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

Percentage Accurate: 84.3% → 97.0%

Time: 8.6s

Alternatives: 17

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: 84.3% 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: 97.0% 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 82.7%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

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

   1. clear-num 97.9%

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

   2. un-div-inv 98.2%

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

6. Applied egg-rr 98.2%

   \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]
7. Add Preprocessing

Alternative 2: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+25}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-227}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.9e+25)
   (- x (* x (/ y z)))
   (if (<= z -3.3e-118)
     (* x (/ y (- t z)))
     (if (<= z -1.3e-227)
       (/ (* x (- y z)) t)
       (if (<= z 7.2e-53)
         (/ x (/ t (- y z)))
         (if (<= z 1.6e-16) (/ (* x (- z y)) z) (* x (/ z (- z t)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e+25) {
		tmp = x - (x * (y / z));
	} else if (z <= -3.3e-118) {
		tmp = x * (y / (t - z));
	} else if (z <= -1.3e-227) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 7.2e-53) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.6e-16) {
		tmp = (x * (z - y)) / 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 (z <= (-3.9d+25)) then
        tmp = x - (x * (y / z))
    else if (z <= (-3.3d-118)) then
        tmp = x * (y / (t - z))
    else if (z <= (-1.3d-227)) then
        tmp = (x * (y - z)) / t
    else if (z <= 7.2d-53) then
        tmp = x / (t / (y - z))
    else if (z <= 1.6d-16) then
        tmp = (x * (z - y)) / 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 (z <= -3.9e+25) {
		tmp = x - (x * (y / z));
	} else if (z <= -3.3e-118) {
		tmp = x * (y / (t - z));
	} else if (z <= -1.3e-227) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 7.2e-53) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.6e-16) {
		tmp = (x * (z - y)) / z;
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.9e+25:
		tmp = x - (x * (y / z))
	elif z <= -3.3e-118:
		tmp = x * (y / (t - z))
	elif z <= -1.3e-227:
		tmp = (x * (y - z)) / t
	elif z <= 7.2e-53:
		tmp = x / (t / (y - z))
	elif z <= 1.6e-16:
		tmp = (x * (z - y)) / z
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.9e+25)
		tmp = Float64(x - Float64(x * Float64(y / z)));
	elseif (z <= -3.3e-118)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= -1.3e-227)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 7.2e-53)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 1.6e-16)
		tmp = Float64(Float64(x * Float64(z - y)) / 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 (z <= -3.9e+25)
		tmp = x - (x * (y / z));
	elseif (z <= -3.3e-118)
		tmp = x * (y / (t - z));
	elseif (z <= -1.3e-227)
		tmp = (x * (y - z)) / t;
	elseif (z <= 7.2e-53)
		tmp = x / (t / (y - z));
	elseif (z <= 1.6e-16)
		tmp = (x * (z - y)) / z;
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.9e+25], N[(x - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-118], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-227], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 7.2e-53], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-16], N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.9000000000000002e25

   1. Initial program 61.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. associate-/l* 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

      4. distribute-frac-neg 82.9%

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

      5. neg-sub0 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 82.9%

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

      8. +-commutative 82.9%

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

      9. sub-neg 82.9%

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

      10. div-sub 82.9%

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

      11. *-inverses 82.9%

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

   7. Simplified 82.9%

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

      1. sub-neg 82.9%

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

      2. distribute-rgt-in 82.9%

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

      3. *-un-lft-identity 82.9%

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

      4. distribute-neg-frac2 82.9%

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

   9. Applied egg-rr 82.9%

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

   if -3.9000000000000002e25 < z < -3.3e-118

   1. Initial program 93.0%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 70.1%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

   if -3.3e-118 < z < -1.30000000000000006e-227

   1. Initial program 99.8%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 94.8%

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

   if -1.30000000000000006e-227 < z < 7.1999999999999998e-53

   1. Initial program 89.2%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

      1. clear-num 98.1%

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

      2. un-div-inv 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in t around inf 90.5%

