Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 92.7% → 97.7%

Time: 12.6s

Alternatives: 15

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.3%

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

   1. associate-*l/ 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 52.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-y}{t}\\ t_2 := \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y) t))) (t_2 (/ z (/ t y))))
   (if (<= z -2.1e+74)
     t_2
     (if (<= z -4.7e-217)
       x
       (if (<= z -1.7e-259)
         t_1
         (if (<= z -2.15e-303)
           x
           (if (<= z 8.6e-242)
             t_1
             (if (<= z 3.1e-28)
               x
               (if (<= z 8.5e+17)
                 (* y (/ z t))
                 (if (<= z 2.35e+104) x t_2))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-y / t);
	double t_2 = z / (t / y);
	double tmp;
	if (z <= -2.1e+74) {
		tmp = t_2;
	} else if (z <= -4.7e-217) {
		tmp = x;
	} else if (z <= -1.7e-259) {
		tmp = t_1;
	} else if (z <= -2.15e-303) {
		tmp = x;
	} else if (z <= 8.6e-242) {
		tmp = t_1;
	} else if (z <= 3.1e-28) {
		tmp = x;
	} else if (z <= 8.5e+17) {
		tmp = y * (z / t);
	} else if (z <= 2.35e+104) {
		tmp = x;
	} 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)
    t_2 = z / (t / y)
    if (z <= (-2.1d+74)) then
        tmp = t_2
    else if (z <= (-4.7d-217)) then
        tmp = x
    else if (z <= (-1.7d-259)) then
        tmp = t_1
    else if (z <= (-2.15d-303)) then
        tmp = x
    else if (z <= 8.6d-242) then
        tmp = t_1
    else if (z <= 3.1d-28) then
        tmp = x
    else if (z <= 8.5d+17) then
        tmp = y * (z / t)
    else if (z <= 2.35d+104) then
        tmp = x
    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);
	double t_2 = z / (t / y);
	double tmp;
	if (z <= -2.1e+74) {
		tmp = t_2;
	} else if (z <= -4.7e-217) {
		tmp = x;
	} else if (z <= -1.7e-259) {
		tmp = t_1;
	} else if (z <= -2.15e-303) {
		tmp = x;
	} else if (z <= 8.6e-242) {
		tmp = t_1;
	} else if (z <= 3.1e-28) {
		tmp = x;
	} else if (z <= 8.5e+17) {
		tmp = y * (z / t);
	} else if (z <= 2.35e+104) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-y / t)
	t_2 = z / (t / y)
	tmp = 0
	if z <= -2.1e+74:
		tmp = t_2
	elif z <= -4.7e-217:
		tmp = x
	elif z <= -1.7e-259:
		tmp = t_1
	elif z <= -2.15e-303:
		tmp = x
	elif z <= 8.6e-242:
		tmp = t_1
	elif z <= 3.1e-28:
		tmp = x
	elif z <= 8.5e+17:
		tmp = y * (z / t)
	elif z <= 2.35e+104:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-y) / t))
	t_2 = Float64(z / Float64(t / y))
	tmp = 0.0
	if (z <= -2.1e+74)
		tmp = t_2;
	elseif (z <= -4.7e-217)
		tmp = x;
	elseif (z <= -1.7e-259)
		tmp = t_1;
	elseif (z <= -2.15e-303)
		tmp = x;
	elseif (z <= 8.6e-242)
		tmp = t_1;
	elseif (z <= 3.1e-28)
		tmp = x;
	elseif (z <= 8.5e+17)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 2.35e+104)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-y / t);
	t_2 = z / (t / y);
	tmp = 0.0;
	if (z <= -2.1e+74)
		tmp = t_2;
	elseif (z <= -4.7e-217)
		tmp = x;
	elseif (z <= -1.7e-259)
		tmp = t_1;
	elseif (z <= -2.15e-303)
		tmp = x;
	elseif (z <= 8.6e-242)
		tmp = t_1;
	elseif (z <= 3.1e-28)
		tmp = x;
	elseif (z <= 8.5e+17)
		tmp = y * (z / t);
	elseif (z <= 2.35e+104)
		tmp = x;
	else
		tmp = t_2;
	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[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+74], t$95$2, If[LessEqual[z, -4.7e-217], x, If[LessEqual[z, -1.7e-259], t$95$1, If[LessEqual[z, -2.15e-303], x, If[LessEqual[z, 8.6e-242], t$95$1, If[LessEqual[z, 3.1e-28], x, If[LessEqual[z, 8.5e+17], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+104], x, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0999999999999999e74 or 2.35000000000000008e104 < z

