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

Percentage Accurate: 89.6% → 98.8%

Time: 14.8s

Alternatives: 13

Speedup: 0.4×

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: 89.6% 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: 98.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (((x + (((y * z) - x) / t_1)) / (x + 1.0)) <= ((double) INFINITY)) {
		tmp = ((y * (z / t_1)) + (x - (x / t_1))) / (x + 1.0);
	} 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 tmp;
	if (((x + (((y * z) - x) / t_1)) / (x + 1.0)) <= Double.POSITIVE_INFINITY) {
		tmp = ((y * (z / t_1)) + (x - (x / t_1))) / (x + 1.0);
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0)) <= Inf)
		tmp = Float64(Float64(Float64(y * Float64(z / t_1)) + Float64(x - Float64(x / t_1))) / Float64(x + 1.0));
	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;
	tmp = 0.0;
	if (((x + (((y * z) - x) / t_1)) / (x + 1.0)) <= Inf)
		tmp = ((y * (z / t_1)) + (x - (x / t_1))) / (x + 1.0);
	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]}, If[LessEqual[N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x - N[(x / t$95$1), $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 2 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 93.4%

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

      1. *-commutative 93.4%

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

   3. Simplified 93.4%

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

      1. +-commutative 93.4%

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

      2. div-sub 93.4%

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

      3. associate-+l- 93.4%

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

      4. *-un-lft-identity 93.4%

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

      5. times-frac 98.5%

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

      6. fma-neg 98.5%

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

   5. Applied egg-rr 98.5%

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

      1. fma-udef 98.5%

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

      2. unsub-neg 98.5%

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

      3. /-rgt-identity 98.5%

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

      4. *-commutative 98.5%

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

      5. *-commutative 98.5%

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

   7. Simplified 98.5%

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

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

   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. Taylor expanded in z around inf 100.0%

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

4. Final simplification 98.5%

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

Alternative 2: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+133}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t_1}{z}}}{x + 1}\\ \mathbf{elif}\;t_2 \leq 10^{+267}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -5e+133)
     (/ (+ x (/ y (/ t_1 z))) (+ x 1.0))
     (if (<= t_2 1e+267) t_2 (+ (/ x (+ x 1.0)) (/ y (+ t (* x t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+133) {
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	} else if (t_2 <= 1e+267) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-5d+133)) then
        tmp = (x + (y / (t_1 / z))) / (x + 1.0d0)
    else if (t_2 <= 1d+267) then
        tmp = t_2
    else
        tmp = (x / (x + 1.0d0)) + (y / (t + (x * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+133) {
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	} else if (t_2 <= 1e+267) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -5e+133:
		tmp = (x + (y / (t_1 / z))) / (x + 1.0)
	elif t_2 <= 1e+267:
		tmp = t_2
	else:
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+133)
		tmp = Float64(Float64(x + Float64(y / Float64(t_1 / z))) / Float64(x + 1.0));
	elseif (t_2 <= 1e+267)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t + Float64(x * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -5e+133)
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	elseif (t_2 <= 1e+267)
		tmp = t_2;
	else
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+133], N[(N[(x + N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+267], t$95$2, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t + N[(x * t), $MachinePrecision]), $MachinePrecision]), $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)) < -4.99999999999999961e133

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in y around inf 73.3%

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

      1. associate-/l* 99.6%

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

   6. Simplified 99.6%

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

   if -4.99999999999999961e133 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 9.9999999999999997e266

   1. Initial program 98.3%

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

   if 9.9999999999999997e266 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 22.9%

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

      1. *-commutative 22.9%

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

   3. Simplified 22.9%

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

   4. Taylor expanded in y around inf 22.9%

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

      1. associate-/l* 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in t around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. distribute-lft-in 86.0%

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

      3. *-rgt-identity 86.0%

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

   9. Simplified 86.0%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+133}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{z \cdot t - x}{z}}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+267}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \end{array} \]

