. (z <= 3.6d-126))) then
        tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0d0)
    else
        tmp = (x + ((x - (y * z)) / 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 ((z <= -2.7e-209) || !(z <= 3.6e-126)) {
		tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.7e-209) or not (z <= 3.6e-126):
		tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0)
	else:
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.7e-209) || !(z <= 3.6e-126))
		tmp = Float64(Float64(x + Float64(z * Float64(y / Float64(Float64(z * t) - x)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / x)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.7e-209) || ~((z <= 3.6e-126)))
		tmp = (x + (z * (y / ((z * t) - x)))) / (x + 1.0);
	else
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.7e-209], N[Not[LessEqual[z, 3.6e-126]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999998e-209 or 3.5999999999999999e-126 < z

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in y around inf 83.1%

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

      1. associate-/l* 94.4%

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

      2. *-commutative 94.4%

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

      3. associate-/r/ 92.7%

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

      4. *-commutative 92.7%

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

   6. Simplified 92.7%

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

   if -2.69999999999999998e-209 < z < 3.5999999999999999e-126

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 86.2%

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

      1. fma-neg 86.2%

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

      2. associate-*r/ 86.2%

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

      3. neg-mul-1 86.2%

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

      4. neg-sub0 86.2%

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

      5. fma-def 86.2%

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

      6. +-commutative 86.2%

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

      7. associate--r+ 86.2%

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

      8. neg-sub0 86.2%

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

      9. remove-double-neg 86.2%

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

      10. *-commutative 86.2%

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

   6. Simplified 86.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-209} \lor \neg \left(z \leq 3.6 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \]

Alternative 4: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-160} \lor \neg \left(z \leq 6 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e-160) (not (<= z 6e-71)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ (- x (* y z)) x)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-160) || !(z <= 6e-71)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / 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 ((z <= (-4d-160)) .or. (.not. (z <= 6d-71))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + ((x - (y * z)) / 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 ((z <= -4e-160) || !(z <= 6e-71)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4e-160) or not (z <= 6e-71):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e-160) || !(z <= 6e-71))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / x)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e-160) || ~((z <= 6e-71)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e-160], N[Not[LessEqual[z, 6e-71]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e-160 or 6.0000000000000003e-71 < z

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -4e-160 < z < 6.0000000000000003e-71

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 81.4%

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

      1. fma-neg 81.4%

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

      2. associate-*r/ 81.4%

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

      3. neg-mul-1 81.4%

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

      4. neg-sub0 81.4%

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

      5. fma-def 81.4%

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

      6. +-commutative 81.4%

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

      7. associate--r+ 81.4%

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

      8. neg-sub0 81.4%

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

      9. remove-double-neg 81.4%

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

      10. *-commutative 81.4%

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

   6. Simplified 81.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-160} \lor \neg \left(z \leq 6 \cdot 10^{-71}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \]

Alternative 5: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-44} \lor \neg \left(z \leq 4.5 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.3e-44) (not (<= z 4.5e-70)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e-44) || !(z <= 4.5e-70)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - 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 ((z <= (-2.3d-44)) .or. (.not. (z <= 4.5d-70))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - 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 ((z <= -2.3e-44) || !(z <= 4.5e-70)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.3e-44) or not (z <= 4.5e-70):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.3e-44) || !(z <= 4.5e-70))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.3e-44) || ~((z <= 4.5e-70)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.3e-44], N[Not[LessEqual[z, 4.5e-70]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999998e-44 or 4.50000000000000022e-70 < z

