Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.2% → 96.9%

Time: 16.3s

Alternatives: 18

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

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

C

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

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)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

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

C

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

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)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. *-un-lft-identity 86.5%

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

   2. times-frac 97.7%

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

3. Applied egg-rr 97.7%

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

4. Final simplification 97.7%

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

Alternative 2: 58.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))))
   (if (<= z -2.4e+57)
     x
     (if (<= z -1.15e+27)
       (* x (/ (- z) t))
       (if (<= z -7.5e-6)
         x
         (if (<= z -1.9e-61)
           t_1
           (if (<= z -1.16e-66)
             x
             (if (<= z -1.8e-150)
               (* z (- (/ x t)))
               (if (<= z 3.4e+47)
                 t_1
                 (if (<= z 9.2e+85)
                   x
                   (if (<= z 3.25e+125) (* x (/ y t)) x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -2.4e+57) {
		tmp = x;
	} else if (z <= -1.15e+27) {
		tmp = x * (-z / t);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.16e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * -(x / t);
	} else if (z <= 3.4e+47) {
		tmp = t_1;
	} else if (z <= 9.2e+85) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x / (t / y)
    if (z <= (-2.4d+57)) then
        tmp = x
    else if (z <= (-1.15d+27)) then
        tmp = x * (-z / t)
    else if (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= (-1.9d-61)) then
        tmp = t_1
    else if (z <= (-1.16d-66)) then
        tmp = x
    else if (z <= (-1.8d-150)) then
        tmp = z * -(x / t)
    else if (z <= 3.4d+47) then
        tmp = t_1
    else if (z <= 9.2d+85) then
        tmp = x
    else if (z <= 3.25d+125) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -2.4e+57) {
		tmp = x;
	} else if (z <= -1.15e+27) {
		tmp = x * (-z / t);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.16e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * -(x / t);
	} else if (z <= 3.4e+47) {
		tmp = t_1;
	} else if (z <= 9.2e+85) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	tmp = 0
	if z <= -2.4e+57:
		tmp = x
	elif z <= -1.15e+27:
		tmp = x * (-z / t)
	elif z <= -7.5e-6:
		tmp = x
	elif z <= -1.9e-61:
		tmp = t_1
	elif z <= -1.16e-66:
		tmp = x
	elif z <= -1.8e-150:
		tmp = z * -(x / t)
	elif z <= 3.4e+47:
		tmp = t_1
	elif z <= 9.2e+85:
		tmp = x
	elif z <= 3.25e+125:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	tmp = 0.0
	if (z <= -2.4e+57)
		tmp = x;
	elseif (z <= -1.15e+27)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.16e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = Float64(z * Float64(-Float64(x / t)));
	elseif (z <= 3.4e+47)
		tmp = t_1;
	elseif (z <= 9.2e+85)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	tmp = 0.0;
	if (z <= -2.4e+57)
		tmp = x;
	elseif (z <= -1.15e+27)
		tmp = x * (-z / t);
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.16e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = z * -(x / t);
	elseif (z <= 3.4e+47)
		tmp = t_1;
	elseif (z <= 9.2e+85)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+57], x, If[LessEqual[z, -1.15e+27], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, -1.9e-61], t$95$1, If[LessEqual[z, -1.16e-66], x, If[LessEqual[z, -1.8e-150], N[(z * (-N[(x / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.4e+47], t$95$1, If[LessEqual[z, 9.2e+85], x, If[LessEqual[z, 3.25e+125], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.40000000000000005e57 or -1.15e27 < z < -7.50000000000000019e-6 or -1.8999999999999999e-61 < z < -1.16000000000000002e-66 or 3.3999999999999998e47 < z < 9.1999999999999996e85 or 3.2499999999999999e125 < z

   1. Initial program 75.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 69.1%

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

   if -2.40000000000000005e57 < z < -1.15e27

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 61.1%

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

      2. associate-*l* 61.1%

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

      3. neg-mul-1 61.1%

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

      4. *-commutative 61.1%

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

   6. Simplified 61.1%

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

      1. clear-num 61.3%

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

      2. associate-*l/ 61.5%

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

      3. *-un-lft-identity 61.5%

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

      4. add-sqr-sqrt 61.3%

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

      5. sqrt-unprod 61.5%

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

      6. sqr-neg 61.5%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 5.8%

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

      9. frac-2neg 5.8%

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

      10. add-sqr-sqrt 5.8%

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

      11. sqrt-unprod 5.8%

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

      12. sqr-neg 5.8%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 61.5%

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

      15. distribute-neg-frac 61.5%

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

   8. Applied egg-rr 61.5%

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

      1. associate-/r/ 71.9%

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

      2. +-commutative 71.9%

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

   10. Simplified 71.9%

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

   11. Taylor expanded in z around 0 62.4%

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

       1. mul-1-neg 62.4%

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

       2. distribute-neg-frac 62.4%

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

   13. Simplified 62.4%

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

   if -7.50000000000000019e-6 < z < -1.8999999999999999e-61 or -1.8000000000000001e-150 < z < 3.3999999999999998e47