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

   if 7.1999999999999998e-53 < z < 1.60000000000000011e-16

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   if 1.60000000000000011e-16 < z

   1. Initial program 81.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-neg-frac2 71.2%

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

      3. neg-sub0 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-/l* 87.5%

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

   7. Simplified 87.5%

      \[\leadsto \color{blue}{x \cdot \frac{z}{z - t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+25}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-227}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.6e+25)
   (* x (- 1.0 (/ y z)))
   (if (<= z -1.3e-118)
     (* x (/ y (- t z)))
     (if (<= z -1.75e-236)
       (/ (* x (- y z)) t)
       (if (<= z 2.6e-54)
         (/ x (/ t (- y z)))
         (if (<= z 2.1e-17) (/ (* x (- z y)) z) (* x (/ z (- z t)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.6e+25) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= -1.3e-118) {
		tmp = x * (y / (t - z));
	} else if (z <= -1.75e-236) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 2.6e-54) {
		tmp = x / (t / (y - z));
	} else if (z <= 2.1e-17) {
		tmp = (x * (z - y)) / 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 (z <= (-7.6d+25)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= (-1.3d-118)) then
        tmp = x * (y / (t - z))
    else if (z <= (-1.75d-236)) then
        tmp = (x * (y - z)) / t
    else if (z <= 2.6d-54) then
        tmp = x / (t / (y - z))
    else if (z <= 2.1d-17) then
        tmp = (x * (z - y)) / 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 (z <= -7.6e+25) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= -1.3e-118) {
		tmp = x * (y / (t - z));
	} else if (z <= -1.75e-236) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 2.6e-54) {
		tmp = x / (t / (y - z));
	} else if (z <= 2.1e-17) {
		tmp = (x * (z - y)) / z;
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.6e+25:
		tmp = x * (1.0 - (y / z))
	elif z <= -1.3e-118:
		tmp = x * (y / (t - z))
	elif z <= -1.75e-236:
		tmp = (x * (y - z)) / t
	elif z <= 2.6e-54:
		tmp = x / (t / (y - z))
	elif z <= 2.1e-17:
		tmp = (x * (z - y)) / z
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.6e+25)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= -1.3e-118)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= -1.75e-236)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 2.6e-54)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 2.1e-17)
		tmp = Float64(Float64(x * Float64(z - y)) / 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 (z <= -7.6e+25)
		tmp = x * (1.0 - (y / z));
	elseif (z <= -1.3e-118)
		tmp = x * (y / (t - z));
	elseif (z <= -1.75e-236)
		tmp = (x * (y - z)) / t;
	elseif (z <= 2.6e-54)
		tmp = x / (t / (y - z));
	elseif (z <= 2.1e-17)
		tmp = (x * (z - y)) / z;
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.6e+25], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-118], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.75e-236], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.6e-54], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-17], N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -7.6000000000000001e25

   1. Initial program 61.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. associate-/l* 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

      4. distribute-frac-neg 82.9%

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

      5. neg-sub0 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 82.9%

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

      8. +-commutative 82.9%

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

      9. sub-neg 82.9%

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

      10. div-sub 82.9%

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

      11. *-inverses 82.9%

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

   7. Simplified 82.9%

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

   if -7.6000000000000001e25 < z < -1.3e-118

   1. Initial program 93.0%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 70.1%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

   if -1.3e-118 < z < -1.74999999999999997e-236

   1. Initial program 99.8%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 94.8%

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

   if -1.74999999999999997e-236 < z < 2.60000000000000002e-54

   1. Initial program 89.2%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

      1. clear-num 98.1%

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

      2. un-div-inv 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in t around inf 90.5%

