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

Percentage Accurate: 89.3% → 98.7%

Time: 11.7s

Alternatives: 14

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: 89.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+59} \lor \neg \left(z \leq 1.08 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.9e+59) (not (<= z 1.08e+55)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e+59) || !(z <= 1.08e+55)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.9d+59)) .or. (.not. (z <= 1.08d+55))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e+59) || !(z <= 1.08e+55)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.9e+59) or not (z <= 1.08e+55):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.9e+59) || !(z <= 1.08e+55))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.9e+59) || ~((z <= 1.08e+55)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.9e+59], N[Not[LessEqual[z, 1.08e+55]], $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[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e59 or 1.08000000000000004e55 < z

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in y around inf 74.7%

      \[\leadsto \frac{x + \color{blue}{\frac{y \cdot z}{t \cdot z - x}}}{x + 1} \]
   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 98.2%

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

      1. mul-1-neg 98.2%

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

      2. unsub-neg 98.2%

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

   9. Simplified 98.2%

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

   if -1.9e59 < z < 1.08000000000000004e55

   1. Initial program 99.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+59} \lor \neg \left(z \leq 1.08 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\\ \end{array} \]

Alternative 2: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ \mathbf{if}\;t \leq -1 \cdot 10^{+126}:\\ \;\;\;\;\frac{x + \left(y \cdot \frac{1}{t} - \frac{x}{t_1}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot \frac{z}{t_1} + \frac{-1}{\frac{t}{\frac{x}{z}} + -1}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)))
   (if (<= t -1e+126)
     (/ (+ x (- (* y (/ 1.0 t)) (/ x t_1))) (+ x 1.0))
     (/ (+ x (+ (* y (/ z t_1)) (/ -1.0 (+ (/ t (/ x z)) -1.0)))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double tmp;
	if (t <= -1e+126) {
		tmp = (x + ((y * (1.0 / t)) - (x / t_1))) / (x + 1.0);
	} else {
		tmp = (x + ((y * (z / t_1)) + (-1.0 / ((t / (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) :: t_1
    real(8) :: tmp
    t_1 = (t * z) - x
    if (t <= (-1d+126)) then
        tmp = (x + ((y * (1.0d0 / t)) - (x / t_1))) / (x + 1.0d0)
    else
        tmp = (x + ((y * (z / t_1)) + ((-1.0d0) / ((t / (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 t_1 = (t * z) - x;
	double tmp;
	if (t <= -1e+126) {
		tmp = (x + ((y * (1.0 / t)) - (x / t_1))) / (x + 1.0);
	} else {
		tmp = (x + ((y * (z / t_1)) + (-1.0 / ((t / (x / z)) + -1.0)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	tmp = 0
	if t <= -1e+126:
		tmp = (x + ((y * (1.0 / t)) - (x / t_1))) / (x + 1.0)
	else:
		tmp = (x + ((y * (z / t_1)) + (-1.0 / ((t / (x / z)) + -1.0)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	tmp = 0.0
	if (t <= -1e+126)
		tmp = Float64(Float64(x + Float64(Float64(y * Float64(1.0 / t)) - Float64(x / t_1))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * Float64(z / t_1)) + Float64(-1.0 / Float64(Float64(t / Float64(x / z)) + -1.0)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	tmp = 0.0;
	if (t <= -1e+126)
		tmp = (x + ((y * (1.0 / t)) - (x / t_1))) / (x + 1.0);
	else
		tmp = (x + ((y * (z / t_1)) + (-1.0 / ((t / (x / z)) + -1.0)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t, -1e+126], N[(N[(x + N[(N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / N[(N[(t / N[(x / z), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.99999999999999925e125

   1. Initial program 70.3%

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

      1. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. div-sub 70.3%

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

      2. *-un-lft-identity 70.3%

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

      3. times-frac 85.6%

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

      4. fma-neg 85.6%

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

   5. Applied egg-rr 85.6%

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

      1. fma-udef 85.6%

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

      2. unsub-neg 85.6%

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

      3. /-rgt-identity 85.6%

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

      4. *-commutative 85.6%

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

      5. *-commutative 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in z around inf 100.0%

