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

Percentage Accurate: 84.2% → 96.9%

Time: 12.4s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

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 82.8%

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

   1. associate-/l* 96.8%

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

3. Simplified 96.8%

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

Alternative 2: 60.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ t_2 := x \cdot \frac{y}{t}\\ t_3 := y \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-175}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-241}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))) (t_2 (* x (/ y t))) (t_3 (* y (/ x t))))
   (if (<= z -2.5e+84)
     x
     (if (<= z -9.5e+22)
       t_2
       (if (<= z -2.2e+20)
         x
         (if (<= z -9e-67)
           t_1
           (if (<= z -7.4e-85)
             x
             (if (<= z -2.7e-175)
               t_3
               (if (<= z -4.9e-181)
                 x
                 (if (<= z -2.6e-217)
                   t_2
                   (if (<= z -2.45e-241)
                     t_3
                     (if (<= z 5.5e+66) t_1 x))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double t_2 = x * (y / t);
	double t_3 = y * (x / t);
	double tmp;
	if (z <= -2.5e+84) {
		tmp = x;
	} else if (z <= -9.5e+22) {
		tmp = t_2;
	} else if (z <= -2.2e+20) {
		tmp = x;
	} else if (z <= -9e-67) {
		tmp = t_1;
	} else if (z <= -7.4e-85) {
		tmp = x;
	} else if (z <= -2.7e-175) {
		tmp = t_3;
	} else if (z <= -4.9e-181) {
		tmp = x;
	} else if (z <= -2.6e-217) {
		tmp = t_2;
	} else if (z <= -2.45e-241) {
		tmp = t_3;
	} else if (z <= 5.5e+66) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (t / y)
    t_2 = x * (y / t)
    t_3 = y * (x / t)
    if (z <= (-2.5d+84)) then
        tmp = x
    else if (z <= (-9.5d+22)) then
        tmp = t_2
    else if (z <= (-2.2d+20)) then
        tmp = x
    else if (z <= (-9d-67)) then
        tmp = t_1
    else if (z <= (-7.4d-85)) then
        tmp = x
    else if (z <= (-2.7d-175)) then
        tmp = t_3
    else if (z <= (-4.9d-181)) then
        tmp = x
    else if (z <= (-2.6d-217)) then
        tmp = t_2
    else if (z <= (-2.45d-241)) then
        tmp = t_3
    else if (z <= 5.5d+66) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double t_2 = x * (y / t);
	double t_3 = y * (x / t);
	double tmp;
	if (z <= -2.5e+84) {
		tmp = x;
	} else if (z <= -9.5e+22) {
		tmp = t_2;
	} else if (z <= -2.2e+20) {
		tmp = x;
	} else if (z <= -9e-67) {
		tmp = t_1;
	} else if (z <= -7.4e-85) {
		tmp = x;
	} else if (z <= -2.7e-175) {
		tmp = t_3;
	} else if (z <= -4.9e-181) {
		tmp = x;
	} else if (z <= -2.6e-217) {
		tmp = t_2;
	} else if (z <= -2.45e-241) {
		tmp = t_3;
	} else if (z <= 5.5e+66) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	t_2 = x * (y / t)
	t_3 = y * (x / t)
	tmp = 0
	if z <= -2.5e+84:
		tmp = x
	elif z <= -9.5e+22:
		tmp = t_2
	elif z <= -2.2e+20:
		tmp = x
	elif z <= -9e-67:
		tmp = t_1
	elif z <= -7.4e-85:
		tmp = x
	elif z <= -2.7e-175:
		tmp = t_3
	elif z <= -4.9e-181:
		tmp = x
	elif z <= -2.6e-217:
		tmp = t_2
	elif z <= -2.45e-241:
		tmp = t_3
	elif z <= 5.5e+66:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	t_2 = Float64(x * Float64(y / t))
	t_3 = Float64(y * Float64(x / t))
	tmp = 0.0
	if (z <= -2.5e+84)
		tmp = x;
	elseif (z <= -9.5e+22)
		tmp = t_2;
	elseif (z <= -2.2e+20)
		tmp = x;
	elseif (z <= -9e-67)
		tmp = t_1;
	elseif (z <= -7.4e-85)
		tmp = x;
	elseif (z <= -2.7e-175)
		tmp = t_3;
	elseif (z <= -4.9e-181)
		tmp = x;
	elseif (z <= -2.6e-217)
		tmp = t_2;
	elseif (z <= -2.45e-241)
		tmp = t_3;
	elseif (z <= 5.5e+66)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	t_2 = x * (y / t);
	t_3 = y * (x / t);
	tmp = 0.0;
	if (z <= -2.5e+84)
		tmp = x;
	elseif (z <= -9.5e+22)
		tmp = t_2;
	elseif (z <= -2.2e+20)
		tmp = x;
	elseif (z <= -9e-67)
		tmp = t_1;
	elseif (z <= -7.4e-85)
		tmp = x;
	elseif (z <= -2.7e-175)
		tmp = t_3;
	elseif (z <= -4.9e-181)
		tmp = x;
	elseif (z <= -2.6e-217)
		tmp = t_2;
	elseif (z <= -2.45e-241)
		tmp = t_3;
	elseif (z <= 5.5e+66)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+84], x, If[LessEqual[z, -9.5e+22], t$95$2, If[LessEqual[z, -2.2e+20], x, If[LessEqual[z, -9e-67], t$95$1, If[LessEqual[z, -7.4e-85], x, If[LessEqual[z, -2.7e-175], t$95$3, If[LessEqual[z, -4.9e-181], x, If[LessEqual[z, -2.6e-217], t$95$2, If[LessEqual[z, -2.45e-241], t$95$3, If[LessEqual[z, 5.5e+66], t$95$1, x]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5e84 or -9.49999999999999937e22 < z < -2.2e20 or -9.00000000000000031e-67 < z < -7.39999999999999966e-85 or -2.69999999999999999e-175 < z < -4.89999999999999963e-181 or 5.5e66 < z

   1. Initial program 72.3%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 63.3%

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

   if -2.5e84 < z < -9.49999999999999937e22 or -4.89999999999999963e-181 < z < -2.59999999999999993e-217

   1. Initial program 85.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 51.4%

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

      1. associate-/l* 62.2%

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

   7. Simplified 62.2%

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

   if -2.2e20 < z < -9.00000000000000031e-67 or -2.4499999999999999e-241 < z < 5.5e66