   1. Initial program 92.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.4%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/r/ 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -2.0999999999999999e74 < z < -4.7000000000000003e-217 or -1.70000000000000006e-259 < z < -2.14999999999999991e-303 or 8.6000000000000004e-242 < z < 3.09999999999999992e-28 or 8.5e17 < z < 2.35000000000000008e104

   1. Initial program 94.1%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 60.6%

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

   if -4.7000000000000003e-217 < z < -1.70000000000000006e-259 or -2.14999999999999991e-303 < z < 8.6000000000000004e-242

   1. Initial program 99.6%

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

      1. associate-*l/ 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf 93.1%

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

      1. mul-1-neg 93.1%

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

      2. unsub-neg 93.1%

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

   7. Simplified 93.1%

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

   8. Taylor expanded in y around inf 66.5%

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

      1. associate-*r/ 66.5%

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

      2. neg-mul-1 66.5%

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

   10. Simplified 66.5%

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

   if 3.09999999999999992e-28 < z < 8.5e17

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-217}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ t y))))
   (if (<= z -7.5e+64)
     t_1
     (if (<= z -2.6e-234)
       x
       (if (<= z -1.26e-259)
         (* y (/ (- x) t))
         (if (<= z -2e-302)
           x
           (if (<= z 1.25e-241)
             (* x (/ (- y) t))
             (if (<= z 1.45e-29)
               x
               (if (<= z 4.6e+17)
                 (* y (/ z t))
                 (if (<= z 2.6e+104) x t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -7.5e+64) {
		tmp = t_1;
	} else if (z <= -2.6e-234) {
		tmp = x;
	} else if (z <= -1.26e-259) {
		tmp = y * (-x / t);
	} else if (z <= -2e-302) {
		tmp = x;
	} else if (z <= 1.25e-241) {
		tmp = x * (-y / t);
	} else if (z <= 1.45e-29) {
		tmp = x;
	} else if (z <= 4.6e+17) {
		tmp = y * (z / t);
	} else if (z <= 2.6e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (t / y)
    if (z <= (-7.5d+64)) then
        tmp = t_1
    else if (z <= (-2.6d-234)) then
        tmp = x
    else if (z <= (-1.26d-259)) then
        tmp = y * (-x / t)
    else if (z <= (-2d-302)) then
        tmp = x
    else if (z <= 1.25d-241) then
        tmp = x * (-y / t)
    else if (z <= 1.45d-29) then
        tmp = x
    else if (z <= 4.6d+17) then
        tmp = y * (z / t)
    else if (z <= 2.6d+104) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -7.5e+64) {
		tmp = t_1;
	} else if (z <= -2.6e-234) {
		tmp = x;
	} else if (z <= -1.26e-259) {
		tmp = y * (-x / t);
	} else if (z <= -2e-302) {
		tmp = x;
	} else if (z <= 1.25e-241) {
		tmp = x * (-y / t);
	} else if (z <= 1.45e-29) {
		tmp = x;
	} else if (z <= 4.6e+17) {
		tmp = y * (z / t);
	} else if (z <= 2.6e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (t / y)
	tmp = 0
	if z <= -7.5e+64:
		tmp = t_1
	elif z <= -2.6e-234:
		tmp = x
	elif z <= -1.26e-259:
		tmp = y * (-x / t)
	elif z <= -2e-302:
		tmp = x
	elif z <= 1.25e-241:
		tmp = x * (-y / t)
	elif z <= 1.45e-29:
		tmp = x
	elif z <= 4.6e+17:
		tmp = y * (z / t)
	elif z <= 2.6e+104:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(t / y))
	tmp = 0.0
	if (z <= -7.5e+64)
		tmp = t_1;
	elseif (z <= -2.6e-234)
		tmp = x;
	elseif (z <= -1.26e-259)
		tmp = Float64(y * Float64(Float64(-x) / t));
	elseif (z <= -2e-302)
		tmp = x;
	elseif (z <= 1.25e-241)
		tmp = Float64(x * Float64(Float64(-y) / t));
	elseif (z <= 1.45e-29)
		tmp = x;
	elseif (z <= 4.6e+17)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 2.6e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (t / y);
	tmp = 0.0;
	if (z <= -7.5e+64)
		tmp = t_1;
	elseif (z <= -2.6e-234)
		tmp = x;
	elseif (z <= -1.26e-259)
		tmp = y * (-x / t);
	elseif (z <= -2e-302)
		tmp = x;
	elseif (z <= 1.25e-241)
		tmp = x * (-y / t);
	elseif (z <= 1.45e-29)
		tmp = x;
	elseif (z <= 4.6e+17)
		tmp = y * (z / t);
	elseif (z <= 2.6e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+64], t$95$1, If[LessEqual[z, -2.6e-234], x, If[LessEqual[z, -1.26e-259], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-302], x, If[LessEqual[z, 1.25e-241], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-29], x, If[LessEqual[z, 4.6e+17], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+104], x, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.5000000000000005e64 or 2.6e104 < z