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

   if 2.60000000000000002e-54 < z < 2.09999999999999992e-17

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

   if 2.09999999999999992e-17 < z

   1. Initial program 81.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-neg-frac2 71.2%

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

      3. neg-sub0 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-/l* 87.5%

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

   7. Simplified 87.5%

      \[\leadsto \color{blue}{x \cdot \frac{z}{z - t}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-18}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+26)
   (* x (- 1.0 (/ y z)))
   (if (<= z -1.45e-118)
     (* x (/ y (- t z)))
     (if (<= z -8.8e-235)
       (/ (* x (- y z)) t)
       (if (<= z 9e-56)
         (/ x (/ t (- y z)))
         (if (<= z 5e-18) (* (- z y) (/ x z)) (* x (/ z (- z t)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+26) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= -1.45e-118) {
		tmp = x * (y / (t - z));
	} else if (z <= -8.8e-235) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 9e-56) {
		tmp = x / (t / (y - z));
	} else if (z <= 5e-18) {
		tmp = (z - y) * (x / 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 (z <= (-1.6d+26)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= (-1.45d-118)) then
        tmp = x * (y / (t - z))
    else if (z <= (-8.8d-235)) then
        tmp = (x * (y - z)) / t
    else if (z <= 9d-56) then
        tmp = x / (t / (y - z))
    else if (z <= 5d-18) then
        tmp = (z - y) * (x / 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 (z <= -1.6e+26) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= -1.45e-118) {
		tmp = x * (y / (t - z));
	} else if (z <= -8.8e-235) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 9e-56) {
		tmp = x / (t / (y - z));
	} else if (z <= 5e-18) {
		tmp = (z - y) * (x / z);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+26:
		tmp = x * (1.0 - (y / z))
	elif z <= -1.45e-118:
		tmp = x * (y / (t - z))
	elif z <= -8.8e-235:
		tmp = (x * (y - z)) / t
	elif z <= 9e-56:
		tmp = x / (t / (y - z))
	elif z <= 5e-18:
		tmp = (z - y) * (x / z)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+26)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= -1.45e-118)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= -8.8e-235)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 9e-56)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 5e-18)
		tmp = Float64(Float64(z - y) * Float64(x / 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 (z <= -1.6e+26)
		tmp = x * (1.0 - (y / z));
	elseif (z <= -1.45e-118)
		tmp = x * (y / (t - z));
	elseif (z <= -8.8e-235)
		tmp = (x * (y - z)) / t;
	elseif (z <= 9e-56)
		tmp = x / (t / (y - z));
	elseif (z <= 5e-18)
		tmp = (z - y) * (x / z);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+26], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e-118], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.8e-235], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 9e-56], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-18], N[(N[(z - y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.60000000000000014e26

   1. Initial program 61.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. associate-/l* 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

      4. distribute-frac-neg 82.9%

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

      5. neg-sub0 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 82.9%

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

      8. +-commutative 82.9%

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

      9. sub-neg 82.9%

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

      10. div-sub 82.9%

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

      11. *-inverses 82.9%

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

   7. Simplified 82.9%

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

   if -1.60000000000000014e26 < z < -1.4499999999999999e-118

   1. Initial program 93.0%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 70.1%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

   if -1.4499999999999999e-118 < z < -8.79999999999999935e-235

   1. Initial program 99.8%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 94.8%

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

   if -8.79999999999999935e-235 < z < 9.0000000000000001e-56

   1. Initial program 89.2%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

      1. clear-num 98.1%

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

      2. un-div-inv 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in t around inf 90.5%