   1. Initial program 95.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-/l* 67.3%

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

      2. associate-/r/ 70.5%

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

   6. Simplified 70.5%

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

      1. *-commutative 70.5%

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

      2. clear-num 70.3%

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

      3. un-div-inv 70.8%

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

   8. Applied egg-rr 70.8%

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

   if -1.16000000000000002e-66 < z < -1.8000000000000001e-150

   1. Initial program 94.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 43.6%

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

      1. associate-*r/ 48.3%

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

      2. associate-*l* 48.3%

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

      3. neg-mul-1 48.3%

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

      4. *-commutative 48.3%

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

   6. Simplified 48.3%

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

   7. Taylor expanded in t around inf 46.7%

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

   if 9.1999999999999996e85 < z < 3.2499999999999999e125

   1. Initial program 80.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in z around 0 42.3%

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

      1. associate-/l* 23.7%

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

      2. associate-/r/ 51.9%

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

   6. Simplified 51.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 58.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))))
   (if (<= z -5.5e+57)
     x
     (if (<= z -7.6e+25)
       (/ (- x) (/ t z))
       (if (<= z -7.5e-6)
         x
         (if (<= z -1.9e-61)
           t_1
           (if (<= z -1.16e-66)
             x
             (if (<= z -1.8e-150)
               (* z (- (/ x t)))
               (if (<= z 4.8e+47)
                 t_1
                 (if (<= z 5e+83)
                   x
                   (if (<= z 3.25e+125) (* x (/ y t)) x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -5.5e+57) {
		tmp = x;
	} else if (z <= -7.6e+25) {
		tmp = -x / (t / z);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.16e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * -(x / t);
	} else if (z <= 4.8e+47) {
		tmp = t_1;
	} else if (z <= 5e+83) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x / (t / y)
    if (z <= (-5.5d+57)) then
        tmp = x
    else if (z <= (-7.6d+25)) then
        tmp = -x / (t / z)
    else if (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= (-1.9d-61)) then
        tmp = t_1
    else if (z <= (-1.16d-66)) then
        tmp = x
    else if (z <= (-1.8d-150)) then
        tmp = z * -(x / t)
    else if (z <= 4.8d+47) then
        tmp = t_1
    else if (z <= 5d+83) then
        tmp = x
    else if (z <= 3.25d+125) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -5.5e+57) {
		tmp = x;
	} else if (z <= -7.6e+25) {
		tmp = -x / (t / z);
	} else if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.16e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * -(x / t);
	} else if (z <= 4.8e+47) {
		tmp = t_1;
	} else if (z <= 5e+83) {
		tmp = x;
	} else if (z <= 3.25e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	tmp = 0
	if z <= -5.5e+57:
		tmp = x
	elif z <= -7.6e+25:
		tmp = -x / (t / z)
	elif z <= -7.5e-6:
		tmp = x
	elif z <= -1.9e-61:
		tmp = t_1
	elif z <= -1.16e-66:
		tmp = x
	elif z <= -1.8e-150:
		tmp = z * -(x / t)
	elif z <= 4.8e+47:
		tmp = t_1
	elif z <= 5e+83:
		tmp = x
	elif z <= 3.25e+125:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	tmp = 0.0
	if (z <= -5.5e+57)
		tmp = x;
	elseif (z <= -7.6e+25)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.16e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = Float64(z * Float64(-Float64(x / t)));
	elseif (z <= 4.8e+47)
		tmp = t_1;
	elseif (z <= 5e+83)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	tmp = 0.0;
	if (z <= -5.5e+57)
		tmp = x;
	elseif (z <= -7.6e+25)
		tmp = -x / (t / z);
	elseif (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.16e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = z * -(x / t);
	elseif (z <= 4.8e+47)
		tmp = t_1;
	elseif (z <= 5e+83)
		tmp = x;
	elseif (z <= 3.25e+125)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+57], x, If[LessEqual[z, -7.6e+25], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, -1.9e-61], t$95$1, If[LessEqual[z, -1.16e-66], x, If[LessEqual[z, -1.8e-150], N[(z * (-N[(x / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 4.8e+47], t$95$1, If[LessEqual[z, 5e+83], x, If[LessEqual[z, 3.25e+125], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.5000000000000002e57 or -7.6000000000000001e25 < z < -7.50000000000000019e-6 or -1.8999999999999999e-61 < z < -1.16000000000000002e-66 or 4.80000000000000037e47 < z < 5.00000000000000029e83 or 3.2499999999999999e125 < z

   1. Initial program 75.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in z around inf 69.1%

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

   if -5.5000000000000002e57 < z < -7.6000000000000001e25

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 61.1%

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

      2. associate-*l* 61.1%

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

      3. neg-mul-1 61.1%

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

      4. *-commutative 61.1%

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

   6. Simplified 61.1%

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

      1. clear-num 61.3%

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

      2. associate-*l/ 61.5%

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

      3. *-un-lft-identity 61.5%

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

      4. add-sqr-sqrt 61.3%

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

      5. sqrt-unprod 61.5%

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

      6. sqr-neg 61.5%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 5.8%

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

      9. frac-2neg 5.8%

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

      10. add-sqr-sqrt 5.8%

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

      11. sqrt-unprod 5.8%

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

      12. sqr-neg 5.8%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 61.5%

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

      15. distribute-neg-frac 61.5%

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

   8. Applied egg-rr 61.5%

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

      1. associate-/r/ 71.9%

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

      2. +-commutative 71.9%

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

   10. Simplified 71.9%

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

   11. Taylor expanded in z around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. *-commutative 62.2%

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

       3. associate-/l* 62.6%

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

       4. distribute-neg-frac 62.6%

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

   13. Simplified 62.6%

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

   if -7.50000000000000019e-6 < z < -1.8999999999999999e-61 or -1.8000000000000001e-150 < z < 4.80000000000000037e47

   1. Initial program 95.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-/l* 67.3%

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

      2. associate-/r/ 70.5%

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

   6. Simplified 70.5%

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

      1. *-commutative 70.5%

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

      2. clear-num 70.3%

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

      3. un-div-inv 70.8%

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

   8. Applied egg-rr 70.8%

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

   if -1.16000000000000002e-66 < z < -1.8000000000000001e-150

   1. Initial program 94.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 43.6%

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

      1. associate-*r/ 48.3%

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

      2. associate-*l* 48.3%

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

      3. neg-mul-1 48.3%

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

      4. *-commutative 48.3%

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

   6. Simplified 48.3%

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

   7. Taylor expanded in t around inf 46.7%

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

   if 5.00000000000000029e83 < z < 3.2499999999999999e125

   1. Initial program 80.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in z around 0 42.3%

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

      1. associate-/l* 23.7%

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

      2. associate-/r/ 51.9%

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

   6. Simplified 51.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+25}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{t - z}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+21}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-234}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+48} \lor \neg \left(z \leq 5.4 \cdot 10^{+85}\right) \land z \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x (- t z)))))
   (if (<= z -2.4e+57)
     x
     (if (<= z -1.75e+21)
       (/ (- x) (/ t z))
       (if (<= z -680000000.0)
         x
         (if (<= z -8.5e-101)
           t_1
           (if (<= z 1.65e-234)
             (* (- y z) (/ x t))
             (if (or (<= z 7.2e+48) (and (not (<= z 5.4e+85)) (<= z 2.7e+129)))
               t_1
               x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double tmp;
	if (z <= -2.4e+57) {
		tmp = x;
	} else if (z <= -1.75e+21) {
		tmp = -x / (t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -8.5e-101) {
		tmp = t_1;
	} else if (z <= 1.65e-234) {
		tmp = (y - z) * (x / t);
	} else if ((z <= 7.2e+48) || (!(z <= 5.4e+85) && (z <= 2.7e+129))) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = y * (x / (t - z))
    if (z <= (-2.4d+57)) then
        tmp = x
    else if (z <= (-1.75d+21)) then
        tmp = -x / (t / z)
    else if (z <= (-680000000.0d0)) then
        tmp = x
    else if (z <= (-8.5d-101)) then
        tmp = t_1
    else if (z <= 1.65d-234) then
        tmp = (y - z) * (x / t)
    else if ((z <= 7.2d+48) .or. (.not. (z <= 5.4d+85)) .and. (z <= 2.7d+129)) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double tmp;
	if (z <= -2.4e+57) {
		tmp = x;
	} else if (z <= -1.75e+21) {
		tmp = -x / (t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -8.5e-101) {
		tmp = t_1;
	} else if (z <= 1.65e-234) {
		tmp = (y - z) * (x / t);
	} else if ((z <= 7.2e+48) || (!(z <= 5.4e+85) && (z <= 2.7e+129))) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / (t - z))
	tmp = 0
	if z <= -2.4e+57:
		tmp = x
	elif z <= -1.75e+21:
		tmp = -x / (t / z)
	elif z <= -680000000.0:
		tmp = x
	elif z <= -8.5e-101:
		tmp = t_1
	elif z <= 1.65e-234:
		tmp = (y - z) * (x / t)
	elif (z <= 7.2e+48) or (not (z <= 5.4e+85) and (z <= 2.7e+129)):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / Float64(t - z)))
	tmp = 0.0
	if (z <= -2.4e+57)
		tmp = x;
	elseif (z <= -1.75e+21)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -8.5e-101)
		tmp = t_1;
	elseif (z <= 1.65e-234)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif ((z <= 7.2e+48) || (!(z <= 5.4e+85) && (z <= 2.7e+129)))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / (t - z));
	tmp = 0.0;
	if (z <= -2.4e+57)
		tmp = x;
	elseif (z <= -1.75e+21)
		tmp = -x / (t / z);
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -8.5e-101)
		tmp = t_1;
	elseif (z <= 1.65e-234)
		tmp = (y - z) * (x / t);
	elseif ((z <= 7.2e+48) || (~((z <= 5.4e+85)) && (z <= 2.7e+129)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+57], x, If[LessEqual[z, -1.75e+21], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -680000000.0], x, If[LessEqual[z, -8.5e-101], t$95$1, If[LessEqual[z, 1.65e-234], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 7.2e+48], And[N[Not[LessEqual[z, 5.4e+85]], $MachinePrecision], LessEqual[z, 2.7e+129]]], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000005e57 or -1.75e21 < z < -6.8e8 or 7.19999999999999967e48 < z < 5.39999999999999966e85 or 2.7000000000000001e129 < z