   1. Initial program 92.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.4%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/r/ 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -7.5000000000000005e64 < z < -2.59999999999999989e-234 or -1.25999999999999996e-259 < z < -1.9999999999999999e-302 or 1.25e-241 < z < 1.45000000000000012e-29 or 4.6e17 < z < 2.6e104

   1. Initial program 94.4%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 59.1%

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

   if -2.59999999999999989e-234 < z < -1.25999999999999996e-259

   1. Initial program 100.0%

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

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in y around inf 99.2%

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

   6. Taylor expanded in z around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. distribute-frac-neg 99.2%

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

   8. Simplified 99.2%

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

   if -1.9999999999999999e-302 < z < 1.25e-241

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   10. Simplified 72.3%

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

   if 1.45000000000000012e-29 < z < 4.6e17

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{-\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ t y))))
   (if (<= z -9.6e+63)
     t_1
     (if (<= z -2.7e-234)
       x
       (if (<= z -8.5e-260)
         (* y (/ (- x) t))
         (if (<= z -5.2e-303)
           x
           (if (<= z 8.6e-242)
             (/ x (- (/ t y)))
             (if (<= z 2.05e-28)
               x
               (if (<= z 1.15e+18)
                 (* y (/ z t))
                 (if (<= z 3.6e+104) x t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -9.6e+63) {
		tmp = t_1;
	} else if (z <= -2.7e-234) {
		tmp = x;
	} else if (z <= -8.5e-260) {
		tmp = y * (-x / t);
	} else if (z <= -5.2e-303) {
		tmp = x;
	} else if (z <= 8.6e-242) {
		tmp = x / -(t / y);
	} else if (z <= 2.05e-28) {
		tmp = x;
	} else if (z <= 1.15e+18) {
		tmp = y * (z / t);
	} else if (z <= 3.6e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (t / y)
    if (z <= (-9.6d+63)) then
        tmp = t_1
    else if (z <= (-2.7d-234)) then
        tmp = x
    else if (z <= (-8.5d-260)) then
        tmp = y * (-x / t)
    else if (z <= (-5.2d-303)) then
        tmp = x
    else if (z <= 8.6d-242) then
        tmp = x / -(t / y)
    else if (z <= 2.05d-28) then
        tmp = x
    else if (z <= 1.15d+18) then
        tmp = y * (z / t)
    else if (z <= 3.6d+104) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -9.6e+63) {
		tmp = t_1;
	} else if (z <= -2.7e-234) {
		tmp = x;
	} else if (z <= -8.5e-260) {
		tmp = y * (-x / t);
	} else if (z <= -5.2e-303) {
		tmp = x;
	} else if (z <= 8.6e-242) {
		tmp = x / -(t / y);
	} else if (z <= 2.05e-28) {
		tmp = x;
	} else if (z <= 1.15e+18) {
		tmp = y * (z / t);
	} else if (z <= 3.6e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (t / y)
	tmp = 0
	if z <= -9.6e+63:
		tmp = t_1
	elif z <= -2.7e-234:
		tmp = x
	elif z <= -8.5e-260:
		tmp = y * (-x / t)
	elif z <= -5.2e-303:
		tmp = x
	elif z <= 8.6e-242:
		tmp = x / -(t / y)
	elif z <= 2.05e-28:
		tmp = x
	elif z <= 1.15e+18:
		tmp = y * (z / t)
	elif z <= 3.6e+104:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(t / y))
	tmp = 0.0
	if (z <= -9.6e+63)
		tmp = t_1;
	elseif (z <= -2.7e-234)
		tmp = x;
	elseif (z <= -8.5e-260)
		tmp = Float64(y * Float64(Float64(-x) / t));
	elseif (z <= -5.2e-303)
		tmp = x;
	elseif (z <= 8.6e-242)
		tmp = Float64(x / Float64(-Float64(t / y)));
	elseif (z <= 2.05e-28)
		tmp = x;
	elseif (z <= 1.15e+18)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 3.6e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (t / y);
	tmp = 0.0;
	if (z <= -9.6e+63)
		tmp = t_1;
	elseif (z <= -2.7e-234)
		tmp = x;
	elseif (z <= -8.5e-260)
		tmp = y * (-x / t);
	elseif (z <= -5.2e-303)
		tmp = x;
	elseif (z <= 8.6e-242)
		tmp = x / -(t / y);
	elseif (z <= 2.05e-28)
		tmp = x;
	elseif (z <= 1.15e+18)
		tmp = y * (z / t);
	elseif (z <= 3.6e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+63], t$95$1, If[LessEqual[z, -2.7e-234], x, If[LessEqual[z, -8.5e-260], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-303], x, If[LessEqual[z, 8.6e-242], N[(x / (-N[(t / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 2.05e-28], x, If[LessEqual[z, 1.15e+18], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+104], x, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.6e63 or 3.60000000000000001e104 < z