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

   if -9.99999999999999925e125 < t

   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. Step-by-step derivation

      1. div-sub 93.3%

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

      2. *-un-lft-identity 93.3%

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

      3. times-frac 98.6%

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

      4. fma-neg 98.6%

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

   5. Applied egg-rr 98.6%

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

      1. fma-udef 98.6%

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

      2. unsub-neg 98.6%

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

      3. /-rgt-identity 98.6%

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

      4. *-commutative 98.6%

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

      5. *-commutative 98.6%

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

   7. Simplified 98.6%

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

      1. clear-num 98.6%

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

      2. inv-pow 98.6%

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

      3. *-commutative 98.6%

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

   9. Applied egg-rr 98.6%

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

       1. unpow-1 98.6%

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

       2. div-sub 98.6%

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

       3. *-commutative 98.6%

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

       4. sub-neg 98.6%

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

       5. associate-/l* 98.6%

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

       6. *-inverses 98.6%

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

       7. metadata-eval 98.6%

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

   11. Simplified 98.6%

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

4. Final simplification 98.8%

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

Alternative 3: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot z - x\\ t_2 := \frac{x}{t_1}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+116}:\\ \;\;\;\;\frac{x + \left(y \cdot \frac{1}{t} - t_2\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot \frac{z}{t_1} - t_2\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* t z) x)) (t_2 (/ x t_1)))
   (if (<= t -5e+116)
     (/ (+ x (- (* y (/ 1.0 t)) t_2)) (+ x 1.0))
     (/ (+ x (- (* y (/ z t_1)) t_2)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * z) - x;
	double t_2 = x / t_1;
	double tmp;
	if (t <= -5e+116) {
		tmp = (x + ((y * (1.0 / t)) - t_2)) / (x + 1.0);
	} else {
		tmp = (x + ((y * (z / t_1)) - t_2)) / (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) :: t_2
    real(8) :: tmp
    t_1 = (t * z) - x
    t_2 = x / t_1
    if (t <= (-5d+116)) then
        tmp = (x + ((y * (1.0d0 / t)) - t_2)) / (x + 1.0d0)
    else
        tmp = (x + ((y * (z / t_1)) - t_2)) / (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 = (t * z) - x;
	double t_2 = x / t_1;
	double tmp;
	if (t <= -5e+116) {
		tmp = (x + ((y * (1.0 / t)) - t_2)) / (x + 1.0);
	} else {
		tmp = (x + ((y * (z / t_1)) - t_2)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * z) - x
	t_2 = x / t_1
	tmp = 0
	if t <= -5e+116:
		tmp = (x + ((y * (1.0 / t)) - t_2)) / (x + 1.0)
	else:
		tmp = (x + ((y * (z / t_1)) - t_2)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * z) - x)
	t_2 = Float64(x / t_1)
	tmp = 0.0
	if (t <= -5e+116)
		tmp = Float64(Float64(x + Float64(Float64(y * Float64(1.0 / t)) - t_2)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * Float64(z / t_1)) - t_2)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * z) - x;
	t_2 = x / t_1;
	tmp = 0.0;
	if (t <= -5e+116)
		tmp = (x + ((y * (1.0 / t)) - t_2)) / (x + 1.0);
	else
		tmp = (x + ((y * (z / t_1)) - t_2)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(x / t$95$1), $MachinePrecision]}, If[LessEqual[t, -5e+116], N[(N[(x + N[(N[(y * N[(1.0 / t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000025e116

   1. Initial program 70.3%

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

      1. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. div-sub 70.3%

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

      2. *-un-lft-identity 70.3%

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

      3. times-frac 85.6%

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

      4. fma-neg 85.6%

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

   5. Applied egg-rr 85.6%

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

      1. fma-udef 85.6%

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

      2. unsub-neg 85.6%

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

      3. /-rgt-identity 85.6%

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

      4. *-commutative 85.6%

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

      5. *-commutative 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in z around inf 100.0%

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

   if -5.00000000000000025e116 < t

   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. Step-by-step derivation

      1. div-sub 93.3%

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

      2. *-un-lft-identity 93.3%

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

      3. times-frac 98.6%

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

      4. fma-neg 98.6%

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

   5. Applied egg-rr 98.6%

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

      1. fma-udef 98.6%

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

      2. unsub-neg 98.6%

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

      3. /-rgt-identity 98.6%

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

      4. *-commutative 98.6%

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

      5. *-commutative 98.6%

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

   7. Simplified 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+116}:\\ \;\;\;\;\frac{x + \left(y \cdot \frac{1}{t} - \frac{x}{t \cdot z - x}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot \frac{z}{t \cdot z - x} - \frac{x}{t \cdot z - x}\right)}{x + 1}\\ \end{array} \]