   1. Initial program 90.0%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in z around 0 61.2%

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

   if -7.39999999999999966e-85 < z < -2.69999999999999999e-175 or -2.59999999999999993e-217 < z < -2.4499999999999999e-241

   1. Initial program 92.7%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

      1. clear-num 86.0%

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

      2. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

      1. clear-num 85.8%

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

      2. associate-/r/ 91.2%

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

   8. Applied egg-rr 91.2%

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

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

      3. associate-*l/ 89.2%

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

      4. *-un-lft-identity 89.2%

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

      5. associate-/l/ 90.5%

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

   10. Applied egg-rr 90.5%

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

       1. unpow-1 90.5%

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

       2. associate-/r* 97.4%

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

   12. Simplified 97.4%

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

   13. Taylor expanded in z around 0 59.1%

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

       1. *-rgt-identity 59.1%

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

       2. times-frac 66.1%

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

       3. /-rgt-identity 66.1%

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

   15. Simplified 66.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ t y))))
   (if (<= z -2.25e+84)
     x
     (if (<= z -2.5e+23)
       (* x (/ y t))
       (if (<= z -1.65e+20)
         x
         (if (<= z -9e-67)
           t_1
           (if (<= z -7.4e-85)
             x
             (if (<= z -2.7e-175)
               (* y (/ x t))
               (if (<= z -4.9e-181)
                 x
                 (if (<= z -2.4e-242)
                   (/ (* x y) t)
                   (if (<= z 3.05e+63) t_1 x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= -2.5e+23) {
		tmp = x * (y / t);
	} else if (z <= -1.65e+20) {
		tmp = x;
	} else if (z <= -9e-67) {
		tmp = t_1;
	} else if (z <= -7.4e-85) {
		tmp = x;
	} else if (z <= -2.7e-175) {
		tmp = y * (x / t);
	} else if (z <= -4.9e-181) {
		tmp = x;
	} else if (z <= -2.4e-242) {
		tmp = (x * y) / t;
	} else if (z <= 3.05e+63) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / y)
    if (z <= (-2.25d+84)) then
        tmp = x
    else if (z <= (-2.5d+23)) then
        tmp = x * (y / t)
    else if (z <= (-1.65d+20)) then
        tmp = x
    else if (z <= (-9d-67)) then
        tmp = t_1
    else if (z <= (-7.4d-85)) then
        tmp = x
    else if (z <= (-2.7d-175)) then
        tmp = y * (x / t)
    else if (z <= (-4.9d-181)) then
        tmp = x
    else if (z <= (-2.4d-242)) then
        tmp = (x * y) / t
    else if (z <= 3.05d+63) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t / y);
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= -2.5e+23) {
		tmp = x * (y / t);
	} else if (z <= -1.65e+20) {
		tmp = x;
	} else if (z <= -9e-67) {
		tmp = t_1;
	} else if (z <= -7.4e-85) {
		tmp = x;
	} else if (z <= -2.7e-175) {
		tmp = y * (x / t);
	} else if (z <= -4.9e-181) {
		tmp = x;
	} else if (z <= -2.4e-242) {
		tmp = (x * y) / t;
	} else if (z <= 3.05e+63) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t / y)
	tmp = 0
	if z <= -2.25e+84:
		tmp = x
	elif z <= -2.5e+23:
		tmp = x * (y / t)
	elif z <= -1.65e+20:
		tmp = x
	elif z <= -9e-67:
		tmp = t_1
	elif z <= -7.4e-85:
		tmp = x
	elif z <= -2.7e-175:
		tmp = y * (x / t)
	elif z <= -4.9e-181:
		tmp = x
	elif z <= -2.4e-242:
		tmp = (x * y) / t
	elif z <= 3.05e+63:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t / y))
	tmp = 0.0
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= -2.5e+23)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= -1.65e+20)
		tmp = x;
	elseif (z <= -9e-67)
		tmp = t_1;
	elseif (z <= -7.4e-85)
		tmp = x;
	elseif (z <= -2.7e-175)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= -4.9e-181)
		tmp = x;
	elseif (z <= -2.4e-242)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 3.05e+63)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t / y);
	tmp = 0.0;
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= -2.5e+23)
		tmp = x * (y / t);
	elseif (z <= -1.65e+20)
		tmp = x;
	elseif (z <= -9e-67)
		tmp = t_1;
	elseif (z <= -7.4e-85)
		tmp = x;
	elseif (z <= -2.7e-175)
		tmp = y * (x / t);
	elseif (z <= -4.9e-181)
		tmp = x;
	elseif (z <= -2.4e-242)
		tmp = (x * y) / t;
	elseif (z <= 3.05e+63)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+84], x, If[LessEqual[z, -2.5e+23], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e+20], x, If[LessEqual[z, -9e-67], t$95$1, If[LessEqual[z, -7.4e-85], x, If[LessEqual[z, -2.7e-175], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.9e-181], x, If[LessEqual[z, -2.4e-242], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.05e+63], t$95$1, x]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2499999999999999e84 or -2.5e23 < z < -1.65e20 or -9.00000000000000031e-67 < z < -7.39999999999999966e-85 or -2.69999999999999999e-175 < z < -4.89999999999999963e-181 or 3.04999999999999984e63 < z

   1. Initial program 72.3%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 63.3%

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

   if -2.2499999999999999e84 < z < -2.5e23

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 35.4%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   if -1.65e20 < z < -9.00000000000000031e-67 or -2.4000000000000001e-242 < z < 3.04999999999999984e63

