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

Percentage Accurate: 89.1% → 98.7%

Time: 9.4s

Alternatives: 12

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.4× speedup

Math

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

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 (/ t_1 z)) (- x (/ x t_1))) (+ x 1.0))
     (-
      (+ (/ y (* t (+ x 1.0))) (/ x (+ x 1.0)))
      (/ x (* (* z 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 / (t_1 / z)) + (x - (x / t_1))) / (x + 1.0);
	} else {
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / ((z * 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 / (t_1 / z)) + (x - (x / t_1))) / (x + 1.0);
	} else {
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / ((z * 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 / (t_1 / z)) + (x - (x / t_1))) / (x + 1.0)
	else:
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / ((z * 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(t_1 / z)) + Float64(x - Float64(x / t_1))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(y / Float64(t * Float64(x + 1.0))) + Float64(x / Float64(x + 1.0))) - Float64(x / Float64(Float64(z * 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 / (t_1 / z)) + (x - (x / t_1))) / (x + 1.0);
	else
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / ((z * 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[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(z * t), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $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 94.4%

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

      1. *-commutative 94.4%

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

   3. Simplified 94.4%

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

      1. +-commutative 94.4%

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

      2. div-sub 94.5%

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

      3. associate-+l- 94.5%

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

      4. associate-/l* 98.1%

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

   5. Applied egg-rr 98.1%

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

   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 t around inf 100.0%

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

4. Final simplification 98.3%

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

Alternative 2: 94.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+125} \lor \neg \left(z \leq 6.4 \cdot 10^{+134}\right):\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{\left(z \cdot t\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.25e+125) (not (<= z 6.4e+134)))
   (- (+ (/ y (* t (+ x 1.0))) (/ x (+ x 1.0))) (/ x (* (* z t) (+ x 1.0))))
   (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.25e+125) || !(z <= 6.4e+134)) {
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / ((z * t) * (x + 1.0)));
	} else {
		tmp = (x + (((y * z) - 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 <= (-3.25d+125)) .or. (.not. (z <= 6.4d+134))) then
        tmp = ((y / (t * (x + 1.0d0))) + (x / (x + 1.0d0))) - (x / ((z * t) * (x + 1.0d0)))
    else
        tmp = (x + (((y * z) - 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 <= -3.25e+125) || !(z <= 6.4e+134)) {
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / ((z * t) * (x + 1.0)));
	} else {
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.25e+125) or not (z <= 6.4e+134):
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / ((z * t) * (x + 1.0)))
	else:
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.25e+125) || !(z <= 6.4e+134))
		tmp = Float64(Float64(Float64(y / Float64(t * Float64(x + 1.0))) + Float64(x / Float64(x + 1.0))) - Float64(x / Float64(Float64(z * t) * Float64(x + 1.0))));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(y * z) - 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 <= -3.25e+125) || ~((z <= 6.4e+134)))
		tmp = ((y / (t * (x + 1.0))) + (x / (x + 1.0))) - (x / ((z * t) * (x + 1.0)));
	else
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.25e+125], N[Not[LessEqual[z, 6.4e+134]], $MachinePrecision]], N[(N[(N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(z * t), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / 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 < -3.2499999999999999e125 or 6.4000000000000001e134 < z

   1. Initial program 64.8%

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

      1. *-commutative 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in t around inf 95.1%

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

   if -3.2499999999999999e125 < z < 6.4000000000000001e134

   1. Initial program 98.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+125} \lor \neg \left(z \leq 6.4 \cdot 10^{+134}\right):\\ \;\;\;\;\left(\frac{y}{t \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right) - \frac{x}{\left(z \cdot t\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 3: 94.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+125} \lor \neg \left(z \leq 1.9 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e+125) (not (<= z 1.9e+140)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+125) || !(z <= 1.9e+140)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((y * z) - 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 <= (-3.2d+125)) .or. (.not. (z <= 1.9d+140))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (((y * z) - 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 <= -3.2e+125) || !(z <= 1.9e+140)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e+125) or not (z <= 1.9e+140):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e+125) || !(z <= 1.9e+140))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(y * z) - 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 <= -3.2e+125) || ~((z <= 1.9e+140)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e+125], N[Not[LessEqual[z, 1.9e+140]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / 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 < -3.19999999999999983e125 or 1.9e140 < z