Alternative 3: 87.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+55} \lor \neg \left(t \leq 4 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{z \cdot t - x}{z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.85e+55) (not (<= t 4e-47)))
   (+ (/ x (+ x 1.0)) (/ y (+ t (* x t))))
   (/ (+ x (/ y (/ (- (* z t) x) z))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.85e+55) || !(t <= 4e-47)) {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	} else {
		tmp = (x + (y / (((z * t) - x) / z))) / (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 <= (-1.85d+55)) .or. (.not. (t <= 4d-47))) then
        tmp = (x / (x + 1.0d0)) + (y / (t + (x * t)))
    else
        tmp = (x + (y / (((z * t) - x) / z))) / (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 <= -1.85e+55) || !(t <= 4e-47)) {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	} else {
		tmp = (x + (y / (((z * t) - x) / z))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.85e+55) or not (t <= 4e-47):
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)))
	else:
		tmp = (x + (y / (((z * t) - x) / z))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.85e+55) || !(t <= 4e-47))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t + Float64(x * t))));
	else
		tmp = Float64(Float64(x + Float64(y / Float64(Float64(Float64(z * t) - x) / z))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.85e+55) || ~((t <= 4e-47)))
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	else
		tmp = (x + (y / (((z * t) - x) / z))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.85e+55], N[Not[LessEqual[t, 4e-47]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8500000000000001e55 or 3.9999999999999999e-47 < t

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in y around inf 78.6%

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

      1. associate-/l* 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in t around inf 94.5%

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

      1. +-commutative 94.5%

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

      2. distribute-lft-in 94.5%

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

      3. *-rgt-identity 94.5%

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

   9. Simplified 94.5%

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

   if -1.8500000000000001e55 < t < 3.9999999999999999e-47

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around inf 81.3%

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

      1. associate-/l* 88.3%

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

   6. Simplified 88.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+55} \lor \neg \left(t \leq 4 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{z \cdot t - x}{z}}}{x + 1}\\ \end{array} \]

Alternative 4: 81.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-109} \lor \neg \left(t \leq 3.25 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.5e-109) (not (<= t 3.25e-146)))
   (+ (/ x (+ x 1.0)) (/ y (+ t (* x t))))
   (- 1.0 (* (/ y x) (/ z (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e-109) || !(t <= 3.25e-146)) {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	} else {
		tmp = 1.0 - ((y / x) * (z / (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 <= (-1.5d-109)) .or. (.not. (t <= 3.25d-146))) then
        tmp = (x / (x + 1.0d0)) + (y / (t + (x * t)))
    else
        tmp = 1.0d0 - ((y / x) * (z / (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 <= -1.5e-109) || !(t <= 3.25e-146)) {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	} else {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.5e-109) or not (t <= 3.25e-146):
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)))
	else:
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.5e-109) || !(t <= 3.25e-146))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t + Float64(x * t))));
	else
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.5e-109) || ~((t <= 3.25e-146)))
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	else
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.5e-109], N[Not[LessEqual[t, 3.25e-146]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000011e-109 or 3.2499999999999999e-146 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around inf 79.9%

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

      1. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in t around inf 88.1%

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

      1. +-commutative 88.1%

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

      2. distribute-lft-in 88.1%

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

      3. *-rgt-identity 88.1%

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

   9. Simplified 88.1%

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

   if -1.50000000000000011e-109 < t < 3.2499999999999999e-146

   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. Step-by-step derivation

      1. +-commutative 95.4%

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

      2. div-sub 95.4%

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

      3. associate-+l- 95.4%

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

      4. *-un-lft-identity 95.4%

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

      5. times-frac 99.8%

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

      6. fma-neg 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. fma-udef 99.8%

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

      2. unsub-neg 99.8%

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

      3. /-rgt-identity 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around inf 96.9%

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

   9. Taylor expanded in z around 0 74.8%

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

       1. mul-1-neg 74.8%

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

       2. unsub-neg 74.8%

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

       3. times-frac 72.3%

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

   11. Simplified 72.3%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-109} \lor \neg \left(t \leq 3.25 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \]

Alternative 5: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-108} \lor \neg \left(t \leq 3.2 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y \cdot z}{x}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.55e-108) (not (<= t 3.2e-146)))
   (+ (/ x (+ x 1.0)) (/ y (+ t (* x t))))
   (/ (+ x (- 1.0 (/ (* y z) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e-108) || !(t <= 3.2e-146)) {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	} else {
		tmp = (x + (1.0 - ((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 ((t <= (-1.55d-108)) .or. (.not. (t <= 3.2d-146))) then
        tmp = (x / (x + 1.0d0)) + (y / (t + (x * t)))
    else
        tmp = (x + (1.0d0 - ((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 ((t <= -1.55e-108) || !(t <= 3.2e-146)) {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	} else {
		tmp = (x + (1.0 - ((y * z) / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.55e-108) or not (t <= 3.2e-146):
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)))
	else:
		tmp = (x + (1.0 - ((y * z) / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.55e-108) || !(t <= 3.2e-146))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t + Float64(x * t))));
	else
		tmp = Float64(Float64(x + Float64(1.0 - Float64(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 ((t <= -1.55e-108) || ~((t <= 3.2e-146)))
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	else
		tmp = (x + (1.0 - ((y * z) / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.55e-108], N[Not[LessEqual[t, 3.2e-146]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55000000000000007e-108 or 3.1999999999999999e-146 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around inf 79.9%