   1. Initial program 74.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in z around inf 70.4%

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

   if -2.40000000000000005e57 < z < -1.75e21

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 61.1%

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

      2. associate-*l* 61.1%

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

      3. neg-mul-1 61.1%

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

      4. *-commutative 61.1%

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

   6. Simplified 61.1%

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

      1. clear-num 61.3%

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

      2. associate-*l/ 61.5%

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

      3. *-un-lft-identity 61.5%

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

      4. add-sqr-sqrt 61.3%

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

      5. sqrt-unprod 61.5%

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

      6. sqr-neg 61.5%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 5.8%

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

      9. frac-2neg 5.8%

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

      10. add-sqr-sqrt 5.8%

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

      11. sqrt-unprod 5.8%

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

      12. sqr-neg 5.8%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 61.5%

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

      15. distribute-neg-frac 61.5%

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

   8. Applied egg-rr 61.5%

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

      1. associate-/r/ 71.9%

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

      2. +-commutative 71.9%

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

   10. Simplified 71.9%

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

   11. Taylor expanded in z around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. *-commutative 62.2%

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

       3. associate-/l* 62.6%

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

       4. distribute-neg-frac 62.6%

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

   13. Simplified 62.6%

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

   if -6.8e8 < z < -8.49999999999999941e-101 or 1.65000000000000007e-234 < z < 7.19999999999999967e48 or 5.39999999999999966e85 < z < 2.7000000000000001e129

   1. Initial program 92.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 71.4%

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

      1. associate-*r/ 71.9%

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

   6. Simplified 71.9%

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

   if -8.49999999999999941e-101 < z < 1.65000000000000007e-234

   1. Initial program 96.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in t around inf 85.6%

      \[\leadsto \color{blue}{\frac{x}{t}} \cdot \left(y - z\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+21}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-234}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+48} \lor \neg \left(z \leq 5.4 \cdot 10^{+85}\right) \land z \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-279}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+47} \lor \neg \left(z \leq 1.6 \cdot 10^{+84}\right) \land z \leq 2.7 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -5.4e+57)
     x
     (if (<= z -5.2e+26)
       (/ (- x) (/ t z))
       (if (<= z -680000000.0)
         x
         (if (<= z -2.8e-97)
           t_1
           (if (<= z -6.5e-279)
             (* (- y z) (/ x t))
             (if (or (<= z 3.8e+47) (and (not (<= z 1.6e+84)) (<= z 2.7e+128)))
               t_1
               x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -5.4e+57) {
		tmp = x;
	} else if (z <= -5.2e+26) {
		tmp = -x / (t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -2.8e-97) {
		tmp = t_1;
	} else if (z <= -6.5e-279) {
		tmp = (y - z) * (x / t);
	} else if ((z <= 3.8e+47) || (!(z <= 1.6e+84) && (z <= 2.7e+128))) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-5.4d+57)) then
        tmp = x
    else if (z <= (-5.2d+26)) then
        tmp = -x / (t / z)
    else if (z <= (-680000000.0d0)) then
        tmp = x
    else if (z <= (-2.8d-97)) then
        tmp = t_1
    else if (z <= (-6.5d-279)) then
        tmp = (y - z) * (x / t)
    else if ((z <= 3.8d+47) .or. (.not. (z <= 1.6d+84)) .and. (z <= 2.7d+128)) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -5.4e+57) {
		tmp = x;
	} else if (z <= -5.2e+26) {
		tmp = -x / (t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -2.8e-97) {
		tmp = t_1;
	} else if (z <= -6.5e-279) {
		tmp = (y - z) * (x / t);
	} else if ((z <= 3.8e+47) || (!(z <= 1.6e+84) && (z <= 2.7e+128))) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -5.4e+57:
		tmp = x
	elif z <= -5.2e+26:
		tmp = -x / (t / z)
	elif z <= -680000000.0:
		tmp = x
	elif z <= -2.8e-97:
		tmp = t_1
	elif z <= -6.5e-279:
		tmp = (y - z) * (x / t)
	elif (z <= 3.8e+47) or (not (z <= 1.6e+84) and (z <= 2.7e+128)):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -5.4e+57)
		tmp = x;
	elseif (z <= -5.2e+26)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -2.8e-97)
		tmp = t_1;
	elseif (z <= -6.5e-279)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif ((z <= 3.8e+47) || (!(z <= 1.6e+84) && (z <= 2.7e+128)))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -5.4e+57)
		tmp = x;
	elseif (z <= -5.2e+26)
		tmp = -x / (t / z);
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -2.8e-97)
		tmp = t_1;
	elseif (z <= -6.5e-279)
		tmp = (y - z) * (x / t);
	elseif ((z <= 3.8e+47) || (~((z <= 1.6e+84)) && (z <= 2.7e+128)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+57], x, If[LessEqual[z, -5.2e+26], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -680000000.0], x, If[LessEqual[z, -2.8e-97], t$95$1, If[LessEqual[z, -6.5e-279], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.8e+47], And[N[Not[LessEqual[z, 1.6e+84]], $MachinePrecision], LessEqual[z, 2.7e+128]]], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.3999999999999997e57 or -5.20000000000000004e26 < z < -6.8e8 or 3.8000000000000003e47 < z < 1.60000000000000005e84 or 2.70000000000000001e128 < z

   1. Initial program 74.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in z around inf 70.4%

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

   if -5.3999999999999997e57 < z < -5.20000000000000004e26

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 61.1%

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

      2. associate-*l* 61.1%

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

      3. neg-mul-1 61.1%

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

      4. *-commutative 61.1%

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

   6. Simplified 61.1%

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

      1. clear-num 61.3%

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

      2. associate-*l/ 61.5%

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

      3. *-un-lft-identity 61.5%

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

      4. add-sqr-sqrt 61.3%

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

      5. sqrt-unprod 61.5%

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

      6. sqr-neg 61.5%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 5.8%

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

      9. frac-2neg 5.8%

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

      10. add-sqr-sqrt 5.8%

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

      11. sqrt-unprod 5.8%

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

      12. sqr-neg 5.8%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 61.5%

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

      15. distribute-neg-frac 61.5%

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

   8. Applied egg-rr 61.5%

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

      1. associate-/r/ 71.9%

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

      2. +-commutative 71.9%

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

   10. Simplified 71.9%

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

   11. Taylor expanded in z around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. *-commutative 62.2%

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

       3. associate-/l* 62.6%

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

       4. distribute-neg-frac 62.6%

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

   13. Simplified 62.6%

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

   if -6.8e8 < z < -2.8000000000000002e-97 or -6.4999999999999997e-279 < z < 3.8000000000000003e47 or 1.60000000000000005e84 < z < 2.70000000000000001e128