   1. Initial program 65.6%

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

      1. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in z around inf 95.0%

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

   if -3.19999999999999983e125 < z < 1.9e140

   1. Initial program 97.9%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+125} \lor \neg \left(z \leq 1.9 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 4: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))) (t_2 (* y (/ z (- (* z t) x)))))
   (if (<= x -1.8e-84)
     t_1
     (if (<= x 4.1e-157)
       t_2
       (if (<= x 7.2e-35) 1.0 (if (<= x 5e-12) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.8e-84) {
		tmp = t_1;
	} else if (x <= 4.1e-157) {
		tmp = t_2;
	} else if (x <= 7.2e-35) {
		tmp = 1.0;
	} else if (x <= 5e-12) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    t_2 = y * (z / ((z * t) - x))
    if (x <= (-1.8d-84)) then
        tmp = t_1
    else if (x <= 4.1d-157) then
        tmp = t_2
    else if (x <= 7.2d-35) then
        tmp = 1.0d0
    else if (x <= 5d-12) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.8e-84) {
		tmp = t_1;
	} else if (x <= 4.1e-157) {
		tmp = t_2;
	} else if (x <= 7.2e-35) {
		tmp = 1.0;
	} else if (x <= 5e-12) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	t_2 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -1.8e-84:
		tmp = t_1
	elif x <= 4.1e-157:
		tmp = t_2
	elif x <= 7.2e-35:
		tmp = 1.0
	elif x <= 5e-12:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (x <= -1.8e-84)
		tmp = t_1;
	elseif (x <= 4.1e-157)
		tmp = t_2;
	elseif (x <= 7.2e-35)
		tmp = 1.0;
	elseif (x <= 5e-12)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	t_2 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (x <= -1.8e-84)
		tmp = t_1;
	elseif (x <= 4.1e-157)
		tmp = t_2;
	elseif (x <= 7.2e-35)
		tmp = 1.0;
	elseif (x <= 5e-12)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e-84], t$95$1, If[LessEqual[x, 4.1e-157], t$95$2, If[LessEqual[x, 7.2e-35], 1.0, If[LessEqual[x, 5e-12], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.80000000000000002e-84 or 4.9999999999999997e-12 < x

   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 t around inf 81.6%

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

      1. +-commutative 81.6%

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

   6. Simplified 81.6%

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

   if -1.80000000000000002e-84 < x < 4.1000000000000002e-157 or 7.20000000000000038e-35 < x < 4.9999999999999997e-12

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. *-commutative 58.8%

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

      3. times-frac 61.4%

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

      4. +-commutative 61.4%

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

      5. *-commutative 61.4%

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

   6. Simplified 61.4%

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

   7. Taylor expanded in x around 0 61.4%

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

   if 4.1000000000000002e-157 < x < 7.20000000000000038e-35

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. +-commutative 86.4%

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

      2. div-sub 86.4%

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

      3. associate-+l- 86.4%

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

      4. associate-/l* 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in z around 0 50.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 5: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x \cdot x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z (- (* z t) x)))))
   (if (<= x -1.85e-84)
     (/ x (+ x 1.0))
     (if (<= x 4.1e-157)
       t_1
       (if (<= x 9.6e-34)
         1.0
         (if (<= x 1.6e-21) t_1 (- 1.0 (/ y (/ (* x x) z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.85e-84) {
		tmp = x / (x + 1.0);
	} else if (x <= 4.1e-157) {
		tmp = t_1;
	} else if (x <= 9.6e-34) {
		tmp = 1.0;
	} else if (x <= 1.6e-21) {
		tmp = t_1;
	} else {
		tmp = 1.0 - (y / ((x * x) / z));
	}
	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 = y * (z / ((z * t) - x))
    if (x <= (-1.85d-84)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 4.1d-157) then
        tmp = t_1
    else if (x <= 9.6d-34) then
        tmp = 1.0d0
    else if (x <= 1.6d-21) then
        tmp = t_1
    else
        tmp = 1.0d0 - (y / ((x * x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.85e-84) {
		tmp = x / (x + 1.0);
	} else if (x <= 4.1e-157) {
		tmp = t_1;
	} else if (x <= 9.6e-34) {
		tmp = 1.0;
	} else if (x <= 1.6e-21) {
		tmp = t_1;
	} else {
		tmp = 1.0 - (y / ((x * x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -1.85e-84:
		tmp = x / (x + 1.0)
	elif x <= 4.1e-157:
		tmp = t_1
	elif x <= 9.6e-34:
		tmp = 1.0
	elif x <= 1.6e-21:
		tmp = t_1
	else:
		tmp = 1.0 - (y / ((x * x) / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (x <= -1.85e-84)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 4.1e-157)
		tmp = t_1;
	elseif (x <= 9.6e-34)
		tmp = 1.0;
	elseif (x <= 1.6e-21)
		tmp = t_1;
	else
		tmp = Float64(1.0 - Float64(y / Float64(Float64(x * x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (x <= -1.85e-84)
		tmp = x / (x + 1.0);
	elseif (x <= 4.1e-157)
		tmp = t_1;
	elseif (x <= 9.6e-34)
		tmp = 1.0;
	elseif (x <= 1.6e-21)
		tmp = t_1;
	else
		tmp = 1.0 - (y / ((x * x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e-84], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e-157], t$95$1, If[LessEqual[x, 9.6e-34], 1.0, If[LessEqual[x, 1.6e-21], t$95$1, N[(1.0 - N[(y / N[(N[(x * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.85e-84