Alternative 4: 90.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-167} \lor \neg \left(z \leq 4.1 \cdot 10^{-178}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{-1}{-1 + \frac{t \cdot z}{x}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e-167) (not (<= z 4.1e-178)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ x (/ -1.0 (+ -1.0 (/ (* t z) x)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-167) || !(z <= 4.1e-178)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (-1.0 / (-1.0 + ((t * z) / x)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.65d-167)) .or. (.not. (z <= 4.1d-178))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x + ((-1.0d0) / ((-1.0d0) + ((t * z) / x)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-167) || !(z <= 4.1e-178)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (-1.0 / (-1.0 + ((t * z) / x)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e-167) or not (z <= 4.1e-178):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x + (-1.0 / (-1.0 + ((t * z) / x)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e-167) || !(z <= 4.1e-178))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(-1.0 / Float64(-1.0 + Float64(Float64(t * z) / x)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e-167) || ~((z <= 4.1e-178)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x + (-1.0 / (-1.0 + ((t * z) / x)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e-167], N[Not[LessEqual[z, 4.1e-178]], $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[(-1.0 / N[(-1.0 + N[(N[(t * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.64999999999999998e-167 or 4.0999999999999999e-178 < 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 y around inf 83.8%

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

      1. associate-/l* 92.5%

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

   6. Simplified 92.5%

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

   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 -1.64999999999999998e-167 < z < 4.0999999999999999e-178

   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. div-sub 99.8%

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

      2. *-un-lft-identity 99.8%

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

      3. times-frac 99.9%

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

      4. fma-neg 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. fma-udef 99.9%

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

      2. unsub-neg 99.9%

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

      3. /-rgt-identity 99.9%

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

      4. *-commutative 99.9%

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

      5. *-commutative 99.9%

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

   7. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. *-commutative 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. unpow-1 99.9%

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

       2. div-sub 99.9%

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

       3. *-commutative 99.9%

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

       4. sub-neg 99.9%

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

       5. associate-/l* 99.9%

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

       6. *-inverses 99.9%

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

       7. metadata-eval 99.9%

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

   11. Simplified 99.9%

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

   12. Taylor expanded in y around 0 93.6%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-167} \lor \neg \left(z \leq 4.1 \cdot 10^{-178}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{-1}{-1 + \frac{t \cdot z}{x}}}{x + 1}\\ \end{array} \]

Alternative 5: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-247} \lor \neg \left(z \leq 8 \cdot 10^{-233}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y \cdot z}{x}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.4e-247) (not (<= z 8e-233)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ 1.0 (- x (/ (* y z) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-247) || !(z <= 8e-233)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - ((y * z) / x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.4d-247)) .or. (.not. (z <= 8d-233))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (1.0d0 + (x - ((y * z) / x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e-247) || !(z <= 8e-233)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - ((y * z) / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.4e-247) or not (z <= 8e-233):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (1.0 + (x - ((y * z) / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.4e-247) || !(z <= 8e-233))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(1.0 + Float64(x - Float64(Float64(y * z) / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.4e-247) || ~((z <= 8e-233)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (1.0 + (x - ((y * z) / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.4e-247], N[Not[LessEqual[z, 8e-233]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000011e-247 or 7.99999999999999966e-233 < z

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in y around inf 81.7%

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

      1. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in t around 0 92.1%

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

      1. mul-1-neg 92.1%

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

      2. unsub-neg 92.1%

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

   9. Simplified 92.1%

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

   if -2.40000000000000011e-247 < z < 7.99999999999999966e-233

   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 t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. *-commutative 100.0%

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

      4. +-commutative 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-247} \lor \neg \left(z \leq 8 \cdot 10^{-233}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y \cdot z}{x}\right)}{x + 1}\\ \end{array} \]

Alternative 6: 90.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-168} \lor \neg \left(z \leq 2.25 \cdot 10^{-180}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.1e-168) (not (<= z 2.25e-180)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (- x (/ x (- (* t z) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e-168) || !(z <= 2.25e-180)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((t * z) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.1d-168)) .or. (.not. (z <= 2.25d-180))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x - (x / ((t * z) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e-168) || !(z <= 2.25e-180)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((t * z) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.1e-168) or not (z <= 2.25e-180):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x - (x / ((t * z) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.1e-168) || !(z <= 2.25e-180))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(t * z) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.1e-168) || ~((z <= 2.25e-180)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x - (x / ((t * z) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.1e-168], N[Not[LessEqual[z, 2.25e-180]], $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[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999994e-168 or 2.25000000000000005e-180 < 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 y around inf 83.8%