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

   if 9.0000000000000001e-56 < z < 5.00000000000000036e-18

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 90.0%

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

   7. Applied egg-rr 90.0%

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

   if 5.00000000000000036e-18 < z

   1. Initial program 81.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-neg-frac2 71.2%

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

      3. neg-sub0 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-/l* 87.5%

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

   7. Simplified 87.5%

      \[\leadsto \color{blue}{x \cdot \frac{z}{z - t}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-19}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+23)
   (* x (- 1.0 (/ y z)))
   (if (<= z 6.2e-53)
     (/ x (/ t (- y z)))
     (if (<= z 2e-19) (* (- z y) (/ x z)) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+23) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 6.2e-53) {
		tmp = x / (t / (y - z));
	} else if (z <= 2e-19) {
		tmp = (z - y) * (x / 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 (z <= (-1.05d+23)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 6.2d-53) then
        tmp = x / (t / (y - z))
    else if (z <= 2d-19) then
        tmp = (z - y) * (x / 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 (z <= -1.05e+23) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 6.2e-53) {
		tmp = x / (t / (y - z));
	} else if (z <= 2e-19) {
		tmp = (z - y) * (x / z);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+23:
		tmp = x * (1.0 - (y / z))
	elif z <= 6.2e-53:
		tmp = x / (t / (y - z))
	elif z <= 2e-19:
		tmp = (z - y) * (x / z)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+23)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 6.2e-53)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 2e-19)
		tmp = Float64(Float64(z - y) * Float64(x / 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 (z <= -1.05e+23)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 6.2e-53)
		tmp = x / (t / (y - z));
	elseif (z <= 2e-19)
		tmp = (z - y) * (x / z);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+23], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-53], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-19], N[(N[(z - y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0500000000000001e23

   1. Initial program 61.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. distribute-frac-neg 83.2%

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

      5. neg-sub0 83.2%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 83.2%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 83.2%

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

      8. +-commutative 83.2%

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

      9. sub-neg 83.2%

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

      10. div-sub 83.2%

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

      11. *-inverses 83.2%

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

   7. Simplified 83.2%

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

   if -1.0500000000000001e23 < z < 6.20000000000000031e-53

   1. Initial program 92.2%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.5%

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

      2. un-div-inv 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in t around inf 82.4%

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

   if 6.20000000000000031e-53 < z < 2e-19

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 90.0%

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

   7. Applied egg-rr 90.0%

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

   if 2e-19 < z

   1. Initial program 81.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-neg-frac2 71.2%

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

      3. neg-sub0 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

Alternative 6: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-16}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+23)
   (* x (- 1.0 (/ y z)))
   (if (<= z 3.8e-82)
     (* x (/ (- y z) t))
     (if (<= z 3.1e-16) (* (- z y) (/ x z)) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+23) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 3.8e-82) {
		tmp = x * ((y - z) / t);
	} else if (z <= 3.1e-16) {
		tmp = (z - y) * (x / 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 (z <= (-1.2d+23)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 3.8d-82) then
        tmp = x * ((y - z) / t)
    else if (z <= 3.1d-16) then
        tmp = (z - y) * (x / 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 (z <= -1.2e+23) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 3.8e-82) {
		tmp = x * ((y - z) / t);
	} else if (z <= 3.1e-16) {
		tmp = (z - y) * (x / z);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+23:
		tmp = x * (1.0 - (y / z))
	elif z <= 3.8e-82:
		tmp = x * ((y - z) / t)
	elif z <= 3.1e-16:
		tmp = (z - y) * (x / z)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+23)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 3.8e-82)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif (z <= 3.1e-16)
		tmp = Float64(Float64(z - y) * Float64(x / 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 (z <= -1.2e+23)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 3.8e-82)
		tmp = x * ((y - z) / t);
	elseif (z <= 3.1e-16)
		tmp = (z - y) * (x / z);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+23], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-82], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-16], N[(N[(z - y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2e23

   1. Initial program 61.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. distribute-frac-neg 83.2%

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

      5. neg-sub0 83.2%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 83.2%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 83.2%