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around inf 83.7%

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

      1. +-commutative 83.7%

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

   6. Simplified 83.7%

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

   if -1.85e-84 < x < 4.1000000000000002e-157 or 9.59999999999999965e-34 < x < 1.6000000000000001e-21

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in y around inf 58.5%

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

      1. *-commutative 58.5%

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

      2. *-commutative 58.5%

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

      3. times-frac 61.2%

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

      4. +-commutative 61.2%

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

      5. *-commutative 61.2%

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

   6. Simplified 61.2%

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

   7. Taylor expanded in x around 0 61.2%

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

   if 4.1000000000000002e-157 < x < 9.59999999999999965e-34

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. +-commutative 86.4%

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

      2. div-sub 86.4%

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

      3. associate-+l- 86.4%

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

      4. associate-/l* 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in z around 0 50.6%

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

   if 1.6000000000000001e-21 < x

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in t around 0 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. associate-/l* 79.2%

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

      5. +-commutative 79.2%

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

   6. Simplified 79.2%

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

   7. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. associate-/l* 79.3%

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

      4. unpow2 79.3%

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

   9. Simplified 79.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x \cdot x}{z}}\\ \end{array} \]

Alternative 6: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{y}{\frac{t_1}{z}}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{z}{t_1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x \cdot x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= x -1.45e-84)
     (/ x (+ x 1.0))
     (if (<= x 3.6e-157)
       (/ y (/ t_1 z))
       (if (<= x 1.35e-36)
         1.0
         (if (<= x 1.15e-19) (* y (/ z t_1)) (- 1.0 (/ y (/ (* x x) z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (x <= -1.45e-84) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.6e-157) {
		tmp = y / (t_1 / z);
	} else if (x <= 1.35e-36) {
		tmp = 1.0;
	} else if (x <= 1.15e-19) {
		tmp = y * (z / t_1);
	} else {
		tmp = 1.0 - (y / ((x * x) / z));
	}
	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 = (z * t) - x
    if (x <= (-1.45d-84)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 3.6d-157) then
        tmp = y / (t_1 / z)
    else if (x <= 1.35d-36) then
        tmp = 1.0d0
    else if (x <= 1.15d-19) then
        tmp = y * (z / t_1)
    else
        tmp = 1.0d0 - (y / ((x * x) / z))
    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 tmp;
	if (x <= -1.45e-84) {
		tmp = x / (x + 1.0);
	} else if (x <= 3.6e-157) {
		tmp = y / (t_1 / z);
	} else if (x <= 1.35e-36) {
		tmp = 1.0;
	} else if (x <= 1.15e-19) {
		tmp = y * (z / t_1);
	} else {
		tmp = 1.0 - (y / ((x * x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if x <= -1.45e-84:
		tmp = x / (x + 1.0)
	elif x <= 3.6e-157:
		tmp = y / (t_1 / z)
	elif x <= 1.35e-36:
		tmp = 1.0
	elif x <= 1.15e-19:
		tmp = y * (z / t_1)
	else:
		tmp = 1.0 - (y / ((x * x) / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (x <= -1.45e-84)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 3.6e-157)
		tmp = Float64(y / Float64(t_1 / z));
	elseif (x <= 1.35e-36)
		tmp = 1.0;
	elseif (x <= 1.15e-19)
		tmp = Float64(y * Float64(z / t_1));
	else
		tmp = Float64(1.0 - Float64(y / Float64(Float64(x * x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if (x <= -1.45e-84)
		tmp = x / (x + 1.0);
	elseif (x <= 3.6e-157)
		tmp = y / (t_1 / z);
	elseif (x <= 1.35e-36)
		tmp = 1.0;
	elseif (x <= 1.15e-19)
		tmp = y * (z / t_1);
	else
		tmp = 1.0 - (y / ((x * x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, -1.45e-84], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e-157], N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e-36], 1.0, If[LessEqual[x, 1.15e-19], N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y / N[(N[(x * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.4500000000000001e-84