   1. Initial program 90.0%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in z around 0 61.2%

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

   if -7.39999999999999966e-85 < z < -2.69999999999999999e-175

   1. Initial program 90.7%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

      1. clear-num 86.6%

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

      2. un-div-inv 90.4%

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

   6. Applied egg-rr 90.4%

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

      1. clear-num 86.5%

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

      2. associate-/r/ 90.4%

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

   8. Applied egg-rr 90.4%

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

      1. clear-num 87.6%

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

      2. inv-pow 87.6%

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

      3. associate-*l/ 87.7%

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

      4. *-un-lft-identity 87.7%

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

      5. associate-/l/ 87.9%

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

   10. Applied egg-rr 87.9%

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

       1. unpow-1 87.9%

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

       2. associate-/r* 96.8%

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

   12. Simplified 96.8%

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

   13. Taylor expanded in z around 0 47.6%

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

       1. *-rgt-identity 47.6%

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

       2. times-frac 56.5%

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

       3. /-rgt-identity 56.5%

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

   15. Simplified 56.5%

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

   if -4.89999999999999963e-181 < z < -2.4000000000000001e-242

   1. Initial program 99.4%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 99.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-181}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-242}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t}\\ t_2 := y \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y t))) (t_2 (* y (/ x t))))
   (if (<= z -2.25e+84)
     x
     (if (<= z -1.4e+24)
       t_1
       (if (<= z -2.2e+20)
         x
         (if (<= z -9e-67)
           t_1
           (if (<= z -3.25e-97)
             x
             (if (<= z -1.85e-142)
               t_2
               (if (<= z -3.8e-217)
                 t_1
                 (if (<= z -1.2e-241) t_2 (if (<= z 1.15e+65) t_1 x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / t);
	double t_2 = y * (x / t);
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= -1.4e+24) {
		tmp = t_1;
	} else if (z <= -2.2e+20) {
		tmp = x;
	} else if (z <= -9e-67) {
		tmp = t_1;
	} else if (z <= -3.25e-97) {
		tmp = x;
	} else if (z <= -1.85e-142) {
		tmp = t_2;
	} else if (z <= -3.8e-217) {
		tmp = t_1;
	} else if (z <= -1.2e-241) {
		tmp = t_2;
	} else if (z <= 1.15e+65) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / t)
    t_2 = y * (x / t)
    if (z <= (-2.25d+84)) then
        tmp = x
    else if (z <= (-1.4d+24)) then
        tmp = t_1
    else if (z <= (-2.2d+20)) then
        tmp = x
    else if (z <= (-9d-67)) then
        tmp = t_1
    else if (z <= (-3.25d-97)) then
        tmp = x
    else if (z <= (-1.85d-142)) then
        tmp = t_2
    else if (z <= (-3.8d-217)) then
        tmp = t_1
    else if (z <= (-1.2d-241)) then
        tmp = t_2
    else if (z <= 1.15d+65) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / t);
	double t_2 = y * (x / t);
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= -1.4e+24) {
		tmp = t_1;
	} else if (z <= -2.2e+20) {
		tmp = x;
	} else if (z <= -9e-67) {
		tmp = t_1;
	} else if (z <= -3.25e-97) {
		tmp = x;
	} else if (z <= -1.85e-142) {
		tmp = t_2;
	} else if (z <= -3.8e-217) {
		tmp = t_1;
	} else if (z <= -1.2e-241) {
		tmp = t_2;
	} else if (z <= 1.15e+65) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / t)
	t_2 = y * (x / t)
	tmp = 0
	if z <= -2.25e+84:
		tmp = x
	elif z <= -1.4e+24:
		tmp = t_1
	elif z <= -2.2e+20:
		tmp = x
	elif z <= -9e-67:
		tmp = t_1
	elif z <= -3.25e-97:
		tmp = x
	elif z <= -1.85e-142:
		tmp = t_2
	elif z <= -3.8e-217:
		tmp = t_1
	elif z <= -1.2e-241:
		tmp = t_2
	elif z <= 1.15e+65:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / t))
	t_2 = Float64(y * Float64(x / t))
	tmp = 0.0
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= -1.4e+24)
		tmp = t_1;
	elseif (z <= -2.2e+20)
		tmp = x;
	elseif (z <= -9e-67)
		tmp = t_1;
	elseif (z <= -3.25e-97)
		tmp = x;
	elseif (z <= -1.85e-142)
		tmp = t_2;
	elseif (z <= -3.8e-217)
		tmp = t_1;
	elseif (z <= -1.2e-241)
		tmp = t_2;
	elseif (z <= 1.15e+65)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / t);
	t_2 = y * (x / t);
	tmp = 0.0;
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= -1.4e+24)
		tmp = t_1;
	elseif (z <= -2.2e+20)
		tmp = x;
	elseif (z <= -9e-67)
		tmp = t_1;
	elseif (z <= -3.25e-97)
		tmp = x;
	elseif (z <= -1.85e-142)
		tmp = t_2;
	elseif (z <= -3.8e-217)
		tmp = t_1;
	elseif (z <= -1.2e-241)
		tmp = t_2;
	elseif (z <= 1.15e+65)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+84], x, If[LessEqual[z, -1.4e+24], t$95$1, If[LessEqual[z, -2.2e+20], x, If[LessEqual[z, -9e-67], t$95$1, If[LessEqual[z, -3.25e-97], x, If[LessEqual[z, -1.85e-142], t$95$2, If[LessEqual[z, -3.8e-217], t$95$1, If[LessEqual[z, -1.2e-241], t$95$2, If[LessEqual[z, 1.15e+65], t$95$1, x]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e84 or -1.4000000000000001e24 < z < -2.2e20 or -9.00000000000000031e-67 < z < -3.2500000000000002e-97 or 1.15e65 < z

   1. Initial program 73.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 63.0%

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

   if -2.2499999999999999e84 < z < -1.4000000000000001e24 or -2.2e20 < z < -9.00000000000000031e-67 or -1.84999999999999993e-142 < z < -3.79999999999999987e-217 or -1.2e-241 < z < 1.15e65

   1. Initial program 88.2%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around 0 52.3%

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

      1. associate-/l* 60.2%

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

   7. Simplified 60.2%

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

   if -3.2500000000000002e-97 < z < -1.84999999999999993e-142 or -3.79999999999999987e-217 < z < -1.2e-241

