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

Percentage Accurate: 89.2% → 98.6%

Time: 16.1s

Alternatives: 12

Speedup: 1.0×

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: 89.2% 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: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-6} \lor \neg \left(z \leq 3 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{\mathsf{fma}\left(z, t, -x\right)}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e-6) (not (<= z 3e-13)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ x (/ (- (* z y) x) (fma z t (- x)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-6) || !(z <= 3e-13)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) / fma(z, t, -x))) / (x + 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e-6) || !(z <= 3e-13))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - x) / fma(z, t, Float64(-x)))) / Float64(x + 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e-6], N[Not[LessEqual[z, 3e-13]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(z * t + (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999996e-6 or 2.99999999999999984e-13 < z

   1. Initial program 80.5%

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

      1. *-commutative 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in y around inf 79.8%

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

      1. associate-/l* 91.2%

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

   6. Simplified 91.2%

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

   7. Taylor expanded in t around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

   9. Simplified 98.5%

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

   if -4.1999999999999996e-6 < z < 2.99999999999999984e-13

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. fma-neg 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-6} \lor \neg \left(z \leq 3 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{\mathsf{fma}\left(z, t, -x\right)}}{x + 1}\\ \end{array} \]

Alternative 2: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-5} \lor \neg \left(z \leq 1.15 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-5) (not (<= z 1.15e-41)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-5) || !(z <= 1.15e-41)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - 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 <= (-9d-5)) .or. (.not. (z <= 1.15d-41))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x + (((z * y) - 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 <= -9e-5) || !(z <= 1.15e-41)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-5) or not (z <= 1.15e-41):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-5) || !(z <= 1.15e-41))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - 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 <= -9e-5) || ~((z <= 1.15e-41)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-5], N[Not[LessEqual[z, 1.15e-41]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(N[(z * y), $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 < -9.00000000000000057e-5 or 1.15000000000000005e-41 < z

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in y around inf 80.7%

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

      1. associate-/l* 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in t around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

   9. Simplified 98.5%

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

   if -9.00000000000000057e-5 < z < 1.15000000000000005e-41

   1. Initial program 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-5} \lor \neg \left(z \leq 1.15 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 3: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-302}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ y (/ x z))) (+ x 1.0)))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -3.1e-99)
     t_2
     (if (<= t -1.4e-212)
       t_1
       (if (<= t -3.4e-302) 1.0 (if (<= t 5.9e-61) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (x / z))) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -3.1e-99) {
		tmp = t_2;
	} else if (t <= -1.4e-212) {
		tmp = t_1;
	} else if (t <= -3.4e-302) {
		tmp = 1.0;
	} else if (t <= 5.9e-61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 - (y / (x / z))) / (x + 1.0d0)
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-3.1d-99)) then
        tmp = t_2
    else if (t <= (-1.4d-212)) then
        tmp = t_1
    else if (t <= (-3.4d-302)) then
        tmp = 1.0d0
    else if (t <= 5.9d-61) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (x / z))) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -3.1e-99) {
		tmp = t_2;
	} else if (t <= -1.4e-212) {
		tmp = t_1;
	} else if (t <= -3.4e-302) {
		tmp = 1.0;
	} else if (t <= 5.9e-61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (x / z))) / (x + 1.0)
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -3.1e-99:
		tmp = t_2
	elif t <= -1.4e-212:
		tmp = t_1
	elif t <= -3.4e-302:
		tmp = 1.0
	elif t <= 5.9e-61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -3.1e-99)
		tmp = t_2;
	elseif (t <= -1.4e-212)
		tmp = t_1;
	elseif (t <= -3.4e-302)
		tmp = 1.0;
	elseif (t <= 5.9e-61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (x / z))) / (x + 1.0);
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -3.1e-99)
		tmp = t_2;
	elseif (t <= -1.4e-212)
		tmp = t_1;
	elseif (t <= -3.4e-302)
		tmp = 1.0;
	elseif (t <= 5.9e-61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.1e-99], t$95$2, If[LessEqual[t, -1.4e-212], t$95$1, If[LessEqual[t, -3.4e-302], 1.0, If[LessEqual[t, 5.9e-61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0999999999999999e-99 or 5.89999999999999972e-61 < t

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around inf 90.2%

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

   if -3.0999999999999999e-99 < t < -1.40000000000000007e-212 or -3.4e-302 < t < 5.89999999999999972e-61

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around inf 81.8%

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

      1. associate-/l* 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in t around 0 63.9%