   1. Initial program 93.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. associate-*r/ 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in y around 0 77.0%

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

      1. associate-/l* 73.8%

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

      2. associate-/r/ 82.0%

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

   9. Simplified 82.0%

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

   if -2.8000000000000002e-97 < z < -6.4999999999999997e-279

   1. Initial program 96.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in t around inf 84.4%

      \[\leadsto \color{blue}{\frac{x}{t}} \cdot \left(y - z\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-279}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+47} \lor \neg \left(z \leq 1.6 \cdot 10^{+84}\right) \land z \leq 2.7 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 66.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -4.4e+57)
     x
     (if (<= z -1.6e+19)
       (/ (- x) (/ t z))
       (if (<= z -680000000.0)
         x
         (if (<= z -3.3e-105)
           t_1
           (if (<= z -4.4e-279)
             (* (- y z) (/ x t))
             (if (<= z 3.9e+48)
               t_1
               (if (<= z 2.6e+85)
                 x
                 (if (<= z 2.55e+129) t_1 (+ x (/ t (/ z x)))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -4.4e+57) {
		tmp = x;
	} else if (z <= -1.6e+19) {
		tmp = -x / (t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -3.3e-105) {
		tmp = t_1;
	} else if (z <= -4.4e-279) {
		tmp = (y - z) * (x / t);
	} else if (z <= 3.9e+48) {
		tmp = t_1;
	} else if (z <= 2.6e+85) {
		tmp = x;
	} else if (z <= 2.55e+129) {
		tmp = t_1;
	} else {
		tmp = x + (t / (z / 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-4.4d+57)) then
        tmp = x
    else if (z <= (-1.6d+19)) then
        tmp = -x / (t / z)
    else if (z <= (-680000000.0d0)) then
        tmp = x
    else if (z <= (-3.3d-105)) then
        tmp = t_1
    else if (z <= (-4.4d-279)) then
        tmp = (y - z) * (x / t)
    else if (z <= 3.9d+48) then
        tmp = t_1
    else if (z <= 2.6d+85) then
        tmp = x
    else if (z <= 2.55d+129) then
        tmp = t_1
    else
        tmp = x + (t / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -4.4e+57) {
		tmp = x;
	} else if (z <= -1.6e+19) {
		tmp = -x / (t / z);
	} else if (z <= -680000000.0) {
		tmp = x;
	} else if (z <= -3.3e-105) {
		tmp = t_1;
	} else if (z <= -4.4e-279) {
		tmp = (y - z) * (x / t);
	} else if (z <= 3.9e+48) {
		tmp = t_1;
	} else if (z <= 2.6e+85) {
		tmp = x;
	} else if (z <= 2.55e+129) {
		tmp = t_1;
	} else {
		tmp = x + (t / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -4.4e+57:
		tmp = x
	elif z <= -1.6e+19:
		tmp = -x / (t / z)
	elif z <= -680000000.0:
		tmp = x
	elif z <= -3.3e-105:
		tmp = t_1
	elif z <= -4.4e-279:
		tmp = (y - z) * (x / t)
	elif z <= 3.9e+48:
		tmp = t_1
	elif z <= 2.6e+85:
		tmp = x
	elif z <= 2.55e+129:
		tmp = t_1
	else:
		tmp = x + (t / (z / x))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -4.4e+57)
		tmp = x;
	elseif (z <= -1.6e+19)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -3.3e-105)
		tmp = t_1;
	elseif (z <= -4.4e-279)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 3.9e+48)
		tmp = t_1;
	elseif (z <= 2.6e+85)
		tmp = x;
	elseif (z <= 2.55e+129)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -4.4e+57)
		tmp = x;
	elseif (z <= -1.6e+19)
		tmp = -x / (t / z);
	elseif (z <= -680000000.0)
		tmp = x;
	elseif (z <= -3.3e-105)
		tmp = t_1;
	elseif (z <= -4.4e-279)
		tmp = (y - z) * (x / t);
	elseif (z <= 3.9e+48)
		tmp = t_1;
	elseif (z <= 2.6e+85)
		tmp = x;
	elseif (z <= 2.55e+129)
		tmp = t_1;
	else
		tmp = x + (t / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+57], x, If[LessEqual[z, -1.6e+19], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -680000000.0], x, If[LessEqual[z, -3.3e-105], t$95$1, If[LessEqual[z, -4.4e-279], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+48], t$95$1, If[LessEqual[z, 2.6e+85], x, If[LessEqual[z, 2.55e+129], t$95$1, N[(x + N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.4000000000000001e57 or -1.6e19 < z < -6.8e8 or 3.9000000000000001e48 < z < 2.60000000000000011e85

   1. Initial program 73.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in z around inf 71.5%

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

   if -4.4000000000000001e57 < z < -1.6e19

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 61.1%

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

      2. associate-*l* 61.1%

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

      3. neg-mul-1 61.1%

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

      4. *-commutative 61.1%

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

   6. Simplified 61.1%

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

      1. clear-num 61.3%

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

      2. associate-*l/ 61.5%

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

      3. *-un-lft-identity 61.5%

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

      4. add-sqr-sqrt 61.3%

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

      5. sqrt-unprod 61.5%

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

      6. sqr-neg 61.5%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 5.8%

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

      9. frac-2neg 5.8%

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

      10. add-sqr-sqrt 5.8%

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

      11. sqrt-unprod 5.8%

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

      12. sqr-neg 5.8%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 61.5%

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

      15. distribute-neg-frac 61.5%

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

   8. Applied egg-rr 61.5%

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

      1. associate-/r/ 71.9%

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

      2. +-commutative 71.9%

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

   10. Simplified 71.9%

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

   11. Taylor expanded in z around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. *-commutative 62.2%

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

       3. associate-/l* 62.6%

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

       4. distribute-neg-frac 62.6%

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

   13. Simplified 62.6%

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

   if -6.8e8 < z < -3.2999999999999999e-105 or -4.40000000000000001e-279 < z < 3.9000000000000001e48 or 2.60000000000000011e85 < z < 2.54999999999999998e129

   1. Initial program 93.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. associate-*r/ 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in y around 0 77.0%

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

      1. associate-/l* 73.8%

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

      2. associate-/r/ 82.0%

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

   9. Simplified 82.0%

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

   if -3.2999999999999999e-105 < z < -4.40000000000000001e-279

   1. Initial program 96.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in t around inf 84.4%

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

   if 2.54999999999999998e129 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in y around 0 63.3%

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

      1. associate-*r/ 54.9%

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

      2. associate-*l* 54.9%

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

      3. neg-mul-1 54.9%

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

      4. *-commutative 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in t around 0 63.0%