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in z around inf 88.4%

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

   if -2.29999999999999998e-44 < z < 4.50000000000000022e-70

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 81.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-44} \lor \neg \left(z \leq 4.5 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 6: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + 1}{x + 1}\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x 1.0) (+ x 1.0))))
   (if (<= x -5.5e-17)
     t_1
     (if (<= x -6.4e-127)
       (* x (+ 1.0 (/ -1.0 (* z t))))
       (if (<= x 1.7e-118) (/ (/ y t) (+ x 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + 1.0) / (x + 1.0);
	double tmp;
	if (x <= -5.5e-17) {
		tmp = t_1;
	} else if (x <= -6.4e-127) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 1.7e-118) {
		tmp = (y / t) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + 1.0d0) / (x + 1.0d0)
    if (x <= (-5.5d-17)) then
        tmp = t_1
    else if (x <= (-6.4d-127)) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z * t)))
    else if (x <= 1.7d-118) then
        tmp = (y / t) / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + 1.0) / (x + 1.0);
	double tmp;
	if (x <= -5.5e-17) {
		tmp = t_1;
	} else if (x <= -6.4e-127) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 1.7e-118) {
		tmp = (y / t) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + 1.0) / (x + 1.0)
	tmp = 0
	if x <= -5.5e-17:
		tmp = t_1
	elif x <= -6.4e-127:
		tmp = x * (1.0 + (-1.0 / (z * t)))
	elif x <= 1.7e-118:
		tmp = (y / t) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + 1.0) / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -5.5e-17)
		tmp = t_1;
	elseif (x <= -6.4e-127)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (x <= 1.7e-118)
		tmp = Float64(Float64(y / t) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + 1.0) / (x + 1.0);
	tmp = 0.0;
	if (x <= -5.5e-17)
		tmp = t_1;
	elseif (x <= -6.4e-127)
		tmp = x * (1.0 + (-1.0 / (z * t)));
	elseif (x <= 1.7e-118)
		tmp = (y / t) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e-17], t$95$1, If[LessEqual[x, -6.4e-127], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-118], N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.50000000000000001e-17 or 1.69999999999999995e-118 < x

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around 0 82.6%

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

   if -5.50000000000000001e-17 < x < -6.40000000000000035e-127

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around 0 67.7%

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

   5. Taylor expanded in x around 0 53.9%

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

   6. Taylor expanded in x around 0 53.9%

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

      1. *-commutative 53.9%

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

   8. Simplified 53.9%

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

   if -6.40000000000000035e-127 < x < 1.69999999999999995e-118

   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. Taylor expanded in z around inf 82.2%

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

   5. Taylor expanded in y around inf 68.8%

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

      1. associate-/r* 68.8%

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

      2. +-commutative 68.8%

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

   7. Simplified 68.8%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \end{array} \]

Alternative 7: 77.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.2e-45)
   (/ (+ x 1.0) (+ x 1.0))
   (if (<= x 6.2e+14) (/ (+ x (/ y t)) (+ x 1.0)) (+ 1.0 (/ -1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-45) {
		tmp = (x + 1.0) / (x + 1.0);
	} else if (x <= 6.2e+14) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (-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 (x <= (-2.2d-45)) then
        tmp = (x + 1.0d0) / (x + 1.0d0)
    else if (x <= 6.2d+14) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((-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 (x <= -2.2e-45) {
		tmp = (x + 1.0) / (x + 1.0);
	} else if (x <= 6.2e+14) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e-45:
		tmp = (x + 1.0) / (x + 1.0)
	elif x <= 6.2e+14:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (-1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.2e-45)
		tmp = Float64(Float64(x + 1.0) / Float64(x + 1.0));
	elseif (x <= 6.2e+14)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.2e-45)
		tmp = (x + 1.0) / (x + 1.0);
	elseif (x <= 6.2e+14)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.2e-45], N[(N[(x + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+14], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.19999999999999993e-45

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in z around 0 86.2%

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

   if -2.19999999999999993e-45 < x < 6.2e14

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in z around inf 73.0%

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

   if 6.2e14 < x

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around inf 96.8%

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

   5. Taylor expanded in x around inf 96.8%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]

Alternative 8: 60.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0115 \lor \neg \left(t \leq 1.1 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.0115) (not (<= t 1.1e+17)))
   (/ x (+ x 1.0))
   (/ (+ x 1.0) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.0115) || !(t <= 1.1e+17)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = (x + 1.0) / (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 ((t <= (-0.0115d0)) .or. (.not. (t <= 1.1d+17))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = (x + 1.0d0) / (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 ((t <= -0.0115) || !(t <= 1.1e+17)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = (x + 1.0) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.0115) or not (t <= 1.1e+17):
		tmp = x / (x + 1.0)
	else:
		tmp = (x + 1.0) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.0115) || !(t <= 1.1e+17))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + 1.0) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.0115) || ~((t <= 1.1e+17)))
		tmp = x / (x + 1.0);
	else
		tmp = (x + 1.0) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.0115], N[Not[LessEqual[t, 1.1e+17]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0115 or 1.1e17 < t

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around inf 72.5%

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

   if -0.0115 < t < 1.1e17

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around 0 49.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0115 \lor \neg \left(t \leq 1.1 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \end{array} \]