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

      1. +-commutative 63.9%

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

      2. mul-1-neg 63.9%

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

      3. unsub-neg 63.9%

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

      4. associate-/l* 70.5%

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

      5. +-commutative 70.5%

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

   9. Simplified 70.5%

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

   if -1.40000000000000007e-212 < t < -3.4e-302

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in t around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   9. Simplified 58.2%

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

   10. Taylor expanded in x around inf 87.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-99}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-212}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-302}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 4: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-302}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ y (/ x z))) (+ x 1.0))))
   (if (<= t -3.3e-99)
     (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0))))
     (if (<= t -6e-213)
       t_1
       (if (<= t -3.4e-302)
         1.0
         (if (<= t 2.7e-62) t_1 (/ (+ x (/ y t)) (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (x / z))) / (x + 1.0);
	double tmp;
	if (t <= -3.3e-99) {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	} else if (t <= -6e-213) {
		tmp = t_1;
	} else if (t <= -3.4e-302) {
		tmp = 1.0;
	} else if (t <= 2.7e-62) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (x / z))) / (x + 1.0d0)
    if (t <= (-3.3d-99)) then
        tmp = (x / (x + 1.0d0)) + (y / (t * (x + 1.0d0)))
    else if (t <= (-6d-213)) then
        tmp = t_1
    else if (t <= (-3.4d-302)) then
        tmp = 1.0d0
    else if (t <= 2.7d-62) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (x / z))) / (x + 1.0);
	double tmp;
	if (t <= -3.3e-99) {
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	} else if (t <= -6e-213) {
		tmp = t_1;
	} else if (t <= -3.4e-302) {
		tmp = 1.0;
	} else if (t <= 2.7e-62) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (x / z))) / (x + 1.0)
	tmp = 0
	if t <= -3.3e-99:
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)))
	elif t <= -6e-213:
		tmp = t_1
	elif t <= -3.4e-302:
		tmp = 1.0
	elif t <= 2.7e-62:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -3.3e-99)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(x + 1.0))));
	elseif (t <= -6e-213)
		tmp = t_1;
	elseif (t <= -3.4e-302)
		tmp = 1.0;
	elseif (t <= 2.7e-62)
		tmp = t_1;
	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 = (x - (y / (x / z))) / (x + 1.0);
	tmp = 0.0;
	if (t <= -3.3e-99)
		tmp = (x / (x + 1.0)) + (y / (t * (x + 1.0)));
	elseif (t <= -6e-213)
		tmp = t_1;
	elseif (t <= -3.4e-302)
		tmp = 1.0;
	elseif (t <= 2.7e-62)
		tmp = t_1;
	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[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-99], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6e-213], t$95$1, If[LessEqual[t, -3.4e-302], 1.0, If[LessEqual[t, 2.7e-62], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.29999999999999986e-99

   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. Taylor expanded in y around inf 82.7%

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

      1. associate-/l* 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in t around inf 89.7%

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

      1. +-commutative 89.7%

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

      2. *-commutative 89.7%

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

      3. +-commutative 89.7%

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

   9. Simplified 89.7%

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

   if -3.29999999999999986e-99 < t < -5.99999999999999973e-213 or -3.4e-302 < t < 2.70000000000000019e-62

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around inf 81.8%

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

      1. associate-/l* 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in t around 0 63.9%

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

      1. +-commutative 63.9%

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

      2. mul-1-neg 63.9%

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

      3. unsub-neg 63.9%

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

      4. associate-/l* 70.5%

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

      5. +-commutative 70.5%

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

   9. Simplified 70.5%

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

   if -5.99999999999999973e-213 < t < -3.4e-302

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 58.3%

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

      1. associate-/l* 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in t around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. unsub-neg 58.2%

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

   9. Simplified 58.2%

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

   10. Taylor expanded in x around inf 87.6%

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

   if 2.70000000000000019e-62 < t

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in z around inf 90.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-213}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-302}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-62}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 5: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-247} \lor \neg \left(z \leq 5.8 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e-247) (not (<= z 5.8e-110)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-247) || !(z <= 5.8e-110)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6d-247)) .or. (.not. (z <= 5.8d-110))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-247) || !(z <= 5.8e-110)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e-247) or not (z <= 5.8e-110):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e-247) || !(z <= 5.8e-110))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6e-247) || ~((z <= 5.8e-110)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e-247], N[Not[LessEqual[z, 5.8e-110]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999995e-247 or 5.8000000000000005e-110 < z