   1. Initial program 99.7%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

      1. clear-num 87.1%

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

      2. un-div-inv 96.9%

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

   6. Applied egg-rr 96.9%

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

      1. clear-num 86.9%

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

      2. associate-/r/ 96.6%

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

   8. Applied egg-rr 96.6%

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

      1. clear-num 92.8%

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

      2. inv-pow 92.8%

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

      3. associate-*l/ 93.1%

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

      4. *-un-lft-identity 93.1%

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

      5. associate-/l/ 95.8%

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

   10. Applied egg-rr 95.8%

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

       1. unpow-1 95.8%

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

       2. associate-/r* 95.8%

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

   12. Simplified 95.8%

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

   13. Taylor expanded in z around 0 76.2%

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

       1. *-rgt-identity 76.2%

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

       2. times-frac 76.2%

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

       3. /-rgt-identity 76.2%

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

   15. Simplified 76.2%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+147} \lor \neg \left(z \leq 1.9 \cdot 10^{+156}\right) \land z \leq 1.65 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -2.25e+84)
     t_2
     (if (<= z -2.6e+20)
       t_1
       (if (<= z -5600000000.0)
         x
         (if (<= z 8.8e+77)
           t_1
           (if (or (<= z 1.1e+147)
                   (and (not (<= z 1.9e+156)) (<= z 1.65e+212)))
             (* x (/ z (- z t)))
             t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.25e+84) {
		tmp = t_2;
	} else if (z <= -2.6e+20) {
		tmp = t_1;
	} else if (z <= -5600000000.0) {
		tmp = x;
	} else if (z <= 8.8e+77) {
		tmp = t_1;
	} else if ((z <= 1.1e+147) || (!(z <= 1.9e+156) && (z <= 1.65e+212))) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-2.25d+84)) then
        tmp = t_2
    else if (z <= (-2.6d+20)) then
        tmp = t_1
    else if (z <= (-5600000000.0d0)) then
        tmp = x
    else if (z <= 8.8d+77) then
        tmp = t_1
    else if ((z <= 1.1d+147) .or. (.not. (z <= 1.9d+156)) .and. (z <= 1.65d+212)) then
        tmp = x * (z / (z - t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.25e+84) {
		tmp = t_2;
	} else if (z <= -2.6e+20) {
		tmp = t_1;
	} else if (z <= -5600000000.0) {
		tmp = x;
	} else if (z <= 8.8e+77) {
		tmp = t_1;
	} else if ((z <= 1.1e+147) || (!(z <= 1.9e+156) && (z <= 1.65e+212))) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -2.25e+84:
		tmp = t_2
	elif z <= -2.6e+20:
		tmp = t_1
	elif z <= -5600000000.0:
		tmp = x
	elif z <= 8.8e+77:
		tmp = t_1
	elif (z <= 1.1e+147) or (not (z <= 1.9e+156) and (z <= 1.65e+212)):
		tmp = x * (z / (z - t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.25e+84)
		tmp = t_2;
	elseif (z <= -2.6e+20)
		tmp = t_1;
	elseif (z <= -5600000000.0)
		tmp = x;
	elseif (z <= 8.8e+77)
		tmp = t_1;
	elseif ((z <= 1.1e+147) || (!(z <= 1.9e+156) && (z <= 1.65e+212)))
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.25e+84)
		tmp = t_2;
	elseif (z <= -2.6e+20)
		tmp = t_1;
	elseif (z <= -5600000000.0)
		tmp = x;
	elseif (z <= 8.8e+77)
		tmp = t_1;
	elseif ((z <= 1.1e+147) || (~((z <= 1.9e+156)) && (z <= 1.65e+212)))
		tmp = x * (z / (z - t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+84], t$95$2, If[LessEqual[z, -2.6e+20], t$95$1, If[LessEqual[z, -5600000000.0], x, If[LessEqual[z, 8.8e+77], t$95$1, If[Or[LessEqual[z, 1.1e+147], And[N[Not[LessEqual[z, 1.9e+156]], $MachinePrecision], LessEqual[z, 1.65e+212]]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2499999999999999e84 or 1.1000000000000001e147 < z < 1.90000000000000012e156 or 1.65e212 < z

   1. Initial program 66.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 61.6%

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

      1. mul-1-neg 61.6%

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

      2. associate-/l* 92.1%

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

      3. distribute-rgt-neg-in 92.1%

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

      4. distribute-frac-neg 92.1%

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

      5. neg-sub0 92.1%

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

      6. associate--r- 92.1%

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

      7. neg-sub0 92.1%

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

      8. +-commutative 92.1%

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

      9. sub-neg 92.1%

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

      10. div-sub 92.1%

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

      11. *-inverses 92.1%

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

   7. Simplified 92.1%

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

   if -2.2499999999999999e84 < z < -2.6e20 or -5.6e9 < z < 8.8000000000000002e77

   1. Initial program 89.3%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around inf 67.4%

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

      1. associate-/l* 73.5%

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

   7. Simplified 73.5%

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

   if -2.6e20 < z < -5.6e9

   1. Initial program 100.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 100.0%

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

   if 8.8000000000000002e77 < z < 1.1000000000000001e147 or 1.90000000000000012e156 < z < 1.65e212