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

      1. +-commutative 63.0%

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

      2. associate-/l* 68.3%

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

   9. Simplified 68.3%

      \[\leadsto \color{blue}{x + \frac{t}{\frac{z}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -680000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ t_2 := \frac{x}{\frac{z}{z - y}}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-279}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+30} \lor \neg \left(z \leq 9.2 \cdot 10^{+85}\right) \land z \leq 1.75 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))) (t_2 (/ x (/ z (- z y)))))
   (if (<= z -7.2e-6)
     t_2
     (if (<= z -1.75e-59)
       t_1
       (if (<= z -4.3e-78)
         t_2
         (if (<= z -2.15e-279)
           (* (- y z) (/ x t))
           (if (or (<= z 1.75e+30) (and (not (<= z 9.2e+85)) (<= z 1.75e+128)))
             t_1
             t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x / (z / (z - y));
	double tmp;
	if (z <= -7.2e-6) {
		tmp = t_2;
	} else if (z <= -1.75e-59) {
		tmp = t_1;
	} else if (z <= -4.3e-78) {
		tmp = t_2;
	} else if (z <= -2.15e-279) {
		tmp = (y - z) * (x / t);
	} else if ((z <= 1.75e+30) || (!(z <= 9.2e+85) && (z <= 1.75e+128))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    t_2 = x / (z / (z - y))
    if (z <= (-7.2d-6)) then
        tmp = t_2
    else if (z <= (-1.75d-59)) then
        tmp = t_1
    else if (z <= (-4.3d-78)) then
        tmp = t_2
    else if (z <= (-2.15d-279)) then
        tmp = (y - z) * (x / t)
    else if ((z <= 1.75d+30) .or. (.not. (z <= 9.2d+85)) .and. (z <= 1.75d+128)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x / (z / (z - y));
	double tmp;
	if (z <= -7.2e-6) {
		tmp = t_2;
	} else if (z <= -1.75e-59) {
		tmp = t_1;
	} else if (z <= -4.3e-78) {
		tmp = t_2;
	} else if (z <= -2.15e-279) {
		tmp = (y - z) * (x / t);
	} else if ((z <= 1.75e+30) || (!(z <= 9.2e+85) && (z <= 1.75e+128))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	t_2 = x / (z / (z - y))
	tmp = 0
	if z <= -7.2e-6:
		tmp = t_2
	elif z <= -1.75e-59:
		tmp = t_1
	elif z <= -4.3e-78:
		tmp = t_2
	elif z <= -2.15e-279:
		tmp = (y - z) * (x / t)
	elif (z <= 1.75e+30) or (not (z <= 9.2e+85) and (z <= 1.75e+128)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	t_2 = Float64(x / Float64(z / Float64(z - y)))
	tmp = 0.0
	if (z <= -7.2e-6)
		tmp = t_2;
	elseif (z <= -1.75e-59)
		tmp = t_1;
	elseif (z <= -4.3e-78)
		tmp = t_2;
	elseif (z <= -2.15e-279)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif ((z <= 1.75e+30) || (!(z <= 9.2e+85) && (z <= 1.75e+128)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	t_2 = x / (z / (z - y));
	tmp = 0.0;
	if (z <= -7.2e-6)
		tmp = t_2;
	elseif (z <= -1.75e-59)
		tmp = t_1;
	elseif (z <= -4.3e-78)
		tmp = t_2;
	elseif (z <= -2.15e-279)
		tmp = (y - z) * (x / t);
	elseif ((z <= 1.75e+30) || (~((z <= 9.2e+85)) && (z <= 1.75e+128)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e-6], t$95$2, If[LessEqual[z, -1.75e-59], t$95$1, If[LessEqual[z, -4.3e-78], t$95$2, If[LessEqual[z, -2.15e-279], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.75e+30], And[N[Not[LessEqual[z, 9.2e+85]], $MachinePrecision], LessEqual[z, 1.75e+128]]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999967e-6 or -1.75e-59 < z < -4.29999999999999994e-78 or 1.75000000000000011e30 < z < 9.1999999999999996e85 or 1.74999999999999984e128 < z

   1. Initial program 78.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 78.1%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in x around 0 78.1%

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

      1. associate-/l* 71.5%

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

      2. sub-neg 71.5%

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

      3. remove-double-neg 71.5%

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

      4. distribute-neg-in 71.5%

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

      5. neg-mul-1 71.5%

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

      6. sub-neg 71.5%

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

      7. remove-double-neg 71.5%

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

      8. distribute-neg-in 71.5%

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

      9. distribute-neg-frac 71.5%

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

      10. neg-mul-1 71.5%

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

      11. times-frac 71.5%

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

      12. metadata-eval 71.5%

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

      13. *-rgt-identity 71.5%

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

      14. associate-*r/ 71.2%

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

      15. associate-*l* 71.2%

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

      16. *-lft-identity 71.2%

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

      17. associate-*r/ 71.5%

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

      18. *-rgt-identity 71.5%

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

      19. associate-/l* 78.1%

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

      20. *-commutative 78.1%

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

      21. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in t around 0 79.0%

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

   if -7.19999999999999967e-6 < z < -1.75e-59 or -2.15000000000000003e-279 < z < 1.75000000000000011e30 or 9.1999999999999996e85 < z < 1.74999999999999984e128

   1. Initial program 93.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in y around inf 78.5%

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

      1. associate-*r/ 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in y around 0 78.5%

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

      1. associate-/l* 74.9%

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

      2. associate-/r/ 84.3%

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

   9. Simplified 84.3%

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

   if -4.29999999999999994e-78 < z < -2.15000000000000003e-279

   1. Initial program 96.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in t around inf 83.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-279}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+30} \lor \neg \left(z \leq 9.2 \cdot 10^{+85}\right) \land z \leq 1.75 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \end{array} \]

Alternative 8: 58.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))))
   (if (<= z -7.5e-6)
     x
     (if (<= z -1.9e-61)
       t_1
       (if (<= z -1.15e-66)
         x
         (if (<= z -1.8e-150)
           (* z (- (/ x t)))
           (if (<= z 3.5e+47)
             t_1
             (if (<= z 4.2e+85) x (if (<= z 5e+125) (* x (/ y t)) x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.15e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * -(x / t);
	} else if (z <= 3.5e+47) {
		tmp = t_1;
	} else if (z <= 4.2e+85) {
		tmp = x;
	} else if (z <= 5e+125) {
		tmp = x * (y / t);
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x / (t / y)
    if (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= (-1.9d-61)) then
        tmp = t_1
    else if (z <= (-1.15d-66)) then
        tmp = x
    else if (z <= (-1.8d-150)) then
        tmp = z * -(x / t)
    else if (z <= 3.5d+47) then
        tmp = t_1
    else if (z <= 4.2d+85) then
        tmp = x
    else if (z <= 5d+125) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= -1.9e-61) {
		tmp = t_1;
	} else if (z <= -1.15e-66) {
		tmp = x;
	} else if (z <= -1.8e-150) {
		tmp = z * -(x / t);
	} else if (z <= 3.5e+47) {
		tmp = t_1;
	} else if (z <= 4.2e+85) {
		tmp = x;
	} else if (z <= 5e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	tmp = 0
	if z <= -7.5e-6:
		tmp = x
	elif z <= -1.9e-61:
		tmp = t_1
	elif z <= -1.15e-66:
		tmp = x
	elif z <= -1.8e-150:
		tmp = z * -(x / t)
	elif z <= 3.5e+47:
		tmp = t_1
	elif z <= 4.2e+85:
		tmp = x
	elif z <= 5e+125:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	tmp = 0.0
	if (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.15e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = Float64(z * Float64(-Float64(x / t)));
	elseif (z <= 3.5e+47)
		tmp = t_1;
	elseif (z <= 4.2e+85)
		tmp = x;
	elseif (z <= 5e+125)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	tmp = 0.0;
	if (z <= -7.5e-6)
		tmp = x;
	elseif (z <= -1.9e-61)
		tmp = t_1;
	elseif (z <= -1.15e-66)
		tmp = x;
	elseif (z <= -1.8e-150)
		tmp = z * -(x / t);
	elseif (z <= 3.5e+47)
		tmp = t_1;
	elseif (z <= 4.2e+85)
		tmp = x;
	elseif (z <= 5e+125)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, -1.9e-61], t$95$1, If[LessEqual[z, -1.15e-66], x, If[LessEqual[z, -1.8e-150], N[(z * (-N[(x / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.5e+47], t$95$1, If[LessEqual[z, 4.2e+85], x, If[LessEqual[z, 5e+125], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.50000000000000019e-6 or -1.8999999999999999e-61 < z < -1.14999999999999996e-66 or 3.50000000000000015e47 < z < 4.2000000000000002e85 or 4.99999999999999962e125 < z