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around inf 83.7%

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

      1. +-commutative 83.7%

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

   6. Simplified 83.7%

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

   if -1.4500000000000001e-84 < x < 3.6e-157

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in y around inf 56.2%

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

      1. *-commutative 56.2%

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

      2. *-commutative 56.2%

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

      3. times-frac 59.0%

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

      4. +-commutative 59.0%

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

      5. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in x around 0 59.0%

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

   8. Taylor expanded in y around 0 56.2%

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

      1. fma-neg 56.2%

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

      2. associate-/l* 59.2%

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

      3. fma-neg 59.2%

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

   10. Simplified 59.2%

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

   if 3.6e-157 < x < 1.35000000000000004e-36

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

      1. +-commutative 86.4%

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

      2. div-sub 86.4%

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

      3. associate-+l- 86.4%

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

      4. associate-/l* 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in z around 0 50.6%

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

   if 1.35000000000000004e-36 < x < 1.1499999999999999e-19

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around inf 99.2%

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

      1. *-commutative 99.2%

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

      2. *-commutative 99.2%

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

      3. times-frac 99.6%

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

      4. +-commutative 99.6%

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

      5. *-commutative 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in x around 0 99.6%

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

   if 1.1499999999999999e-19 < x

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in t around 0 72.6%

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

      1. +-commutative 72.6%

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

      2. mul-1-neg 72.6%

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

      3. unsub-neg 72.6%

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

      4. associate-/l* 79.2%

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

      5. +-commutative 79.2%

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

   6. Simplified 79.2%

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

   7. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

      3. associate-/l* 79.3%

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

      4. unpow2 79.3%

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

   9. Simplified 79.3%

      \[\leadsto \color{blue}{1 - \frac{y}{\frac{x \cdot x}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-157}:\\ \;\;\;\;\frac{y}{\frac{z \cdot t - x}{z}}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x \cdot x}{z}}\\ \end{array} \]

Alternative 7: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-39} \lor \neg \left(t \leq 5.9 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - \frac{y}{\frac{x}{z}}\right) + 1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e-39) (not (<= t 5.9e-36)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ (- x (/ y (/ x z))) 1.0) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-39) || !(t <= 5.9e-36)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x - (y / (x / z))) + 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 <= (-3.5d-39)) .or. (.not. (t <= 5.9d-36))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((x - (y / (x / z))) + 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 <= -3.5e-39) || !(t <= 5.9e-36)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e-39) or not (t <= 5.9e-36):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e-39) || !(t <= 5.9e-36))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x - Float64(y / Float64(x / z))) + 1.0) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.5e-39) || ~((t <= 5.9e-36)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((x - (y / (x / z))) + 1.0) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e-39], N[Not[LessEqual[t, 5.9e-36]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5e-39 or 5.89999999999999995e-36 < t

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in z around inf 92.0%

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

   if -3.5e-39 < t < 5.89999999999999995e-36

   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. Taylor expanded in t around 0 78.1%

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

      1. +-commutative 78.1%

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

      2. mul-1-neg 78.1%

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

      3. unsub-neg 78.1%

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

      4. associate-/l* 82.7%

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

      5. +-commutative 82.7%

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

   6. Simplified 82.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-39} \lor \neg \left(t \leq 5.9 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - \frac{y}{\frac{x}{z}}\right) + 1}{x + 1}\\ \end{array} \]

Alternative 8: 75.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-113} \lor \neg \left(t \leq 1.32 \cdot 10^{-176}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{x} \cdot \frac{t - y}{x} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-113) (not (<= t 1.32e-176)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ (* (/ z x) (/ (- t y) x)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-113) || !(t <= 1.32e-176)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((z / x) * ((t - y) / 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 <= (-6.2d-113)) .or. (.not. (t <= 1.32d-176))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((z / x) * ((t - y) / 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 <= -6.2e-113) || !(t <= 1.32e-176)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((z / x) * ((t - y) / x)) + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-113) or not (t <= 1.32e-176):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((z / x) * ((t - y) / x)) + 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-113) || !(t <= 1.32e-176))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(z / x) * Float64(Float64(t - y) / x)) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.2e-113) || ~((t <= 1.32e-176)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((z / x) * ((t - y) / x)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.2e-113], N[Not[LessEqual[t, 1.32e-176]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / x), $MachinePrecision] * N[(N[(t - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000024e-113 or 1.32e-176 < t

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 86.7%

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

   if -6.20000000000000024e-113 < t < 1.32e-176

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around -inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

      3. distribute-rgt-out-- 61.1%

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

      4. unpow2 61.1%

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

      5. times-frac 65.3%

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

   6. Simplified 65.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-113} \lor \neg \left(t \leq 1.32 \cdot 10^{-176}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{x} \cdot \frac{t - y}{x} + 1\\ \end{array} \]