   1. Initial program 79.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around 0 64.8%

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

      1. mul-1-neg 64.8%

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

      2. distribute-neg-frac2 64.8%

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

      3. neg-sub0 64.8%

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

      4. associate--r- 64.8%

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

      5. neg-sub0 64.8%

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

      6. +-commutative 64.8%

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

      7. sub-neg 64.8%

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

      8. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -5600000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+147} \lor \neg \left(z \leq 1.9 \cdot 10^{+156}\right) \land z \leq 1.65 \cdot 10^{+212}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-125}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+84)
   x
   (if (<= z -1.5e+21)
     (* x (/ y t))
     (if (<= z -1.02e+20)
       x
       (if (<= z -7.6e-70)
         (* x (/ z (- t)))
         (if (<= z -2.3e-75)
           x
           (if (<= z -2.05e-125)
             (/ (* x z) (- t))
             (if (<= z 3e+65) (/ x (/ t y)) x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= -1.5e+21) {
		tmp = x * (y / t);
	} else if (z <= -1.02e+20) {
		tmp = x;
	} else if (z <= -7.6e-70) {
		tmp = x * (z / -t);
	} else if (z <= -2.3e-75) {
		tmp = x;
	} else if (z <= -2.05e-125) {
		tmp = (x * z) / -t;
	} else if (z <= 3e+65) {
		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 <= (-2.25d+84)) then
        tmp = x
    else if (z <= (-1.5d+21)) then
        tmp = x * (y / t)
    else if (z <= (-1.02d+20)) then
        tmp = x
    else if (z <= (-7.6d-70)) then
        tmp = x * (z / -t)
    else if (z <= (-2.3d-75)) then
        tmp = x
    else if (z <= (-2.05d-125)) then
        tmp = (x * z) / -t
    else if (z <= 3d+65) 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 <= -2.25e+84) {
		tmp = x;
	} else if (z <= -1.5e+21) {
		tmp = x * (y / t);
	} else if (z <= -1.02e+20) {
		tmp = x;
	} else if (z <= -7.6e-70) {
		tmp = x * (z / -t);
	} else if (z <= -2.3e-75) {
		tmp = x;
	} else if (z <= -2.05e-125) {
		tmp = (x * z) / -t;
	} else if (z <= 3e+65) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+84:
		tmp = x
	elif z <= -1.5e+21:
		tmp = x * (y / t)
	elif z <= -1.02e+20:
		tmp = x
	elif z <= -7.6e-70:
		tmp = x * (z / -t)
	elif z <= -2.3e-75:
		tmp = x
	elif z <= -2.05e-125:
		tmp = (x * z) / -t
	elif z <= 3e+65:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= -1.5e+21)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= -1.02e+20)
		tmp = x;
	elseif (z <= -7.6e-70)
		tmp = Float64(x * Float64(z / Float64(-t)));
	elseif (z <= -2.3e-75)
		tmp = x;
	elseif (z <= -2.05e-125)
		tmp = Float64(Float64(x * z) / Float64(-t));
	elseif (z <= 3e+65)
		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 <= -2.25e+84)
		tmp = x;
	elseif (z <= -1.5e+21)
		tmp = x * (y / t);
	elseif (z <= -1.02e+20)
		tmp = x;
	elseif (z <= -7.6e-70)
		tmp = x * (z / -t);
	elseif (z <= -2.3e-75)
		tmp = x;
	elseif (z <= -2.05e-125)
		tmp = (x * z) / -t;
	elseif (z <= 3e+65)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.25e+84], x, If[LessEqual[z, -1.5e+21], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e+20], x, If[LessEqual[z, -7.6e-70], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-75], x, If[LessEqual[z, -2.05e-125], N[(N[(x * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 3e+65], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2499999999999999e84 or -1.5e21 < z < -1.02e20 or -7.5999999999999995e-70 < z < -2.3e-75 or 3.0000000000000002e65 < z

   1. Initial program 71.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.0%

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

   if -2.2499999999999999e84 < z < -1.5e21

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 35.4%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   if -1.02e20 < z < -7.5999999999999995e-70

   1. Initial program 99.7%

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

      1. remove-double-neg 99.7%

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

      2. distribute-lft-neg-out 99.7%

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

      3. distribute-neg-frac 99.7%

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

      4. distribute-neg-frac2 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. sub-neg 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. remove-double-neg 99.7%

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

      15. +-commutative 99.7%

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

      16. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 50.3%

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

   6. Taylor expanded in z around 0 43.7%

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

      1. mul-1-neg 43.7%

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

      2. associate-/l* 44.0%

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

      3. distribute-rgt-neg-in 44.0%

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

   8. Simplified 44.0%

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

   if -2.3e-75 < z < -2.0499999999999999e-125

   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 y around 0 68.1%

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

   6. Taylor expanded in z around 0 57.0%

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

      1. associate-*r/ 57.0%

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

      2. associate-*r* 57.0%

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

      3. neg-mul-1 57.0%

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

   8. Simplified 57.0%

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

   if -2.0499999999999999e-125 < z < 3.0000000000000002e65

   1. Initial program 88.7%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 93.3%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 64.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-125}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+84)
   x
   (if (<= z -6.6e+20)
     (* x (/ y t))
     (if (<= z -5e+19)
       x
       (if (<= z -1.55e-70)
         (* x (/ z (- t)))
         (if (<= z -3.8e-77)
           x
           (if (<= z -1.05e-125)
             (* z (/ x (- t)))
             (if (<= z 6e+68) (/ x (/ t y)) x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= -6.6e+20) {
		tmp = x * (y / t);
	} else if (z <= -5e+19) {
		tmp = x;
	} else if (z <= -1.55e-70) {
		tmp = x * (z / -t);
	} else if (z <= -3.8e-77) {
		tmp = x;
	} else if (z <= -1.05e-125) {
		tmp = z * (x / -t);
	} else if (z <= 6e+68) {
		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 <= (-2.25d+84)) then
        tmp = x
    else if (z <= (-6.6d+20)) then
        tmp = x * (y / t)
    else if (z <= (-5d+19)) then
        tmp = x
    else if (z <= (-1.55d-70)) then
        tmp = x * (z / -t)
    else if (z <= (-3.8d-77)) then
        tmp = x
    else if (z <= (-1.05d-125)) then
        tmp = z * (x / -t)
    else if (z <= 6d+68) 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 <= -2.25e+84) {
		tmp = x;
	} else if (z <= -6.6e+20) {
		tmp = x * (y / t);
	} else if (z <= -5e+19) {
		tmp = x;
	} else if (z <= -1.55e-70) {
		tmp = x * (z / -t);
	} else if (z <= -3.8e-77) {
		tmp = x;
	} else if (z <= -1.05e-125) {
		tmp = z * (x / -t);
	} else if (z <= 6e+68) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+84:
		tmp = x
	elif z <= -6.6e+20:
		tmp = x * (y / t)
	elif z <= -5e+19:
		tmp = x
	elif z <= -1.55e-70:
		tmp = x * (z / -t)
	elif z <= -3.8e-77:
		tmp = x
	elif z <= -1.05e-125:
		tmp = z * (x / -t)
	elif z <= 6e+68:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= -6.6e+20)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= -5e+19)
		tmp = x;
	elseif (z <= -1.55e-70)
		tmp = Float64(x * Float64(z / Float64(-t)));
	elseif (z <= -3.8e-77)
		tmp = x;
	elseif (z <= -1.05e-125)
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif (z <= 6e+68)
		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 <= -2.25e+84)
		tmp = x;
	elseif (z <= -6.6e+20)
		tmp = x * (y / t);
	elseif (z <= -5e+19)
		tmp = x;
	elseif (z <= -1.55e-70)
		tmp = x * (z / -t);
	elseif (z <= -3.8e-77)
		tmp = x;
	elseif (z <= -1.05e-125)
		tmp = z * (x / -t);
	elseif (z <= 6e+68)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.25e+84], x, If[LessEqual[z, -6.6e+20], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e+19], x, If[LessEqual[z, -1.55e-70], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-77], x, If[LessEqual[z, -1.05e-125], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+68], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2499999999999999e84 or -6.6e20 < z < -5e19 or -1.55e-70 < z < -3.7999999999999999e-77 or 6.0000000000000004e68 < z