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

      1. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in t around inf 88.1%

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

      1. +-commutative 88.1%

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

      2. distribute-lft-in 88.1%

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

      3. *-rgt-identity 88.1%

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

   9. Simplified 88.1%

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

   if -1.55000000000000007e-108 < t < 3.1999999999999999e-146

   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 t around 0 74.9%

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

      1. associate-+r+ 74.9%

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

      2. +-commutative 74.9%

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

      3. associate-+l+ 74.9%

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

      4. mul-1-neg 74.9%

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

      5. unsub-neg 74.9%

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

      6. *-commutative 74.9%

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

      7. +-commutative 74.9%

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

   6. Simplified 74.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-108} \lor \neg \left(t \leq 3.2 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y \cdot z}{x}\right)}{x + 1}\\ \end{array} \]

Alternative 6: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-108} \lor \neg \left(t \leq 3.9 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - y \cdot \frac{z}{x}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.5e-108) (not (<= t 3.9e-146)))
   (+ (/ x (+ x 1.0)) (/ y (+ t (* x t))))
   (/ (+ x (- 1.0 (* y (/ z x)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.5e-108) || !(t <= 3.9e-146)) {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	} else {
		tmp = (x + (1.0 - (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 ((t <= (-2.5d-108)) .or. (.not. (t <= 3.9d-146))) then
        tmp = (x / (x + 1.0d0)) + (y / (t + (x * t)))
    else
        tmp = (x + (1.0d0 - (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 ((t <= -2.5e-108) || !(t <= 3.9e-146)) {
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	} else {
		tmp = (x + (1.0 - (y * (z / x)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.5e-108) or not (t <= 3.9e-146):
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)))
	else:
		tmp = (x + (1.0 - (y * (z / x)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.5e-108) || !(t <= 3.9e-146))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t + Float64(x * t))));
	else
		tmp = Float64(Float64(x + Float64(1.0 - Float64(y * Float64(z / x)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.5e-108) || ~((t <= 3.9e-146)))
		tmp = (x / (x + 1.0)) + (y / (t + (x * t)));
	else
		tmp = (x + (1.0 - (y * (z / x)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.5e-108], N[Not[LessEqual[t, 3.9e-146]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5e-108 or 3.90000000000000002e-146 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around inf 79.9%

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

      1. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in t around inf 88.1%

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

      1. +-commutative 88.1%

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

      2. distribute-lft-in 88.1%

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

      3. *-rgt-identity 88.1%

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

   9. Simplified 88.1%

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

   if -2.5e-108 < t < 3.90000000000000002e-146

   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. Step-by-step derivation

      1. +-commutative 95.4%

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

      2. div-sub 95.4%

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

      3. associate-+l- 95.4%

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

      4. *-un-lft-identity 95.4%

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

      5. times-frac 99.8%

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

      6. fma-neg 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. fma-udef 99.8%

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

      2. unsub-neg 99.8%

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

      3. /-rgt-identity 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around inf 96.9%

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

   9. Taylor expanded in z around 0 74.9%

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

       1. +-commutative 74.9%

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

       2. mul-1-neg 74.9%

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

       3. associate-/l* 79.3%

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

       4. sub-neg 79.3%

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

       5. associate-+l- 79.3%

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

       6. *-rgt-identity 79.3%

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

       7. associate-*r/ 79.3%

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

       8. associate-/r/ 79.1%

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

       9. associate-*l/ 79.3%

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

       10. *-lft-identity 79.3%

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

   11. Simplified 79.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-108} \lor \neg \left(t \leq 3.9 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - y \cdot \frac{z}{x}\right)}{x + 1}\\ \end{array} \]

Alternative 7: 81.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-109} \lor \neg \left(t \leq 3.5 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6e-109) (not (<= t 3.5e-146)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* (/ y x) (/ z (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6e-109) || !(t <= 3.5e-146)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / x) * (z / (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 <= (-6d-109)) .or. (.not. (t <= 3.5d-146))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / x) * (z / (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 <= -6e-109) || !(t <= 3.5e-146)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6e-109) or not (t <= 3.5e-146):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6e-109) || !(t <= 3.5e-146))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6e-109) || ~((t <= 3.5e-146)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / x) * (z / (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6e-109], N[Not[LessEqual[t, 3.5e-146]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.00000000000000043e-109 or 3.5000000000000001e-146 < t