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

      1. associate-/l* 92.5%

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

   6. Simplified 92.5%

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

   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 -2.09999999999999994e-168 < z < 2.25000000000000005e-180

   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. Taylor expanded in y around 0 93.5%

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

      1. +-commutative 93.5%

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

   6. Simplified 93.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-168} \lor \neg \left(z \leq 2.25 \cdot 10^{-180}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{t \cdot z - x}}{x + 1}\\ \end{array} \]

Alternative 7: 77.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -17:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 25000000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -17.0)
   (- 1.0 (* (/ z x) (/ y x)))
   (if (<= x 25000000000.0) (/ (+ x (/ y t)) (+ x 1.0)) (+ 1.0 (/ -1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -17.0) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 25000000000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-17.0d0)) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else if (x <= 25000000000.0d0) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -17.0) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 25000000000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -17.0:
		tmp = 1.0 - ((z / x) * (y / x))
	elif x <= 25000000000.0:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (-1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -17.0)
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	elseif (x <= 25000000000.0)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -17.0)
		tmp = 1.0 - ((z / x) * (y / x));
	elseif (x <= 25000000000.0)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -17.0], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 25000000000.0], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -17

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around -inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

      3. distribute-rgt-out-- 82.6%

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

      4. unpow2 82.6%

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

      5. times-frac 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in y around inf 95.4%

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

   if -17 < x < 2.5e10

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in z around inf 66.4%

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

   if 2.5e10 < x

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around inf 98.4%

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

      1. +-commutative 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in x around inf 98.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -17:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 25000000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]

Alternative 8: 77.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.38 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 12500000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.38e-8)
   (/ (- x (/ y (/ x z))) (+ x 1.0))
   (if (<= x 12500000000.0) (/ (+ x (/ y t)) (+ x 1.0)) (+ 1.0 (/ -1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.38e-8) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (x <= 12500000000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.38d-8)) then
        tmp = (x - (y / (x / z))) / (x + 1.0d0)
    else if (x <= 12500000000.0d0) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.38e-8) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (x <= 12500000000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.38e-8:
		tmp = (x - (y / (x / z))) / (x + 1.0)
	elif x <= 12500000000.0:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (-1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.38e-8)
		tmp = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (x <= 12500000000.0)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.38e-8)
		tmp = (x - (y / (x / z))) / (x + 1.0);
	elseif (x <= 12500000000.0)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.38e-8], N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 12500000000.0], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.37999999999999995e-8

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 91.4%

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

      1. associate-/l* 98.9%

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

   6. Simplified 98.9%

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

   7. Taylor expanded in t around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

      3. associate-/l* 94.5%

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

      4. +-commutative 94.5%

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

   9. Simplified 94.5%

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

   if -1.37999999999999995e-8 < x < 1.25e10

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in z around inf 67.4%

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

   if 1.25e10 < x

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in t around inf 98.4%

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

      1. +-commutative 98.4%

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

   6. Simplified 98.4%

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

   7. Taylor expanded in x around inf 98.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.38 \cdot 10^{-8}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 12500000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]

Alternative 9: 68.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{-55} \lor \neg \left(x \leq 2.6 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.3e-55) (not (<= x 2.6e-18)))
   (/ x (+ x 1.0))
   (/ y (+ t (* t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.3e-55) || !(x <= 2.6e-18)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t + (t * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-6.3d-55)) .or. (.not. (x <= 2.6d-18))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / (t + (t * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.3e-55) || !(x <= 2.6e-18)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t + (t * x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.3e-55) or not (x <= 2.6e-18):
		tmp = x / (x + 1.0)
	else:
		tmp = y / (t + (t * x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.3e-55) || !(x <= 2.6e-18))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / Float64(t + Float64(t * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6.3e-55) || ~((x <= 2.6e-18)))
		tmp = x / (x + 1.0);
	else
		tmp = y / (t + (t * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.3e-55], N[Not[LessEqual[x, 2.6e-18]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(t + N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2999999999999997e-55 or 2.6e-18 < x