   1. Initial program 71.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.0%

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

   if -2.2499999999999999e84 < z < -6.6e20

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 35.4%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   if -5e19 < z < -1.55e-70

   1. Initial program 99.7%

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

      1. remove-double-neg 99.7%

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

      2. distribute-lft-neg-out 99.7%

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

      3. distribute-neg-frac 99.7%

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

      4. distribute-neg-frac2 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. distribute-rgt-neg-in 99.7%

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

      7. sub-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. +-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. sub-neg 99.7%

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

      13. distribute-neg-in 99.7%

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

      14. remove-double-neg 99.7%

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

      15. +-commutative 99.7%

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

      16. sub-neg 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 50.3%

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

   6. Taylor expanded in z around 0 43.7%

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

      1. mul-1-neg 43.7%

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

      2. associate-/l* 44.0%

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

      3. distribute-rgt-neg-in 44.0%

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

   8. Simplified 44.0%

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

   if -3.7999999999999999e-77 < z < -1.05e-125

   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 y around 0 68.1%

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

      1. associate-/l* 67.9%

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

      2. *-commutative 67.9%

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

   7. Applied egg-rr 67.9%

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

   8. Taylor expanded in z around 0 57.0%

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

      1. mul-1-neg 57.0%

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

      2. associate-*l/ 56.9%

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

      3. distribute-rgt-neg-in 56.9%

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

   10. Simplified 56.9%

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

   if -1.05e-125 < z < 6.0000000000000004e68

   1. Initial program 88.7%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 93.3%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 64.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{-t}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- t)))))
   (if (<= z -2.25e+84)
     x
     (if (<= z -4.2e+24)
       (* x (/ y t))
       (if (<= z -1.05e+20)
         x
         (if (<= z -1.52e-71)
           t_1
           (if (<= z -1.55e-75)
             x
             (if (<= z -2.05e-125)
               t_1
               (if (<= z 5.5e+66) (/ x (/ t y)) x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / -t);
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= -4.2e+24) {
		tmp = x * (y / t);
	} else if (z <= -1.05e+20) {
		tmp = x;
	} else if (z <= -1.52e-71) {
		tmp = t_1;
	} else if (z <= -1.55e-75) {
		tmp = x;
	} else if (z <= -2.05e-125) {
		tmp = t_1;
	} else if (z <= 5.5e+66) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (z / -t)
    if (z <= (-2.25d+84)) then
        tmp = x
    else if (z <= (-4.2d+24)) then
        tmp = x * (y / t)
    else if (z <= (-1.05d+20)) then
        tmp = x
    else if (z <= (-1.52d-71)) then
        tmp = t_1
    else if (z <= (-1.55d-75)) then
        tmp = x
    else if (z <= (-2.05d-125)) then
        tmp = t_1
    else if (z <= 5.5d+66) 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 t_1 = x * (z / -t);
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= -4.2e+24) {
		tmp = x * (y / t);
	} else if (z <= -1.05e+20) {
		tmp = x;
	} else if (z <= -1.52e-71) {
		tmp = t_1;
	} else if (z <= -1.55e-75) {
		tmp = x;
	} else if (z <= -2.05e-125) {
		tmp = t_1;
	} else if (z <= 5.5e+66) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / -t)
	tmp = 0
	if z <= -2.25e+84:
		tmp = x
	elif z <= -4.2e+24:
		tmp = x * (y / t)
	elif z <= -1.05e+20:
		tmp = x
	elif z <= -1.52e-71:
		tmp = t_1
	elif z <= -1.55e-75:
		tmp = x
	elif z <= -2.05e-125:
		tmp = t_1
	elif z <= 5.5e+66:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(-t)))
	tmp = 0.0
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= -4.2e+24)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= -1.05e+20)
		tmp = x;
	elseif (z <= -1.52e-71)
		tmp = t_1;
	elseif (z <= -1.55e-75)
		tmp = x;
	elseif (z <= -2.05e-125)
		tmp = t_1;
	elseif (z <= 5.5e+66)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / -t);
	tmp = 0.0;
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= -4.2e+24)
		tmp = x * (y / t);
	elseif (z <= -1.05e+20)
		tmp = x;
	elseif (z <= -1.52e-71)
		tmp = t_1;
	elseif (z <= -1.55e-75)
		tmp = x;
	elseif (z <= -2.05e-125)
		tmp = t_1;
	elseif (z <= 5.5e+66)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+84], x, If[LessEqual[z, -4.2e+24], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e+20], x, If[LessEqual[z, -1.52e-71], t$95$1, If[LessEqual[z, -1.55e-75], x, If[LessEqual[z, -2.05e-125], t$95$1, If[LessEqual[z, 5.5e+66], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2499999999999999e84 or -4.2000000000000003e24 < z < -1.05e20 or -1.52000000000000001e-71 < z < -1.55000000000000003e-75 or 5.5e66 < z

   1. Initial program 71.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.0%

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

   if -2.2499999999999999e84 < z < -4.2000000000000003e24

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 35.4%

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

      1. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   if -1.05e20 < z < -1.52000000000000001e-71 or -1.55000000000000003e-75 < z < -2.0499999999999999e-125

   1. Initial program 99.8%

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

      1. remove-double-neg 99.8%

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

      2. distribute-lft-neg-out 99.8%

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

      3. distribute-neg-frac 99.8%

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

      4. distribute-neg-frac2 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. sub-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. +-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. sub-neg 99.8%