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in z around inf 88.0%

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

   if -6.00000000000000043e-109 < t < 3.5000000000000001e-146

   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. Step-by-step derivation

      1. +-commutative 95.4%

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

      2. div-sub 95.4%

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

      3. associate-+l- 95.4%

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

      4. *-un-lft-identity 95.4%

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

      5. times-frac 99.8%

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

      6. fma-neg 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. fma-udef 99.8%

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

      2. unsub-neg 99.8%

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

      3. /-rgt-identity 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around inf 96.9%

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

   9. Taylor expanded in z around 0 74.8%

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

       1. mul-1-neg 74.8%

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

       2. unsub-neg 74.8%

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

       3. times-frac 72.3%

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

   11. Simplified 72.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-109} \lor \neg \left(t \leq 3.5 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x + 1}\\ \end{array} \]

Alternative 8: 77.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+24} \lor \neg \left(x \leq 1.08 \cdot 10^{+73}\right):\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.06e+24) (not (<= x 1.08e+73)))
   (- 1.0 (* (/ z x) (/ y x)))
   (/ (+ x (/ y t)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.06e+24) || !(x <= 1.08e+73)) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.06d+24)) .or. (.not. (x <= 1.08d+73))) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.06e+24) || !(x <= 1.08e+73)) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.06e+24) or not (x <= 1.08e+73):
		tmp = 1.0 - ((z / x) * (y / x))
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.06e+24) || !(x <= 1.08e+73))
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	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)
	tmp = 0.0;
	if ((x <= -1.06e+24) || ~((x <= 1.08e+73)))
		tmp = 1.0 - ((z / x) * (y / x));
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.06e+24], N[Not[LessEqual[x, 1.08e+73]], $MachinePrecision]], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.06e24 or 1.08e73 < 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 x around -inf 77.3%

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

      1. mul-1-neg 77.3%

         \[\leadsto 1 + \color{blue}{\left(-\frac{y \cdot z - t \cdot z}{{x}^{2}}\right)} \]

      2. unsub-neg 77.3%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out-- 77.3%

         \[\leadsto 1 - \frac{\color{blue}{z \cdot \left(y - t\right)}}{{x}^{2}} \]

      4. unpow2 77.3%

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

      5. times-frac 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in y around inf 87.8%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{{x}^{2}}} \]
   8. Step-by-step derivation

      1. *-commutative 87.8%

         \[\leadsto 1 - \frac{\color{blue}{z \cdot y}}{{x}^{2}} \]

      2. unpow2 87.8%

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

      3. times-frac 95.7%

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

   9. Simplified 95.7%

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

   if -1.06e24 < x < 1.08e73

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in z around inf 76.0%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{+24} \lor \neg \left(x \leq 1.08 \cdot 10^{+73}\right):\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 9: 68.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-45} \lor \neg \left(x \leq 1.45 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.8e-45) (not (<= x 1.45e-13)))
   (/ x (+ x 1.0))
   (/ y (* t (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.8e-45) || !(x <= 1.45e-13)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t * (x + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.8d-45)) .or. (.not. (x <= 1.45d-13))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / (t * (x + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.8e-45) || !(x <= 1.45e-13)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t * (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.8e-45) or not (x <= 1.45e-13):
		tmp = x / (x + 1.0)
	else:
		tmp = y / (t * (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.8e-45) || !(x <= 1.45e-13))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.8e-45) || ~((x <= 1.45e-13)))
		tmp = x / (x + 1.0);
	else
		tmp = y / (t * (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.8e-45], N[Not[LessEqual[x, 1.45e-13]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e-45 or 1.4499999999999999e-13 < x

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in t around inf 85.7%

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

      1. +-commutative 85.7%

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

   6. Simplified 85.7%

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

   if -1.8e-45 < x < 1.4499999999999999e-13

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in y around inf 54.6%

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

   5. Taylor expanded in z around inf 62.0%

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

      1. +-commutative 62.0%

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

   7. Simplified 62.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-45} \lor \neg \left(x \leq 1.45 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \]

Alternative 10: 68.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-46} \lor \neg \left(x \leq 2.55 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.5e-46) (not (<= x 2.55e-21))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e-46) || !(x <= 2.55e-21)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-8.5d-46)) .or. (.not. (x <= 2.55d-21))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e-46) || !(x <= 2.55e-21)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.5e-46) or not (x <= 2.55e-21):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.5e-46) || !(x <= 2.55e-21))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.5e-46) || ~((x <= 2.55e-21)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.5e-46], N[Not[LessEqual[x, 2.55e-21]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000001e-46 or 2.55000000000000002e-21 < x