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in y around inf 84.2%

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

      1. associate-/l* 91.4%

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

   6. Simplified 91.4%

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

   7. Taylor expanded in t around 0 96.0%

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

      1. mul-1-neg 96.0%

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

      2. unsub-neg 96.0%

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

   9. Simplified 96.0%

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

   if -5.9999999999999995e-247 < z < 5.8000000000000005e-110

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 91.2%

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

      1. +-commutative 91.2%

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

   6. Simplified 91.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-247} \lor \neg \left(z \leq 5.8 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 6: 69.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-125}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 0.000185:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -1.95e-44)
     t_1
     (if (<= x 2.15e-125)
       (/ y (* t (+ x 1.0)))
       (if (<= x 0.000185) (* z (/ y (- (* z t) x))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -1.95e-44) {
		tmp = t_1;
	} else if (x <= 2.15e-125) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= 0.000185) {
		tmp = z * (y / ((z * t) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-1.95d-44)) then
        tmp = t_1
    else if (x <= 2.15d-125) then
        tmp = y / (t * (x + 1.0d0))
    else if (x <= 0.000185d0) then
        tmp = z * (y / ((z * t) - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -1.95e-44) {
		tmp = t_1;
	} else if (x <= 2.15e-125) {
		tmp = y / (t * (x + 1.0));
	} else if (x <= 0.000185) {
		tmp = z * (y / ((z * t) - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -1.95e-44:
		tmp = t_1
	elif x <= 2.15e-125:
		tmp = y / (t * (x + 1.0))
	elif x <= 0.000185:
		tmp = z * (y / ((z * t) - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -1.95e-44)
		tmp = t_1;
	elseif (x <= 2.15e-125)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (x <= 0.000185)
		tmp = Float64(z * Float64(y / Float64(Float64(z * t) - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -1.95e-44)
		tmp = t_1;
	elseif (x <= 2.15e-125)
		tmp = y / (t * (x + 1.0));
	elseif (x <= 0.000185)
		tmp = z * (y / ((z * t) - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e-44], t$95$1, If[LessEqual[x, 2.15e-125], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.000185], N[(z * N[(y / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9500000000000001e-44 or 1.85e-4 < x

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around inf 85.1%

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

      1. +-commutative 85.1%

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

   6. Simplified 85.1%

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

   if -1.9500000000000001e-44 < x < 2.1500000000000001e-125

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. times-frac 51.9%

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

      2. +-commutative 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in t around inf 57.9%

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

   if 2.1500000000000001e-125 < x < 1.85e-4

   1. Initial program 96.1%

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

      1. *-commutative 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around inf 49.4%

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

      1. times-frac 46.3%

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

      2. +-commutative 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in x around 0 45.0%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-125}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;x \leq 0.000185:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 7: 75.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-240} \lor \neg \left(z \leq 2.3 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.2e-240) (not (<= z 2.3e-110)))
   (/ (+ x (/ y t)) (+ x 1.0))
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.2e-240) || !(z <= 2.3e-110)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.2d-240)) .or. (.not. (z <= 2.3d-110))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.2e-240) || !(z <= 2.3e-110)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.2e-240) or not (z <= 2.3e-110):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.2e-240) || !(z <= 2.3e-110))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.2e-240) || ~((z <= 2.3e-110)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.2e-240], N[Not[LessEqual[z, 2.3e-110]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000003e-240 or 2.3000000000000001e-110 < z

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in z around inf 78.2%

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

   if -8.2000000000000003e-240 < z < 2.3000000000000001e-110

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 66.0%

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

      1. associate-/l* 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in t around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. unsub-neg 66.0%

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

   9. Simplified 66.0%

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

   10. Taylor expanded in x around inf 76.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-240} \lor \neg \left(z \leq 2.3 \cdot 10^{-110}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 88.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

   1. *-commutative 89.9%

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

3. Simplified 89.9%

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

4. Taylor expanded in y around inf 80.9%

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

   1. associate-/l* 86.7%

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

6. Simplified 86.7%

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

7. Taylor expanded in t around 0 90.5%

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

   1. mul-1-neg 90.5%

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

   2. unsub-neg 90.5%

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

9. Simplified 90.5%

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

10. Final simplification 90.5%

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

Alternative 9: 68.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-43} \lor \neg \left(x \leq 6.2 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.7e-43) (not (<= x 6.2e-132)))
   (/ x (+ x 1.0))
   (/ y (* t (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.7e-43) || !(x <= 6.2e-132)) {
		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 <= (-2.7d-43)) .or. (.not. (x <= 6.2d-132))) 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 <= -2.7e-43) || !(x <= 6.2e-132)) {
		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 <= -2.7e-43) or not (x <= 6.2e-132):
		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 <= -2.7e-43) || !(x <= 6.2e-132))
		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 <= -2.7e-43) || ~((x <= 6.2e-132)))
		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, -2.7e-43], N[Not[LessEqual[x, 6.2e-132]], $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 < -2.69999999999999991e-43 or 6.20000000000000016e-132 < x