   1. Initial program 77.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in z around inf 65.1%

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

   if -7.50000000000000019e-6 < z < -1.8999999999999999e-61 or -1.8000000000000001e-150 < z < 3.50000000000000015e47

   1. Initial program 95.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. associate-/l* 67.3%

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

      2. associate-/r/ 70.5%

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

   6. Simplified 70.5%

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

      1. *-commutative 70.5%

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

      2. clear-num 70.3%

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

      3. un-div-inv 70.8%

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

   8. Applied egg-rr 70.8%

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

   if -1.14999999999999996e-66 < z < -1.8000000000000001e-150

   1. Initial program 94.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 43.6%

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

      1. associate-*r/ 48.3%

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

      2. associate-*l* 48.3%

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

      3. neg-mul-1 48.3%

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

      4. *-commutative 48.3%

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

   6. Simplified 48.3%

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

   7. Taylor expanded in t around inf 46.7%

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

   if 4.2000000000000002e85 < z < 4.99999999999999962e125

   1. Initial program 80.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in z around 0 42.3%

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

      1. associate-/l* 23.7%

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

      2. associate-/r/ 51.9%

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

   6. Simplified 51.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -150000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+47} \lor \neg \left(z \leq 3.5 \cdot 10^{+82}\right) \land z \leq 1.9 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.7e+57)
   x
   (if (<= z -2.55e+23)
     (/ (- x) (/ t z))
     (if (<= z -150000000.0)
       x
       (if (or (<= z 7e+47) (and (not (<= z 3.5e+82)) (<= z 1.9e+128)))
         (* y (/ x (- t z)))
         x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.7e+57) {
		tmp = x;
	} else if (z <= -2.55e+23) {
		tmp = -x / (t / z);
	} else if (z <= -150000000.0) {
		tmp = x;
	} else if ((z <= 7e+47) || (!(z <= 3.5e+82) && (z <= 1.9e+128))) {
		tmp = y * (x / (t - z));
	} else {
		tmp = 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 (z <= (-5.7d+57)) then
        tmp = x
    else if (z <= (-2.55d+23)) then
        tmp = -x / (t / z)
    else if (z <= (-150000000.0d0)) then
        tmp = x
    else if ((z <= 7d+47) .or. (.not. (z <= 3.5d+82)) .and. (z <= 1.9d+128)) then
        tmp = y * (x / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.7e+57) {
		tmp = x;
	} else if (z <= -2.55e+23) {
		tmp = -x / (t / z);
	} else if (z <= -150000000.0) {
		tmp = x;
	} else if ((z <= 7e+47) || (!(z <= 3.5e+82) && (z <= 1.9e+128))) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.7e+57:
		tmp = x
	elif z <= -2.55e+23:
		tmp = -x / (t / z)
	elif z <= -150000000.0:
		tmp = x
	elif (z <= 7e+47) or (not (z <= 3.5e+82) and (z <= 1.9e+128)):
		tmp = y * (x / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.7e+57)
		tmp = x;
	elseif (z <= -2.55e+23)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= -150000000.0)
		tmp = x;
	elseif ((z <= 7e+47) || (!(z <= 3.5e+82) && (z <= 1.9e+128)))
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.7e+57)
		tmp = x;
	elseif (z <= -2.55e+23)
		tmp = -x / (t / z);
	elseif (z <= -150000000.0)
		tmp = x;
	elseif ((z <= 7e+47) || (~((z <= 3.5e+82)) && (z <= 1.9e+128)))
		tmp = y * (x / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.7e+57], x, If[LessEqual[z, -2.55e+23], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -150000000.0], x, If[Or[LessEqual[z, 7e+47], And[N[Not[LessEqual[z, 3.5e+82]], $MachinePrecision], LessEqual[z, 1.9e+128]]], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6999999999999998e57 or -2.5500000000000001e23 < z < -1.5e8 or 7.00000000000000031e47 < z < 3.5e82 or 1.89999999999999995e128 < z

   1. Initial program 74.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in z around inf 70.4%

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

   if -5.6999999999999998e57 < z < -2.5500000000000001e23

   1. Initial program 99.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 61.1%

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

      2. associate-*l* 61.1%

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

      3. neg-mul-1 61.1%

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

      4. *-commutative 61.1%

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

   6. Simplified 61.1%

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

      1. clear-num 61.3%

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

      2. associate-*l/ 61.5%

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

      3. *-un-lft-identity 61.5%

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

      4. add-sqr-sqrt 61.3%

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

      5. sqrt-unprod 61.5%

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

      6. sqr-neg 61.5%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 5.8%

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

      9. frac-2neg 5.8%

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

      10. add-sqr-sqrt 5.8%

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

      11. sqrt-unprod 5.8%

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

      12. sqr-neg 5.8%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 61.5%

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

      15. distribute-neg-frac 61.5%

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

   8. Applied egg-rr 61.5%

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

      1. associate-/r/ 71.9%

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

      2. +-commutative 71.9%

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

   10. Simplified 71.9%

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

   11. Taylor expanded in z around 0 62.2%

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

       1. mul-1-neg 62.2%

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

       2. *-commutative 62.2%

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

       3. associate-/l* 62.6%

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

       4. distribute-neg-frac 62.6%

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

   13. Simplified 62.6%

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

   if -1.5e8 < z < 7.00000000000000031e47 or 3.5e82 < z < 1.89999999999999995e128

   1. Initial program 94.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in y around inf 76.6%

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

      1. associate-*r/ 74.4%

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

   6. Simplified 74.4%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -150000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+47} \lor \neg \left(z \leq 3.5 \cdot 10^{+82}\right) \land z \leq 1.9 \cdot 10^{+128}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+47} \lor \neg \left(z \leq 4 \cdot 10^{+83}\right) \land z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-6)
   x
   (if (or (<= z 4.5e+47) (and (not (<= z 4e+83)) (<= z 3.25e+125)))
     (* x (/ y t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if ((z <= 4.5e+47) || (!(z <= 4e+83) && (z <= 3.25e+125))) {
		tmp = x * (y / t);
	} else {
		tmp = 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 (z <= (-7.5d-6)) then
        tmp = x
    else if ((z <= 4.5d+47) .or. (.not. (z <= 4d+83)) .and. (z <= 3.25d+125)) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if ((z <= 4.5e+47) || (!(z <= 4e+83) && (z <= 3.25e+125))) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-6:
		tmp = x
	elif (z <= 4.5e+47) or (not (z <= 4e+83) and (z <= 3.25e+125)):
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-6)
		tmp = x;
	elseif ((z <= 4.5e+47) || (!(z <= 4e+83) && (z <= 3.25e+125)))
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-6)
		tmp = x;
	elseif ((z <= 4.5e+47) || (~((z <= 4e+83)) && (z <= 3.25e+125)))
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-6], x, If[Or[LessEqual[z, 4.5e+47], And[N[Not[LessEqual[z, 4e+83]], $MachinePrecision], LessEqual[z, 3.25e+125]]], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000019e-6 or 4.49999999999999979e47 < z < 4.00000000000000012e83 or 3.2499999999999999e125 < z