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in t around inf 85.2%

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

      1. +-commutative 85.2%

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

   6. Simplified 85.2%

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

   if -8.5000000000000001e-46 < x < 2.55000000000000002e-21

   1. Initial program 84.3%

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

      1. *-commutative 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in y around inf 54.7%

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

   5. Taylor expanded in x around 0 46.7%

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

      1. *-commutative 46.7%

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

   7. Simplified 46.7%

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

   8. Taylor expanded in y around 0 62.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-46} \lor \neg \left(x \leq 2.55 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]

Alternative 11: 67.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-41}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-41) 1.0 (if (<= x 6.5e-12) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-41) {
		tmp = 1.0;
	} else if (x <= 6.5e-12) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.6d-41)) then
        tmp = 1.0d0
    else if (x <= 6.5d-12) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-41) {
		tmp = 1.0;
	} else if (x <= 6.5e-12) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-41:
		tmp = 1.0
	elif x <= 6.5e-12:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-41)
		tmp = 1.0;
	elseif (x <= 6.5e-12)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e-41)
		tmp = 1.0;
	elseif (x <= 6.5e-12)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-41], 1.0, If[LessEqual[x, 6.5e-12], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e-41 or 6.5000000000000002e-12 < x

   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. Step-by-step derivation

      1. +-commutative 90.6%

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

      2. div-sub 90.6%

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

      3. associate-+l- 90.6%

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

      4. *-un-lft-identity 90.6%

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

      5. times-frac 99.2%

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

      6. fma-neg 99.2%

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

   5. Applied egg-rr 99.2%

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

      1. fma-udef 99.2%

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

      2. unsub-neg 99.2%

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

      3. /-rgt-identity 99.2%

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

      4. *-commutative 99.2%

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

      5. *-commutative 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in z around 0 84.1%

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

   if -2.5999999999999999e-41 < x < 6.5000000000000002e-12

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around inf 54.6%

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

   5. Taylor expanded in x around 0 46.0%

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

      1. *-commutative 46.0%

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

   7. Simplified 46.0%

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

   8. Taylor expanded in y around 0 60.9%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-41}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 56.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-33}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.35e-33) 1.0 (if (<= x 1.4e-9) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.35e-33) {
		tmp = 1.0;
	} else if (x <= 1.4e-9) {
		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 <= (-2.35d-33)) then
        tmp = 1.0d0
    else if (x <= 1.4d-9) 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 <= -2.35e-33) {
		tmp = 1.0;
	} else if (x <= 1.4e-9) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.35e-33:
		tmp = 1.0
	elif x <= 1.4e-9:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.35e-33)
		tmp = 1.0;
	elseif (x <= 1.4e-9)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.35e-33)
		tmp = 1.0;
	elseif (x <= 1.4e-9)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.35e-33], 1.0, If[LessEqual[x, 1.4e-9], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3500000000000001e-33 or 1.39999999999999992e-9 < x

   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. Step-by-step derivation

      1. +-commutative 90.4%

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

      2. div-sub 90.4%

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

      3. associate-+l- 90.4%

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

      4. *-un-lft-identity 90.4%

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

      5. times-frac 99.2%

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

      6. fma-neg 99.2%

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

   5. Applied egg-rr 99.2%

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

      1. fma-udef 99.2%

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

      2. unsub-neg 99.2%

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

      3. /-rgt-identity 99.2%

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

      4. *-commutative 99.2%

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

      5. *-commutative 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in z around 0 85.1%

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

   if -2.3500000000000001e-33 < x < 1.39999999999999992e-9

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around inf 20.9%

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

      1. +-commutative 20.9%

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

   6. Simplified 20.9%

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

   7. Taylor expanded in x around 0 20.6%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-33}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 53.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. *-commutative 87.9%

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

3. Simplified 87.9%

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

   1. +-commutative 87.9%

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

   2. div-sub 87.9%

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

   3. associate-+l- 87.9%

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

   4. *-un-lft-identity 87.9%

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

   5. times-frac 95.1%

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

   6. fma-neg 95.1%

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

5. Applied egg-rr 95.1%

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

   1. fma-udef 95.1%

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

   2. unsub-neg 95.1%

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

   3. /-rgt-identity 95.1%

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

   4. *-commutative 95.1%

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

   5. *-commutative 95.1%

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

7. Simplified 95.1%

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

8. Taylor expanded in z around 0 49.8%

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

9. Final simplification 49.8%

   \[\leadsto 1 \]

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 2023279 
(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)))