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

      13. distribute-neg-in 99.8%

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

      14. remove-double-neg 99.8%

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

      15. +-commutative 99.8%

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

      16. sub-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 57.0%

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

   6. Taylor expanded in z around 0 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-/l* 48.8%

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

      3. distribute-rgt-neg-in 48.8%

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

   8. Simplified 48.8%

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

   if -2.0499999999999999e-125 < z < 5.5e66

   1. Initial program 88.7%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 93.3%

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

      2. un-div-inv 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around 0 64.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -2.25e+84)
     t_2
     (if (<= z -1e+22)
       t_1
       (if (<= z -4.2e+19) x (if (<= z 5.8e+47) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.25e+84) {
		tmp = t_2;
	} else if (z <= -1e+22) {
		tmp = t_1;
	} else if (z <= -4.2e+19) {
		tmp = x;
	} else if (z <= 5.8e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-2.25d+84)) then
        tmp = t_2
    else if (z <= (-1d+22)) then
        tmp = t_1
    else if (z <= (-4.2d+19)) then
        tmp = x
    else if (z <= 5.8d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.25e+84) {
		tmp = t_2;
	} else if (z <= -1e+22) {
		tmp = t_1;
	} else if (z <= -4.2e+19) {
		tmp = x;
	} else if (z <= 5.8e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -2.25e+84:
		tmp = t_2
	elif z <= -1e+22:
		tmp = t_1
	elif z <= -4.2e+19:
		tmp = x
	elif z <= 5.8e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.25e+84)
		tmp = t_2;
	elseif (z <= -1e+22)
		tmp = t_1;
	elseif (z <= -4.2e+19)
		tmp = x;
	elseif (z <= 5.8e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.25e+84)
		tmp = t_2;
	elseif (z <= -1e+22)
		tmp = t_1;
	elseif (z <= -4.2e+19)
		tmp = x;
	elseif (z <= 5.8e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+84], t$95$2, If[LessEqual[z, -1e+22], t$95$1, If[LessEqual[z, -4.2e+19], x, If[LessEqual[z, 5.8e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e84 or 5.79999999999999961e47 < 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 t around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. associate-/l* 80.3%

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

      3. distribute-rgt-neg-in 80.3%

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

      4. distribute-frac-neg 80.3%

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

      5. neg-sub0 80.3%

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

      6. associate--r- 80.3%

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

      7. neg-sub0 80.3%

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

      8. +-commutative 80.3%

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

      9. sub-neg 80.3%

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

      10. div-sub 80.3%

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

      11. *-inverses 80.3%

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

   7. Simplified 80.3%

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

   if -2.2499999999999999e84 < z < -1e22 or -4.2e19 < z < 5.79999999999999961e47

   1. Initial program 89.4%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf 66.3%

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

      1. associate-/l* 72.1%

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

   7. Simplified 72.1%

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

   if -1e22 < z < -4.2e19

   1. Initial program 100.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 100.0%

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

Alternative 10: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-159}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -3.8e-19)
     t_1
     (if (<= z -1.55e-159)
       (* z (/ x (- t)))
       (if (<= z 2.65e-166) (/ x (/ t y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.8e-19) {
		tmp = t_1;
	} else if (z <= -1.55e-159) {
		tmp = z * (x / -t);
	} else if (z <= 2.65e-166) {
		tmp = x / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-3.8d-19)) then
        tmp = t_1
    else if (z <= (-1.55d-159)) then
        tmp = z * (x / -t)
    else if (z <= 2.65d-166) then
        tmp = x / (t / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.8e-19) {
		tmp = t_1;
	} else if (z <= -1.55e-159) {
		tmp = z * (x / -t);
	} else if (z <= 2.65e-166) {
		tmp = x / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -3.8e-19:
		tmp = t_1
	elif z <= -1.55e-159:
		tmp = z * (x / -t)
	elif z <= 2.65e-166:
		tmp = x / (t / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.8e-19)
		tmp = t_1;
	elseif (z <= -1.55e-159)
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif (z <= 2.65e-166)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.8e-19)
		tmp = t_1;
	elseif (z <= -1.55e-159)
		tmp = z * (x / -t);
	elseif (z <= 2.65e-166)
		tmp = x / (t / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-19], t$95$1, If[LessEqual[z, -1.55e-159], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e-166], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e-19 or 2.64999999999999998e-166 < z

   1. Initial program 78.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. associate-/l* 65.1%

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

      3. distribute-rgt-neg-in 65.1%

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

      4. distribute-frac-neg 65.1%

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

      5. neg-sub0 65.1%

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

      6. associate--r- 65.1%

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

      7. neg-sub0 65.1%

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

      8. +-commutative 65.1%

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

      9. sub-neg 65.1%

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

      10. div-sub 65.1%

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

      11. *-inverses 65.1%

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

   7. Simplified 65.1%

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

   if -3.8e-19 < z < -1.55e-159

   1. Initial program 96.8%

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

      1. remove-double-neg 96.8%

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

      2. distribute-lft-neg-out 96.8%

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

      3. distribute-neg-frac 96.8%

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

      4. distribute-neg-frac2 96.8%

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

      5. distribute-lft-neg-out 96.8%

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

      6. distribute-rgt-neg-in 96.8%

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

      7. sub-neg 96.8%

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

      8. distribute-neg-in 96.8%

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

      9. remove-double-neg 96.8%

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

      10. +-commutative 96.8%

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

      11. sub-neg 96.8%

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

      12. sub-neg 96.8%

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

      13. distribute-neg-in 96.8%

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

      14. remove-double-neg 96.8%

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

      15. +-commutative 96.8%

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

      16. sub-neg 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around 0 67.3%

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

      1. associate-/l* 62.9%

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

      2. *-commutative 62.9%

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

   7. Applied egg-rr 62.9%

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

   8. Taylor expanded in z around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. associate-*l/ 58.4%

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

      3. distribute-rgt-neg-in 58.4%

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

   10. Simplified 58.4%

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

   if -1.55e-159 < z < 2.64999999999999998e-166

   1. Initial program 87.3%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

      1. clear-num 90.1%

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

      2. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

   7. Taylor expanded in z around 0 82.6%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-159}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-166}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-20} \lor \neg \left(t \leq 5.6 \cdot 10^{-87}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.1e-20) (not (<= t 5.6e-87)))
   (* x (/ (- y z) t))
   (* x (/ (- z y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e-20) || !(t <= 5.6e-87)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.1d-20)) .or. (.not. (t <= 5.6d-87))) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e-20) || !(t <= 5.6e-87)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.1e-20) or not (t <= 5.6e-87):
		tmp = x * ((y - z) / t)
	else:
		tmp = x * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.1e-20) || !(t <= 5.6e-87))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.1e-20) || ~((t <= 5.6e-87)))
		tmp = x * ((y - z) / t);
	else
		tmp = x * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.1e-20], N[Not[LessEqual[t, 5.6e-87]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1e-20 or 5.6000000000000002e-87 < t