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

      8. +-commutative 83.2%

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

      9. sub-neg 83.2%

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

      10. div-sub 83.2%

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

      11. *-inverses 83.2%

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

   7. Simplified 83.2%

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

   if -1.2e23 < z < 3.8000000000000002e-82

   1. Initial program 92.7%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.2%

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

      1. associate-/l* 82.7%

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

   7. Simplified 82.7%

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

   if 3.8000000000000002e-82 < z < 3.1000000000000001e-16

   1. Initial program 93.1%

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

      1. remove-double-neg 93.1%

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

      2. distribute-lft-neg-out 93.1%

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

      3. distribute-neg-frac 93.1%

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

      4. distribute-neg-frac2 93.1%

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

      5. distribute-lft-neg-out 93.1%

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

      6. distribute-rgt-neg-in 93.1%

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

      7. sub-neg 93.1%

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

      8. distribute-neg-in 93.1%

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

      9. remove-double-neg 93.1%

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

      10. +-commutative 93.1%

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

      11. sub-neg 93.1%

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

      12. sub-neg 93.1%

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

      13. distribute-neg-in 93.1%

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

      14. remove-double-neg 93.1%

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

      15. +-commutative 93.1%

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

      16. sub-neg 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-/l* 79.6%

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

   7. Applied egg-rr 79.6%

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

   if 3.1000000000000001e-16 < z

   1. Initial program 81.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-neg-frac2 71.2%

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

      3. neg-sub0 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

Alternative 7: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.55e+23)
   (* x (- 1.0 (/ y z)))
   (if (<= z 7.8e-53)
     (* x (/ (- y z) t))
     (if (<= z 9.5e-21) (/ (* x (- y)) z) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.55e+23) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 7.8e-53) {
		tmp = x * ((y - z) / t);
	} else if (z <= 9.5e-21) {
		tmp = (x * -y) / 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 (z <= (-2.55d+23)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 7.8d-53) then
        tmp = x * ((y - z) / t)
    else if (z <= 9.5d-21) then
        tmp = (x * -y) / 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 (z <= -2.55e+23) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 7.8e-53) {
		tmp = x * ((y - z) / t);
	} else if (z <= 9.5e-21) {
		tmp = (x * -y) / z;
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.55e+23:
		tmp = x * (1.0 - (y / z))
	elif z <= 7.8e-53:
		tmp = x * ((y - z) / t)
	elif z <= 9.5e-21:
		tmp = (x * -y) / z
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.55e+23)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 7.8e-53)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif (z <= 9.5e-21)
		tmp = Float64(Float64(x * Float64(-y)) / 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 (z <= -2.55e+23)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 7.8e-53)
		tmp = x * ((y - z) / t);
	elseif (z <= 9.5e-21)
		tmp = (x * -y) / z;
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.55e+23], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-53], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-21], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5500000000000001e23

   1. Initial program 61.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. associate-/l* 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. distribute-frac-neg 83.2%

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

      5. neg-sub0 83.2%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 83.2%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 83.2%

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

      8. +-commutative 83.2%

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

      9. sub-neg 83.2%

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

      10. div-sub 83.2%

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

      11. *-inverses 83.2%

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

   7. Simplified 83.2%

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

   if -2.5500000000000001e23 < z < 7.8000000000000004e-53

   1. Initial program 92.2%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 76.7%

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

      1. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   if 7.8000000000000004e-53 < z < 9.4999999999999994e-21

   1. Initial program 100.0%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

      4. distribute-frac-neg 80.4%

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

      5. neg-sub0 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 80.4%

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

      8. +-commutative 80.4%

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

      9. sub-neg 80.4%

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

      10. div-sub 80.4%

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

      11. *-inverses 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in y around inf 89.2%

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

      1. associate-*r/ 89.2%

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

      2. associate-*r* 89.2%

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

      3. neg-mul-1 89.2%

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

   10. Simplified 89.2%

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

   if 9.4999999999999994e-21 < z

   1. Initial program 81.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-neg-frac2 71.2%

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

      3. neg-sub0 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e+24)
   x
   (if (<= z 6.2e-53) (/ x (/ t y)) (if (<= z 1.08e-16) (/ (* x (- y)) z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+24) {
		tmp = x;
	} else if (z <= 6.2e-53) {
		tmp = x / (t / y);
	} else if (z <= 1.08e-16) {
		tmp = (x * -y) / 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 <= (-4.8d+24)) then
        tmp = x
    else if (z <= 6.2d-53) then
        tmp = x / (t / y)
    else if (z <= 1.08d-16) then
        tmp = (x * -y) / 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 <= -4.8e+24) {
		tmp = x;
	} else if (z <= 6.2e-53) {
		tmp = x / (t / y);
	} else if (z <= 1.08e-16) {
		tmp = (x * -y) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e+24:
		tmp = x
	elif z <= 6.2e-53:
		tmp = x / (t / y)
	elif z <= 1.08e-16:
		tmp = (x * -y) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e+24)
		tmp = x;
	elseif (z <= 6.2e-53)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 1.08e-16)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e+24)
		tmp = x;
	elseif (z <= 6.2e-53)
		tmp = x / (t / y);
	elseif (z <= 1.08e-16)
		tmp = (x * -y) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e+24], x, If[LessEqual[z, 6.2e-53], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.08e-16], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000001e24 or 1.08e-16 < z