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. +-commutative 74.1%

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

   6. Simplified 74.1%

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

   if -2.69999999999999991e-43 < x < 6.20000000000000016e-132

   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 y around inf 59.9%

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

      1. times-frac 52.4%

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

      2. +-commutative 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in t around inf 58.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-43} \lor \neg \left(x \leq 6.2 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \]

Alternative 10: 59.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-140} \lor \neg \left(t \leq 6.5 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.42e-140) (not (<= t 6.5e-72))) (/ x (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.42e-140) || !(t <= 6.5e-72)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.42d-140)) .or. (.not. (t <= 6.5d-72))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.42e-140) || !(t <= 6.5e-72)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.42e-140) or not (t <= 6.5e-72):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.42e-140) || !(t <= 6.5e-72))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.42e-140) || ~((t <= 6.5e-72)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.42e-140], N[Not[LessEqual[t, 6.5e-72]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -1.42e-140 or 6.4999999999999997e-72 < t

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around inf 64.7%

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

      1. +-commutative 64.7%

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

   6. Simplified 64.7%

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

   if -1.42e-140 < t < 6.4999999999999997e-72

   1. Initial program 93.3%

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

      1. *-commutative 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 76.2%

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

      1. associate-/l* 81.6%

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

   6. Simplified 81.6%

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

   7. Taylor expanded in t around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   9. Simplified 81.6%

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

   10. Taylor expanded in x around inf 51.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-140} \lor \neg \left(t \leq 6.5 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 55.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-27}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-125}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.35e-27) 1.0 (if (<= x 7.6e-125) (- x (* x x)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.35e-27) {
		tmp = 1.0;
	} else if (x <= 7.6e-125) {
		tmp = x - (x * 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-27)) then
        tmp = 1.0d0
    else if (x <= 7.6d-125) then
        tmp = x - (x * 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-27) {
		tmp = 1.0;
	} else if (x <= 7.6e-125) {
		tmp = x - (x * x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.35e-27:
		tmp = 1.0
	elif x <= 7.6e-125:
		tmp = x - (x * x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.35e-27)
		tmp = 1.0;
	elseif (x <= 7.6e-125)
		tmp = Float64(x - Float64(x * 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-27)
		tmp = 1.0;
	elseif (x <= 7.6e-125)
		tmp = x - (x * x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.35e-27], 1.0, If[LessEqual[x, 7.6e-125], N[(x - N[(x * x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.35000000000000016e-27 or 7.6000000000000002e-125 < x

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 83.9%

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

      1. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in t around 0 92.9%

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

      1. mul-1-neg 92.9%

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

      2. unsub-neg 92.9%

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

   9. Simplified 92.9%

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

   10. Taylor expanded in x around inf 75.6%

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

   if -2.35000000000000016e-27 < x < 7.6000000000000002e-125

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around inf 23.9%

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

      1. +-commutative 23.9%

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

   6. Simplified 23.9%

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

   7. Taylor expanded in x around 0 23.9%

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

      1. +-commutative 23.9%

         \[\leadsto \color{blue}{x + -1 \cdot {x}^{2}} \]

      2. mul-1-neg 23.9%

         \[\leadsto x + \color{blue}{\left(-{x}^{2}\right)} \]

      3. unsub-neg 23.9%

         \[\leadsto \color{blue}{x - {x}^{2}} \]

      4. unpow2 23.9%

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

   9. Simplified 23.9%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-27}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-125}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 53.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

   1. *-commutative 89.9%

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

3. Simplified 89.9%

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

4. Taylor expanded in y around inf 80.9%

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

   1. associate-/l* 86.7%

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

6. Simplified 86.7%

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

7. Taylor expanded in t around 0 90.5%

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

   1. mul-1-neg 90.5%

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

   2. unsub-neg 90.5%

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

9. Simplified 90.5%

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

10. Taylor expanded in x around inf 49.4%

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

11. Final simplification 49.4%

    \[\leadsto 1 \]

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 2023274 
(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)))