   1. Initial program 81.6%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around inf 68.5%

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

      1. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   if -3.1e-20 < t < 5.6000000000000002e-87

   1. Initial program 84.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 x around 0 84.3%

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

      1. remove-double-neg 84.3%

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

      2. distribute-neg-frac2 84.3%

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

      3. *-commutative 84.3%

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

      4. associate-/l* 84.7%

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

      5. distribute-lft-neg-out 84.7%

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

      6. neg-sub0 84.7%

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

      7. associate--r- 84.7%

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

      8. neg-sub0 84.7%

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

      9. +-commutative 84.7%

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

      10. sub-neg 84.7%

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

      11. neg-sub0 84.7%

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

      12. associate--r- 84.7%

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

      13. neg-sub0 84.7%

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

      14. +-commutative 84.7%

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

      15. sub-neg 84.7%

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

      16. *-commutative 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in t around 0 67.7%

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

      1. associate-/l* 81.6%

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

   10. Simplified 81.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-20} \lor \neg \left(t \leq 5.6 \cdot 10^{-87}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-27} \lor \neg \left(t \leq 5.6 \cdot 10^{-87}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.4e-27) (not (<= t 5.6e-87)))
   (* x (/ (- y z) t))
   (* x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.4e-27) || !(t <= 5.6e-87)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.4d-27)) .or. (.not. (t <= 5.6d-87))) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.4e-27) || !(t <= 5.6e-87)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.4e-27) or not (t <= 5.6e-87):
		tmp = x * ((y - z) / t)
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.4e-27) || !(t <= 5.6e-87))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.4e-27) || ~((t <= 5.6e-87)))
		tmp = x * ((y - z) / t);
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.4e-27], N[Not[LessEqual[t, 5.6e-87]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.39999999999999978e-27 or 5.6000000000000002e-87 < t

   1. Initial program 81.6%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around inf 68.5%

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

      1. associate-/l* 76.1%

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

   7. Simplified 76.1%

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

   if -5.39999999999999978e-27 < t < 5.6000000000000002e-87

   1. Initial program 84.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 t around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-/l* 81.6%

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

      3. distribute-rgt-neg-in 81.6%

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

      4. distribute-frac-neg 81.6%

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

      5. neg-sub0 81.6%

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

      6. associate--r- 81.6%

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

      7. neg-sub0 81.6%

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

      8. +-commutative 81.6%

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

      9. sub-neg 81.6%

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

      10. div-sub 81.6%

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

      11. *-inverses 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-27} \lor \neg \left(t \leq 5.6 \cdot 10^{-87}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.7e-21)
   (* x (/ (- y z) t))
   (if (<= t 6.8e-43) (* x (/ (- z y) z)) (/ x (/ t (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-21) {
		tmp = x * ((y - z) / t);
	} else if (t <= 6.8e-43) {
		tmp = x * ((z - y) / z);
	} else {
		tmp = x / (t / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.7d-21)) then
        tmp = x * ((y - z) / t)
    else if (t <= 6.8d-43) then
        tmp = x * ((z - y) / z)
    else
        tmp = x / (t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-21) {
		tmp = x * ((y - z) / t);
	} else if (t <= 6.8e-43) {
		tmp = x * ((z - y) / z);
	} else {
		tmp = x / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.7e-21:
		tmp = x * ((y - z) / t)
	elif t <= 6.8e-43:
		tmp = x * ((z - y) / z)
	else:
		tmp = x / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.7e-21)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif (t <= 6.8e-43)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	else
		tmp = Float64(x / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.7e-21)
		tmp = x * ((y - z) / t);
	elseif (t <= 6.8e-43)
		tmp = x * ((z - y) / z);
	else
		tmp = x / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.7e-21], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-43], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e-21

   1. Initial program 80.8%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around inf 70.5%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   if -1.7e-21 < t < 6.8000000000000001e-43

   1. Initial program 85.3%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around 0 85.3%

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

      1. remove-double-neg 85.3%

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

      2. distribute-neg-frac2 85.3%

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

      3. *-commutative 85.3%

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

      4. associate-/l* 84.9%

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

      5. distribute-lft-neg-out 84.9%

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

      6. neg-sub0 84.9%

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

      7. associate--r- 84.9%

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

      8. neg-sub0 84.9%

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

      9. +-commutative 84.9%

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

      10. sub-neg 84.9%

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

      11. neg-sub0 84.9%

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

      12. associate--r- 84.9%

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

      13. neg-sub0 84.9%

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

      14. +-commutative 84.9%

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

      15. sub-neg 84.9%

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

      16. *-commutative 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in t around 0 67.5%

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

      1. associate-/l* 80.4%

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

   10. Simplified 80.4%

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

   if 6.8000000000000001e-43 < t

   1. Initial program 80.1%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

      1. clear-num 97.1%

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

      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 78.7%

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

Alternative 14: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+84) x (if (<= z 5.8e+63) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+84) {
		tmp = x;
	} else if (z <= 5.8e+63) {
		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 <= (-2.25d+84)) then
        tmp = x
    else if (z <= 5.8d+63) 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 <= -2.25e+84) {
		tmp = x;
	} else if (z <= 5.8e+63) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+84:
		tmp = x
	elif z <= 5.8e+63:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.25e+84)
		tmp = x;
	elseif (z <= 5.8e+63)
		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 <= -2.25e+84)
		tmp = x;
	elseif (z <= 5.8e+63)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.25e+84], x, If[LessEqual[z, 5.8e+63], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2499999999999999e84 or 5.7999999999999999e63 < z

   1. Initial program 70.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 65.0%

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

   if -2.2499999999999999e84 < z < 5.7999999999999999e63

   1. Initial program 89.8%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in z around 0 52.2%

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

      1. associate-/l* 57.8%

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

   7. Simplified 57.8%

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

Alternative 15: 96.8% 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 82.8%

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

   1. associate-/l* 96.8%

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

3. Simplified 96.8%

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

Alternative 16: 34.8% 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 82.8%

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

   1. associate-/l* 96.8%

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

3. Simplified 96.8%

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

5. Taylor expanded in z around inf 31.5%

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

Developer target: 96.9% 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 2024107 
(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)))