   1. Initial program 72.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 67.6%

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

   if -4.8000000000000001e24 < z < 6.20000000000000031e-53

   1. Initial program 92.2%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.5%

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

      2. un-div-inv 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in z around 0 70.2%

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

   if 6.20000000000000031e-53 < z < 1.08e-16

   1. Initial program 100.0%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

      4. distribute-frac-neg 80.4%

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

      5. neg-sub0 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 80.4%

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

      8. +-commutative 80.4%

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

      9. sub-neg 80.4%

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

      10. div-sub 80.4%

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

      11. *-inverses 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in y around inf 89.2%

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

      1. associate-*r/ 89.2%

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

      2. associate-*r* 89.2%

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

      3. neg-mul-1 89.2%

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

   10. Simplified 89.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7e+24)
   x
   (if (<= z 2.2e-53) (/ x (/ t y)) (if (<= z 3.1e-16) (* y (/ (- x) z)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e+24) {
		tmp = x;
	} else if (z <= 2.2e-53) {
		tmp = x / (t / y);
	} else if (z <= 3.1e-16) {
		tmp = y * (-x / 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 <= (-7d+24)) then
        tmp = x
    else if (z <= 2.2d-53) then
        tmp = x / (t / y)
    else if (z <= 3.1d-16) then
        tmp = y * (-x / 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 <= -7e+24) {
		tmp = x;
	} else if (z <= 2.2e-53) {
		tmp = x / (t / y);
	} else if (z <= 3.1e-16) {
		tmp = y * (-x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e+24:
		tmp = x
	elif z <= 2.2e-53:
		tmp = x / (t / y)
	elif z <= 3.1e-16:
		tmp = y * (-x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e+24)
		tmp = x;
	elseif (z <= 2.2e-53)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 3.1e-16)
		tmp = Float64(y * Float64(Float64(-x) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7e+24)
		tmp = x;
	elseif (z <= 2.2e-53)
		tmp = x / (t / y);
	elseif (z <= 3.1e-16)
		tmp = y * (-x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e+24], x, If[LessEqual[z, 2.2e-53], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-16], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000004e24 or 3.1000000000000001e-16 < z

   1. Initial program 72.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 67.6%

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

   if -7.0000000000000004e24 < z < 2.20000000000000018e-53

   1. Initial program 92.2%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.5%

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

      2. un-div-inv 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in z around 0 70.2%

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

   if 2.20000000000000018e-53 < z < 3.1000000000000001e-16

   1. Initial program 100.0%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

      4. distribute-frac-neg 80.4%

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

      5. neg-sub0 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 80.4%

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

      8. +-commutative 80.4%

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

      9. sub-neg 80.4%

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

      10. div-sub 80.4%

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

      11. *-inverses 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in y around inf 89.2%