Alternative 9: 75.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-109} \lor \neg \left(t \leq 2.1 \cdot 10^{-182}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x \cdot x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.9e-109) (not (<= t 2.1e-182)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ y (/ (* x x) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.9e-109) || !(t <= 2.1e-182)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y / ((x * x) / z));
	}
	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 <= (-1.9d-109)) .or. (.not. (t <= 2.1d-182))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y / ((x * x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.9e-109) || !(t <= 2.1e-182)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y / ((x * x) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.9e-109) or not (t <= 2.1e-182):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (y / ((x * x) / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.9e-109) || !(t <= 2.1e-182))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y / Float64(Float64(x * x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.9e-109) || ~((t <= 2.1e-182)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (y / ((x * x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.9e-109], N[Not[LessEqual[t, 2.1e-182]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y / N[(N[(x * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.90000000000000001e-109 or 2.1e-182 < t

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in z around inf 86.7%

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

   if -1.90000000000000001e-109 < t < 2.1e-182

   1. Initial program 95.9%

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

      1. *-commutative 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. +-commutative 83.0%

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

      2. mul-1-neg 83.0%

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

      3. unsub-neg 83.0%

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

      4. associate-/l* 86.9%

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

      5. +-commutative 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

      3. associate-/l* 62.6%

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

      4. unpow2 62.6%

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

   9. Simplified 62.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-109} \lor \neg \left(t \leq 2.1 \cdot 10^{-182}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x \cdot x}{z}}\\ \end{array} \]

Alternative 10: 67.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0066:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.0066) 1.0 (if (<= x 1.6e-111) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.0066) {
		tmp = 1.0;
	} else if (x <= 1.6e-111) {
		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 <= (-0.0066d0)) then
        tmp = 1.0d0
    else if (x <= 1.6d-111) 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 <= -0.0066) {
		tmp = 1.0;
	} else if (x <= 1.6e-111) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.0066:
		tmp = 1.0
	elif x <= 1.6e-111:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.0066)
		tmp = 1.0;
	elseif (x <= 1.6e-111)
		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 <= -0.0066)
		tmp = 1.0;
	elseif (x <= 1.6e-111)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.0066], 1.0, If[LessEqual[x, 1.6e-111], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0066 or 1.5999999999999999e-111 < x

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

      1. +-commutative 87.2%

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

      2. div-sub 87.2%

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

      3. associate-+l- 87.2%

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

      4. associate-/l* 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in z around 0 80.0%

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

   if -0.0066 < x < 1.5999999999999999e-111

   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 z around inf 71.4%

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

   5. Taylor expanded in y around inf 46.2%

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

   6. Taylor expanded in x around 0 46.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0066:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 67.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8e-114) (/ x (+ x 1.0)) (if (<= x 9e-111) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-114) {
		tmp = x / (x + 1.0);
	} else if (x <= 9e-111) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.8d-114)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 9d-111) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-114) {
		tmp = x / (x + 1.0);
	} else if (x <= 9e-111) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e-114:
		tmp = x / (x + 1.0)
	elif x <= 9e-111:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e-114)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 9e-111)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.8e-114)
		tmp = x / (x + 1.0);
	elseif (x <= 9e-111)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e-114], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-111], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -1.80000000000000009e-114

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around inf 81.3%

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

      1. +-commutative 81.3%

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

   6. Simplified 81.3%

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

   if -1.80000000000000009e-114 < x < 8.99999999999999987e-111

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in z around inf 71.3%

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

   5. Taylor expanded in y around inf 51.6%

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

   6. Taylor expanded in x around 0 51.6%

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

   if 8.99999999999999987e-111 < x

   1. Initial program 82.7%

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

      1. *-commutative 82.7%

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

   3. Simplified 82.7%

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

      1. +-commutative 82.7%

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

      2. div-sub 82.7%

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

      3. associate-+l- 82.7%

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

      4. associate-/l* 92.8%

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

   5. Applied egg-rr 92.8%

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

   6. Taylor expanded in z around 0 67.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 53.7% 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 87.8%

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

   1. *-commutative 87.8%

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

3. Simplified 87.8%

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

   1. +-commutative 87.8%

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

   2. div-sub 87.8%

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

   3. associate-+l- 87.8%

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

   4. associate-/l* 93.7%

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

5. Applied egg-rr 93.7%

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

6. Taylor expanded in z around 0 54.3%

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

7. Final simplification 54.3%

   \[\leadsto 1 \]

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 2023200 
(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)))