   1. Initial program 76.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in z around inf 64.5%

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

   if -7.50000000000000019e-6 < z < 4.49999999999999979e47 or 4.00000000000000012e83 < z < 3.2499999999999999e125

   1. Initial program 94.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in z around 0 61.7%

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

      1. associate-/l* 59.2%

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

      2. associate-/r/ 63.7%

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

   6. Simplified 63.7%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+47} \lor \neg \left(z \leq 4 \cdot 10^{+83}\right) \land z \leq 3.25 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-6)
   x
   (if (<= z 8.2e+47)
     (/ x (/ t y))
     (if (<= z 1.95e+85) x (if (<= z 3.5e+125) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= 8.2e+47) {
		tmp = x / (t / y);
	} else if (z <= 1.95e+85) {
		tmp = x;
	} else if (z <= 3.5e+125) {
		tmp = x * (y / t);
	} else {
		tmp = 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 (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= 8.2d+47) then
        tmp = x / (t / y)
    else if (z <= 1.95d+85) then
        tmp = x
    else if (z <= 3.5d+125) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= 8.2e+47) {
		tmp = x / (t / y);
	} else if (z <= 1.95e+85) {
		tmp = x;
	} else if (z <= 3.5e+125) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-6:
		tmp = x
	elif z <= 8.2e+47:
		tmp = x / (t / y)
	elif z <= 1.95e+85:
		tmp = x
	elif z <= 3.5e+125:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-6)
		tmp = x;
	elseif (z <= 8.2e+47)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 1.95e+85)
		tmp = x;
	elseif (z <= 3.5e+125)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-6)
		tmp = x;
	elseif (z <= 8.2e+47)
		tmp = x / (t / y);
	elseif (z <= 1.95e+85)
		tmp = x;
	elseif (z <= 3.5e+125)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, 8.2e+47], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+85], x, If[LessEqual[z, 3.5e+125], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000019e-6 or 8.2000000000000002e47 < z < 1.95000000000000017e85 or 3.50000000000000011e125 < z

   1. Initial program 76.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in z around inf 64.5%

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

   if -7.50000000000000019e-6 < z < 8.2000000000000002e47

   1. Initial program 95.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 63.2%

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

      1. associate-/l* 61.9%

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

      2. associate-/r/ 64.5%

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

   6. Simplified 64.5%

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

      1. *-commutative 64.5%

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

      2. clear-num 64.4%

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

      3. un-div-inv 64.8%

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

   8. Applied egg-rr 64.8%

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

   if 1.95000000000000017e85 < z < 3.50000000000000011e125

   1. Initial program 80.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in z around 0 42.3%

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

      1. associate-/l* 23.7%

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

      2. associate-/r/ 51.9%

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

   6. Simplified 51.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 88.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+151}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+43)
   (* x (/ z (- z t)))
   (if (<= z 5.1e+151) (* (- y z) (/ x (- t z))) (/ x (/ (- z t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+43) {
		tmp = x * (z / (z - t));
	} else if (z <= 5.1e+151) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.5d+43)) then
        tmp = x * (z / (z - t))
    else if (z <= 5.1d+151) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = x / ((z - t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+43) {
		tmp = x * (z / (z - t));
	} else if (z <= 5.1e+151) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e+43:
		tmp = x * (z / (z - t))
	elif z <= 5.1e+151:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = x / ((z - t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+43)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 5.1e+151)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(z - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e+43)
		tmp = x * (z / (z - t));
	elseif (z <= 5.1e+151)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = x / ((z - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+43], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e+151], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999989e43

   1. Initial program 72.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in y around 0 62.2%

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

      1. associate-*r/ 57.8%

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

      2. associate-*l* 57.8%

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

      3. neg-mul-1 57.8%

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

      4. *-commutative 57.8%

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

   6. Simplified 57.8%

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

      1. clear-num 56.9%

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

      2. associate-*l/ 57.1%

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

      3. *-un-lft-identity 57.1%

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

      4. add-sqr-sqrt 56.8%

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

      5. sqrt-unprod 27.1%

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

      6. sqr-neg 27.1%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 8.4%

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

      9. frac-2neg 8.4%

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

      10. add-sqr-sqrt 8.4%

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

      11. sqrt-unprod 3.3%

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

      12. sqr-neg 3.3%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 57.1%

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

      15. distribute-neg-frac 57.1%

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

   8. Applied egg-rr 57.1%

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

      1. associate-/r/ 85.5%

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

      2. +-commutative 85.5%

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

   10. Simplified 85.5%

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

   if -5.49999999999999989e43 < z < 5.09999999999999996e151

   1. Initial program 94.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

   if 5.09999999999999996e151 < z

   1. Initial program 73.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 73.4%

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

      2. times-frac 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in x around 0 73.4%

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

      1. associate-/l* 54.4%

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

      2. sub-neg 54.4%

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

      3. remove-double-neg 54.4%

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

      4. distribute-neg-in 54.4%

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

      5. neg-mul-1 54.4%

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

      6. sub-neg 54.4%

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

      7. remove-double-neg 54.4%

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

      8. distribute-neg-in 54.4%

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

      9. distribute-neg-frac 54.4%

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

      10. neg-mul-1 54.4%

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

      11. times-frac 54.4%

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

      12. metadata-eval 54.4%

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

      13. *-rgt-identity 54.4%

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

      14. associate-*r/ 54.3%

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

      15. associate-*l* 54.3%

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

      16. *-lft-identity 54.3%

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

      17. associate-*r/ 54.4%

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

      18. *-rgt-identity 54.4%

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

      19. associate-/l* 73.4%

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

      20. *-commutative 73.4%

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

      21. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around 0 88.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+151}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \]

Alternative 13: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-100} \lor \neg \left(y \leq 20000000\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e-100) (not (<= y 20000000.0)))
   (* x (/ y (- t z)))
   (/ x (/ (- z t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e-100) || !(y <= 20000000.0)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4d-100)) .or. (.not. (y <= 20000000.0d0))) then
        tmp = x * (y / (t - z))
    else
        tmp = x / ((z - t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e-100) || !(y <= 20000000.0)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4e-100) or not (y <= 20000000.0):
		tmp = x * (y / (t - z))
	else:
		tmp = x / ((z - t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4e-100) || !(y <= 20000000.0))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(z - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4e-100) || ~((y <= 20000000.0)))
		tmp = x * (y / (t - z));
	else
		tmp = x / ((z - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4e-100], N[Not[LessEqual[y, 20000000.0]], $MachinePrecision]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000001e-100 or 2e7 < y

   1. Initial program 86.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in y around inf 71.4%

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

      1. associate-*r/ 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in y around 0 71.4%