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

      1. mul-1-neg 89.2%

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

      2. distribute-frac-neg2 89.2%

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

      3. associate-*r/ 79.2%

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

   10. Simplified 79.2%

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

   11. Taylor expanded in x around 0 89.2%

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

       1. associate-*r/ 89.2%

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

       2. neg-mul-1 89.2%

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

       3. distribute-rgt-neg-in 89.2%

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

       4. associate-*l/ 88.8%

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

   13. Simplified 88.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e+24)
   x
   (if (<= z 7e-53) (/ x (/ t y)) (if (<= z 4.5e-19) (* x (/ y (- z))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+24) {
		tmp = x;
	} else if (z <= 7e-53) {
		tmp = x / (t / y);
	} else if (z <= 4.5e-19) {
		tmp = x * (y / -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 <= (-2.5d+24)) then
        tmp = x
    else if (z <= 7d-53) then
        tmp = x / (t / y)
    else if (z <= 4.5d-19) then
        tmp = x * (y / -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 <= -2.5e+24) {
		tmp = x;
	} else if (z <= 7e-53) {
		tmp = x / (t / y);
	} else if (z <= 4.5e-19) {
		tmp = x * (y / -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e+24:
		tmp = x
	elif z <= 7e-53:
		tmp = x / (t / y)
	elif z <= 4.5e-19:
		tmp = x * (y / -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e+24)
		tmp = x;
	elseif (z <= 7e-53)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 4.5e-19)
		tmp = Float64(x * Float64(y / Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.5e+24)
		tmp = x;
	elseif (z <= 7e-53)
		tmp = x / (t / y);
	elseif (z <= 4.5e-19)
		tmp = x * (y / -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e+24], x, If[LessEqual[z, 7e-53], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-19], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000023e24 or 4.50000000000000013e-19 < z

   1. Initial program 72.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 67.6%

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

   if -2.50000000000000023e24 < z < 6.99999999999999987e-53

   1. Initial program 92.2%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

      1. clear-num 96.5%

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

      2. un-div-inv 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in z around 0 70.2%

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

   if 6.99999999999999987e-53 < z < 4.50000000000000013e-19

   1. Initial program 100.0%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

      4. distribute-frac-neg 80.4%

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

      5. neg-sub0 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 80.4%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 80.4%

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

      8. +-commutative 80.4%

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

      9. sub-neg 80.4%

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

      10. div-sub 80.4%

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

      11. *-inverses 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in y around inf 89.2%

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

      1. mul-1-neg 89.2%

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

      2. distribute-frac-neg2 89.2%

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

      3. associate-*r/ 79.2%

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

   10. Simplified 79.2%

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

Alternative 11: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+25} \lor \neg \left(z \leq 2.1 \cdot 10^{-79}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+25) (not (<= z 2.1e-79)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+25) || !(z <= 2.1e-79)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (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 <= (-2.8d+25)) .or. (.not. (z <= 2.1d-79))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (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 <= -2.8e+25) || !(z <= 2.1e-79)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+25) or not (z <= 2.1e-79):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e+25) || !(z <= 2.1e-79))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.8e+25) || ~((z <= 2.1e-79)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e+25], N[Not[LessEqual[z, 2.1e-79]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000002e25 or 2.0999999999999999e-79 < z

   1. Initial program 74.3%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. associate-/l* 81.1%

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

      3. distribute-rgt-neg-in 81.1%

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

      4. distribute-frac-neg 81.1%

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

      5. neg-sub0 81.1%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 81.1%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 81.1%

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

      8. +-commutative 81.1%

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

      9. sub-neg 81.1%

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

      10. div-sub 81.1%

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

      11. *-inverses 81.1%

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

   7. Simplified 81.1%

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

   if -2.8000000000000002e25 < z < 2.0999999999999999e-79

   1. Initial program 92.8%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.8%

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

      1. associate-/l* 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+25} \lor \neg \left(z \leq 2.1 \cdot 10^{-79}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+23} \lor \neg \left(z \leq 2.9 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05e+23) (not (<= z 2.9e-81)))
   (* x (- 1.0 (/ y z)))
   (/ x (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e+23) || !(z <= 2.9e-81)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.05d+23)) .or. (.not. (z <= 2.9d-81))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e+23) || !(z <= 2.9e-81)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05e+23) or not (z <= 2.9e-81):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e+23) || !(z <= 2.9e-81))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e+23) || ~((z <= 2.9e-81)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e+23], N[Not[LessEqual[z, 2.9e-81]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e23 or 2.89999999999999989e-81 < z

   1. Initial program 74.4%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. associate-/l* 81.2%

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

      3. distribute-rgt-neg-in 81.2%

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

      4. distribute-frac-neg 81.2%

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

      5. neg-sub0 81.2%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 81.2%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 81.2%