Alternative 9: 67.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e-126)
   (/ x (+ x 1.0))
   (if (<= x 1.65e-118) (/ (/ y t) (+ x 1.0)) (/ (+ x 1.0) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e-126) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.65e-118) {
		tmp = (y / t) / (x + 1.0);
	} else {
		tmp = (x + 1.0) / (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 <= (-6d-126)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 1.65d-118) then
        tmp = (y / t) / (x + 1.0d0)
    else
        tmp = (x + 1.0d0) / (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 <= -6e-126) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.65e-118) {
		tmp = (y / t) / (x + 1.0);
	} else {
		tmp = (x + 1.0) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e-126:
		tmp = x / (x + 1.0)
	elif x <= 1.65e-118:
		tmp = (y / t) / (x + 1.0)
	else:
		tmp = (x + 1.0) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e-126)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 1.65e-118)
		tmp = Float64(Float64(y / t) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + 1.0) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6e-126)
		tmp = x / (x + 1.0);
	elseif (x <= 1.65e-118)
		tmp = (y / t) / (x + 1.0);
	else
		tmp = (x + 1.0) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e-126], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-118], N[(N[(y / t), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0000000000000003e-126

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around inf 75.7%

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

   if -6.0000000000000003e-126 < x < 1.65e-118

   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. Taylor expanded in z around inf 82.2%

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

   5. Taylor expanded in y around inf 68.8%

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

      1. associate-/r* 68.8%

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

      2. +-commutative 68.8%

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

   7. Simplified 68.8%

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

   if 1.65e-118 < x

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in z around 0 77.4%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-118}:\\ \;\;\;\;\frac{\frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{x + 1}\\ \end{array} \]

Alternative 10: 45.3% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{-1}{x} \end{array} \]

FPCore

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

C

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

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 + ((-1.0d0) / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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. Taylor expanded in x around inf 54.2%

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

5. Taylor expanded in x around inf 44.3%

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

6. Final simplification 44.3%

   \[\leadsto 1 + \frac{-1}{x} \]

Alternative 11: 55.9% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + 1} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

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. Taylor expanded in x around inf 54.2%

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

5. Final simplification 54.2%

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

Alternative 12: 3.3% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-x)

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. Taylor expanded in x around inf 54.2%

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

   1. frac-2neg 54.2%

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

   2. neg-sub0 54.2%

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

   3. div-sub 54.2%

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

   4. add-sqr-sqrt 26.9%

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

   5. sqrt-unprod 13.8%

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

   6. sqr-neg 13.8%

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

   7. sqrt-unprod 1.3%

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

   8. add-sqr-sqrt 2.6%

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

   9. frac-2neg 2.6%

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

6. Applied egg-rr 2.6%

   \[\leadsto \color{blue}{\frac{0}{-\left(x + 1\right)} - \frac{x}{x + 1}} \]
7. Step-by-step derivation

   1. div0 2.6%

      \[\leadsto \color{blue}{0} - \frac{x}{x + 1} \]

   2. +-commutative 2.6%

      \[\leadsto 0 - \frac{x}{\color{blue}{1 + x}} \]

   3. neg-sub0 2.6%

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

   4. distribute-neg-frac 2.6%

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

   5. +-commutative 2.6%

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

8. Simplified 2.6%

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

9. Taylor expanded in x around 0 3.2%

   \[\leadsto \color{blue}{-1 \cdot x} \]
10. Step-by-step derivation

    1. mul-1-neg 3.2%

       \[\leadsto \color{blue}{-x} \]

11. Simplified 3.2%

    \[\leadsto \color{blue}{-x} \]

12. Final simplification 3.2%

    \[\leadsto -x \]

Alternative 13: 2.6% 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. Taylor expanded in x around inf 54.2%

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

   1. frac-2neg 54.2%

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

   2. neg-sub0 54.2%

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

   3. div-sub 54.2%

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

   4. add-sqr-sqrt 26.9%

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

   5. sqrt-unprod 13.8%

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

   6. sqr-neg 13.8%

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

   7. sqrt-unprod 1.3%

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

   8. add-sqr-sqrt 2.6%

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

   9. frac-2neg 2.6%

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

6. Applied egg-rr 2.6%

   \[\leadsto \color{blue}{\frac{0}{-\left(x + 1\right)} - \frac{x}{x + 1}} \]
7. Step-by-step derivation

   1. div0 2.6%

      \[\leadsto \color{blue}{0} - \frac{x}{x + 1} \]

   2. +-commutative 2.6%

      \[\leadsto 0 - \frac{x}{\color{blue}{1 + x}} \]

   3. neg-sub0 2.6%

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

   4. distribute-neg-frac 2.6%

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

   5. +-commutative 2.6%

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

8. Simplified 2.6%

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

9. Taylor expanded in x around inf 2.6%

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

10. Final simplification 2.6%

    \[\leadsto -1 \]

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 2023332 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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