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

      1. associate-/l* 67.1%

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

      2. associate-/r/ 75.4%

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

   9. Simplified 75.4%

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

   if -4.0000000000000001e-100 < y < 2e7

   1. Initial program 87.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 87.1%

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

      2. times-frac 98.5%

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

   3. Applied egg-rr 98.5%

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

   4. Taylor expanded in x around 0 87.1%

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

      1. associate-/l* 78.4%

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

      2. sub-neg 78.4%

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

      3. remove-double-neg 78.4%

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

      4. distribute-neg-in 78.4%

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

      5. neg-mul-1 78.4%

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

      6. sub-neg 78.4%

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

      7. remove-double-neg 78.4%

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

      8. distribute-neg-in 78.4%

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

      9. distribute-neg-frac 78.4%

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

      10. neg-mul-1 78.4%

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

      11. times-frac 78.4%

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

      12. metadata-eval 78.4%

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

      13. *-rgt-identity 78.4%

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

      14. associate-*r/ 78.2%

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

      15. associate-*l* 78.2%

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

      16. *-lft-identity 78.2%

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

      17. associate-*r/ 78.4%

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

      18. *-rgt-identity 78.4%

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

      19. associate-/l* 87.1%

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

      20. *-commutative 87.1%

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

      21. associate-/l* 97.5%

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

   6. Simplified 97.5%

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

   7. Taylor expanded in y around 0 88.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-100} \lor \neg \left(y \leq 20000000\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \]

Alternative 14: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-97} \lor \neg \left(y \leq 19000000\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e-97) (not (<= y 19000000.0)))
   (* x (/ y (- t z)))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-97) || !(y <= 19000000.0)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - 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 ((y <= (-4.3d-97)) .or. (.not. (y <= 19000000.0d0))) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-97) || !(y <= 19000000.0)) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.3e-97) or not (y <= 19000000.0):
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.3e-97) || !(y <= 19000000.0))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.3e-97) || ~((y <= 19000000.0)))
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.3e-97], N[Not[LessEqual[y, 19000000.0]], $MachinePrecision]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3e-97 or 1.9e7 < y

   1. Initial program 86.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in y around inf 71.4%

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

      1. associate-*r/ 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in y around 0 71.4%

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

      1. associate-/l* 67.1%

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

      2. associate-/r/ 75.4%

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

   9. Simplified 75.4%

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

   if -4.3e-97 < y < 1.9e7

   1. Initial program 87.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in y around 0 78.3%

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

      1. associate-*r/ 72.1%

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

      2. associate-*l* 72.1%

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

      3. neg-mul-1 72.1%

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

      4. *-commutative 72.1%

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

   6. Simplified 72.1%

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

      1. clear-num 70.9%

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

      2. associate-*l/ 71.1%

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

      3. *-un-lft-identity 71.1%

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

      4. add-sqr-sqrt 40.1%

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

      5. sqrt-unprod 38.6%

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

      6. sqr-neg 38.6%

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

      7. sqrt-unprod 9.5%

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

      8. add-sqr-sqrt 19.6%

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

      9. frac-2neg 19.6%

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

      10. add-sqr-sqrt 10.0%

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

      11. sqrt-unprod 34.2%

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

      12. sqr-neg 34.2%

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

      13. sqrt-unprod 30.8%

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

      14. add-sqr-sqrt 71.1%

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

      15. distribute-neg-frac 71.1%

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

   8. Applied egg-rr 71.1%

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

      1. associate-/r/ 89.7%

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

      2. +-commutative 89.7%

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

   10. Simplified 89.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-97} \lor \neg \left(y \leq 19000000\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 15: 37.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e-6) x (if (<= z 1.2e-67) (* x (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e-6) {
		tmp = x;
	} else if (z <= 1.2e-67) {
		tmp = x * (z / t);
	} else {
		tmp = 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 (z <= (-7.2d-6)) then
        tmp = x
    else if (z <= 1.2d-67) then
        tmp = x * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e-6) {
		tmp = x;
	} else if (z <= 1.2e-67) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e-6:
		tmp = x
	elif z <= 1.2e-67:
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e-6)
		tmp = x;
	elseif (z <= 1.2e-67)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.2e-6)
		tmp = x;
	elseif (z <= 1.2e-67)
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e-6], x, If[LessEqual[z, 1.2e-67], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999967e-6 or 1.2e-67 < z

   1. Initial program 78.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in z around inf 53.9%

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

   if -7.19999999999999967e-6 < z < 1.2e-67

   1. Initial program 96.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around 0 33.7%

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

      1. associate-*r/ 34.6%

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

      2. associate-*l* 34.6%

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

      3. neg-mul-1 34.6%

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

      4. *-commutative 34.6%

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

   6. Simplified 34.6%

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

   7. Taylor expanded in t around inf 31.9%

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

      1. expm1-log1p-u 29.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{t} \cdot \left(-z\right)\right)\right)} \]

      2. expm1-udef 20.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \left(-z\right)\right)} - 1} \]

      3. add-sqr-sqrt 11.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}\right)} - 1 \]

      4. sqrt-unprod 20.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right)} - 1 \]

      5. sqr-neg 20.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \sqrt{\color{blue}{z \cdot z}}\right)} - 1 \]

      6. sqrt-unprod 10.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right)} - 1 \]

      7. add-sqr-sqrt 20.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{t} \cdot \color{blue}{z}\right)} - 1 \]

      8. *-commutative 20.9%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{z \cdot \frac{x}{t}}\right)} - 1 \]

   9. Applied egg-rr 20.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(z \cdot \frac{x}{t}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 20.9%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(z \cdot \frac{x}{t}\right)\right)} \]

       2. expm1-log1p 23.0%

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

       3. associate-*r/ 21.1%

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

       4. associate-*l/ 21.2%

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

       5. *-commutative 21.2%

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

   11. Simplified 21.2%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-6) x (if (<= z 3.2e+46) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= 3.2e+46) {
		tmp = y * (x / t);
	} else {
		tmp = 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 (z <= (-7.5d-6)) then
        tmp = x
    else if (z <= 3.2d+46) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-6) {
		tmp = x;
	} else if (z <= 3.2e+46) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-6:
		tmp = x
	elif z <= 3.2e+46:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.5e-6)
		tmp = x;
	elseif (z <= 3.2e+46)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-6)
		tmp = x;
	elseif (z <= 3.2e+46)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-6], x, If[LessEqual[z, 3.2e+46], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000019e-6 or 3.1999999999999998e46 < z

   1. Initial program 77.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-*l/ 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in z around inf 59.6%

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

   if -7.50000000000000019e-6 < z < 3.1999999999999998e46

   1. Initial program 95.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. *-un-lft-identity 95.3%

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

      2. times-frac 95.7%

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

   3. Applied egg-rr 95.7%

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

   4. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

      2. associate-*l/ 62.9%

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

      3. *-commutative 62.9%

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

   6. Simplified 62.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. associate-*l/ 82.5%

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

3. Simplified 82.5%

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

   1. associate-/r/ 97.5%

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

5. Applied egg-rr 97.5%

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

6. Final simplification 97.5%

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

Alternative 18: 35.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. associate-*l/ 82.5%

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

3. Simplified 82.5%

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

4. Taylor expanded in z around inf 33.4%

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

5. Final simplification 33.4%

   \[\leadsto x \]

Developer target: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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