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

      8. +-commutative 81.2%

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

      9. sub-neg 81.2%

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

      10. div-sub 81.2%

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

      11. *-inverses 81.2%

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

   7. Simplified 81.2%

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

   if -1.0500000000000001e23 < z < 2.89999999999999989e-81

   1. Initial program 92.7%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. clear-num 96.4%

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

      2. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around 0 71.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+23} \lor \neg \left(z \leq 2.9 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.75e+25)
   (* x (- 1.0 (/ y z)))
   (if (<= z 1.5e-16) (* x (/ y (- t z))) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+25) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 1.5e-16) {
		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 (z <= (-2.75d+25)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 1.5d-16) 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 (z <= -2.75e+25) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 1.5e-16) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.75e+25:
		tmp = x * (1.0 - (y / z))
	elif z <= 1.5e-16:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.75e+25)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.5e-16)
		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 (z <= -2.75e+25)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 1.5e-16)
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.75e+25], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-16], 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 3 regimes

2. if z < -2.75000000000000009e25

   1. Initial program 61.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. associate-/l* 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

      4. distribute-frac-neg 82.9%

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

      5. neg-sub0 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 82.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 82.9%

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

      8. +-commutative 82.9%

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

      9. sub-neg 82.9%

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

      10. div-sub 82.9%

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

      11. *-inverses 82.9%

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

   7. Simplified 82.9%

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

   if -2.75000000000000009e25 < z < 1.49999999999999997e-16

   1. Initial program 92.8%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.0%

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

      1. associate-/l* 79.4%

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

   7. Simplified 79.4%

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

   if 1.49999999999999997e-16 < z

   1. Initial program 81.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-neg-frac2 71.2%

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

      3. neg-sub0 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 71.2%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 71.2%

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

      6. +-commutative 71.2%

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

      7. sub-neg 71.2%

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

      8. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

Alternative 14: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e+24) x (if (<= z 4e-12) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+24) {
		tmp = x;
	} else if (z <= 4e-12) {
		tmp = x / (t / y);
	} 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 <= (-4.8d+24)) then
        tmp = x
    else if (z <= 4d-12) then
        tmp = x / (t / y)
    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 <= -4.8e+24) {
		tmp = x;
	} else if (z <= 4e-12) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e+24:
		tmp = x
	elif z <= 4e-12:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e+24)
		tmp = x;
	elseif (z <= 4e-12)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e+24)
		tmp = x;
	elseif (z <= 4e-12)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e+24], x, If[LessEqual[z, 4e-12], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000001e24 or 3.99999999999999992e-12 < z

   1. Initial program 71.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 68.6%

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

   if -4.8000000000000001e24 < z < 3.99999999999999992e-12

   1. Initial program 92.8%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

      1. clear-num 96.1%

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

      2. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in z around 0 66.1%

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

Alternative 15: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.3e+23) x (if (<= z 2.55e-12) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.3e+23) {
		tmp = x;
	} else if (z <= 2.55e-12) {
		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 <= (-4.3d+23)) then
        tmp = x
    else if (z <= 2.55d-12) 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 <= -4.3e+23) {
		tmp = x;
	} else if (z <= 2.55e-12) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.3e+23:
		tmp = x
	elif z <= 2.55e-12:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.3e+23)
		tmp = x;
	elseif (z <= 2.55e-12)
		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 <= -4.3e+23)
		tmp = x;
	elseif (z <= 2.55e-12)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.3e+23], x, If[LessEqual[z, 2.55e-12], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2999999999999999e23 or 2.54999999999999984e-12 < z

   1. Initial program 71.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 68.6%

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

   if -4.2999999999999999e23 < z < 2.54999999999999984e-12

   1. Initial program 92.8%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 60.8%

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

      1. associate-/l* 65.5%

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

   7. Simplified 65.5%

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

Alternative 16: 97.0% 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 82.7%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 17: 35.1% 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 82.7%

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

   1. associate-/l* 98.0%

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

3. Simplified 98.0%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 37.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 97.0% 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 2024087 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))