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in t around inf 88.9%

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

      1. +-commutative 88.9%

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

   6. Simplified 88.9%

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

   if -6.2999999999999997e-55 < x < 2.6e-18

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around inf 48.9%

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

   5. Taylor expanded in z around inf 45.8%

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

      1. distribute-lft-in 45.8%

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

      2. *-rgt-identity 45.8%

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

   7. Simplified 45.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{-55} \lor \neg \left(x \leq 2.6 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t + t \cdot x}\\ \end{array} \]

Alternative 10: 67.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-5}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.75e-5)
   (- 1.0 (* (/ z x) (/ y x)))
   (if (<= x 3.4e-17) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.75e-5) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 3.4e-17) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.75d-5)) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else if (x <= 3.4d-17) then
        tmp = y / t
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.75e-5) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 3.4e-17) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.75e-5:
		tmp = 1.0 - ((z / x) * (y / x))
	elif x <= 3.4e-17:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.75e-5)
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	elseif (x <= 3.4e-17)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.75e-5)
		tmp = 1.0 - ((z / x) * (y / x));
	elseif (x <= 3.4e-17)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.75e-5], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-17], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7499999999999998e-5

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around -inf 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

      3. distribute-rgt-out-- 82.6%

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

      4. unpow2 82.6%

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

      5. times-frac 86.8%

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

   6. Simplified 86.8%

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

   7. Taylor expanded in y around inf 95.4%

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

   if -1.7499999999999998e-5 < x < 3.3999999999999998e-17

   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. Step-by-step derivation

      1. div-sub 90.1%

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

      2. *-un-lft-identity 90.1%

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

      3. times-frac 93.7%

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

      4. fma-neg 93.7%

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

   5. Applied egg-rr 93.7%

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

      1. fma-udef 93.7%

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

      2. unsub-neg 93.7%

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

      3. /-rgt-identity 93.7%

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

      4. *-commutative 93.7%

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

      5. *-commutative 93.7%

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

   7. Simplified 93.7%

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

      1. clear-num 93.7%

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

      2. inv-pow 93.7%

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

      3. *-commutative 93.7%

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

   9. Applied egg-rr 93.7%

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

       1. unpow-1 93.7%

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

       2. div-sub 93.7%

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

       3. *-commutative 93.7%

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

       4. sub-neg 93.7%

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

       5. associate-/l* 93.8%

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

       6. *-inverses 93.8%

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

       7. metadata-eval 93.8%

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

   11. Simplified 93.8%

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

   12. Taylor expanded in x around 0 44.1%

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

   if 3.3999999999999998e-17 < 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 94.1%

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

      1. +-commutative 94.1%

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

   6. Simplified 94.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-5}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 11: 68.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-54} \lor \neg \left(x \leq 2.8 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.75e-54) (not (<= x 2.8e-18))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e-54) || !(x <= 2.8e-18)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.75d-54)) .or. (.not. (x <= 2.8d-18))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.75e-54) || !(x <= 2.8e-18)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.75e-54) or not (x <= 2.8e-18):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.75e-54) || !(x <= 2.8e-18))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.75e-54) || ~((x <= 2.8e-18)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.75e-54], N[Not[LessEqual[x, 2.8e-18]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.74999999999999991e-54 or 2.80000000000000012e-18 < x

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in t around inf 88.9%

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

      1. +-commutative 88.9%

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

   6. Simplified 88.9%

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

   if -1.74999999999999991e-54 < x < 2.80000000000000012e-18

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

      1. div-sub 90.6%

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

      2. *-un-lft-identity 90.6%

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

      3. times-frac 93.4%

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

      4. fma-neg 93.4%

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

   5. Applied egg-rr 93.4%

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

      1. fma-udef 93.4%

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

      2. unsub-neg 93.4%

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

      3. /-rgt-identity 93.4%

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

      4. *-commutative 93.4%

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

      5. *-commutative 93.4%

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

   7. Simplified 93.4%

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

      1. clear-num 93.4%

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

      2. inv-pow 93.4%

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

      3. *-commutative 93.4%

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

   9. Applied egg-rr 93.4%

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

       1. unpow-1 93.4%

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

       2. div-sub 93.5%

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

       3. *-commutative 93.5%

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

       4. sub-neg 93.5%

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

       5. associate-/l* 93.5%

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

       6. *-inverses 93.5%

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

       7. metadata-eval 93.5%

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

   11. Simplified 93.5%

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

   12. Taylor expanded in x around 0 45.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-54} \lor \neg \left(x \leq 2.8 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]

Alternative 12: 67.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.35e-5) 1.0 (if (<= x 5.2e-64) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-5) {
		tmp = 1.0;
	} else if (x <= 5.2e-64) {
		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 <= (-1.35d-5)) then
        tmp = 1.0d0
    else if (x <= 5.2d-64) 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 <= -1.35e-5) {
		tmp = 1.0;
	} else if (x <= 5.2e-64) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e-5:
		tmp = 1.0
	elif x <= 5.2e-64:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e-5)
		tmp = 1.0;
	elseif (x <= 5.2e-64)
		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 <= -1.35e-5)
		tmp = 1.0;
	elseif (x <= 5.2e-64)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.35e-5], 1.0, If[LessEqual[x, 5.2e-64], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3499999999999999e-5 or 5.2e-64 < x

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

      1. div-sub 90.6%

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

      2. *-un-lft-identity 90.6%

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

      3. times-frac 99.4%

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

      4. fma-neg 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. fma-udef 99.4%

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

      2. unsub-neg 99.4%

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

      3. /-rgt-identity 99.4%

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

      4. *-commutative 99.4%

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

      5. *-commutative 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around inf 85.6%

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

   if -1.3499999999999999e-5 < x < 5.2e-64

   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. Step-by-step derivation

      1. div-sub 89.9%

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

      2. *-un-lft-identity 89.9%

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

      3. times-frac 93.0%

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

      4. fma-neg 93.0%

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

   5. Applied egg-rr 93.0%

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

      1. fma-udef 93.0%

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

      2. unsub-neg 93.0%

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

      3. /-rgt-identity 93.0%

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

      4. *-commutative 93.0%

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

      5. *-commutative 93.0%

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

   7. Simplified 93.0%

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

      1. clear-num 93.0%

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

      2. inv-pow 93.0%

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

      3. *-commutative 93.0%

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

   9. Applied egg-rr 93.0%

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

       1. unpow-1 93.0%

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

       2. div-sub 93.0%

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

       3. *-commutative 93.0%

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

       4. sub-neg 93.0%

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

       5. associate-/l* 93.0%

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

       6. *-inverses 93.0%

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

       7. metadata-eval 93.0%

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

   11. Simplified 93.0%

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

   12. Taylor expanded in x around 0 44.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 54.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e-7) 1.0 (if (<= x 1.45e-216) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e-7) {
		tmp = 1.0;
	} else if (x <= 1.45e-216) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6d-7)) then
        tmp = 1.0d0
    else if (x <= 1.45d-216) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e-7) {
		tmp = 1.0;
	} else if (x <= 1.45e-216) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e-7:
		tmp = 1.0
	elif x <= 1.45e-216:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e-7)
		tmp = 1.0;
	elseif (x <= 1.45e-216)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6e-7)
		tmp = 1.0;
	elseif (x <= 1.45e-216)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e-7], 1.0, If[LessEqual[x, 1.45e-216], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999997e-7 or 1.45e-216 < x

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

      1. div-sub 90.5%

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

      2. *-un-lft-identity 90.5%

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

      3. times-frac 99.0%

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

      4. fma-neg 99.0%

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

   5. Applied egg-rr 99.0%

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

      1. fma-udef 99.0%

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

      2. unsub-neg 99.0%

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

      3. /-rgt-identity 99.0%

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

      4. *-commutative 99.0%

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

      5. *-commutative 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around inf 76.3%

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

   if -5.9999999999999997e-7 < x < 1.45e-216

   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 t around inf 28.7%

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

      1. +-commutative 28.7%

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

   6. Simplified 28.7%

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

   7. Taylor expanded in x around 0 28.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-216}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14: 53.1% 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 90.4%

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

   1. *-commutative 90.4%

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

3. Simplified 90.4%

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

   1. div-sub 90.4%

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

   2. *-un-lft-identity 90.4%

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

   3. times-frac 96.9%

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

   4. fma-neg 96.9%

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

5. Applied egg-rr 96.9%

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

   1. fma-udef 96.9%

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

   2. unsub-neg 96.9%

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

   3. /-rgt-identity 96.9%

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

   4. *-commutative 96.9%

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

   5. *-commutative 96.9%

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

7. Simplified 96.9%

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

8. Taylor expanded in x around inf 57.7%

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

9. Final simplification 57.7%

   \[\leadsto 1 \]

Developer target: 99.5% 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 2023290 
(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)))