   1. Initial program 92.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.4%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/r/ 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -9.6e63 < z < -2.7000000000000002e-234 or -8.5000000000000003e-260 < z < -5.20000000000000009e-303 or 8.6000000000000004e-242 < z < 2.0500000000000001e-28 or 1.15e18 < z < 3.60000000000000001e104

   1. Initial program 94.4%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 59.1%

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

   if -2.7000000000000002e-234 < z < -8.5000000000000003e-260

   1. Initial program 100.0%

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

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in y around inf 99.2%

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

   6. Taylor expanded in z around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. distribute-frac-neg 99.2%

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

   8. Simplified 99.2%

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

   if -5.20000000000000009e-303 < z < 8.6000000000000004e-242

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   10. Simplified 72.3%

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

       1. *-commutative 72.3%

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

       2. frac-2neg 72.3%

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

       3. remove-double-neg 72.3%

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

       4. associate-*l/ 72.3%

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

   12. Applied egg-rr 72.3%

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

       1. neg-mul-1 72.3%

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

       2. times-frac 58.6%

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

   14. Applied egg-rr 58.6%

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

       1. *-commutative 58.6%

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

       2. times-frac 72.3%

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

       3. associate-/l* 72.4%

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

       4. *-commutative 72.4%

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

       5. neg-mul-1 72.4%

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

   16. Simplified 72.4%

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

   if 2.0500000000000001e-28 < z < 1.15e18

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+63}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-260}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{-\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-259}:\\ \;\;\;\;\frac{y}{\frac{-t}{x}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-240}:\\ \;\;\;\;\frac{x}{-\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ t y))))
   (if (<= z -1.1e+59)
     t_1
     (if (<= z -2.6e-234)
       x
       (if (<= z -1.85e-259)
         (/ y (/ (- t) x))
         (if (<= z -5.5e-303)
           x
           (if (<= z 1.8e-240)
             (/ x (- (/ t y)))
             (if (<= z 3.2e-28)
               x
               (if (<= z 3.4e+18)
                 (* y (/ z t))
                 (if (<= z 5.5e+104) x t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -1.1e+59) {
		tmp = t_1;
	} else if (z <= -2.6e-234) {
		tmp = x;
	} else if (z <= -1.85e-259) {
		tmp = y / (-t / x);
	} else if (z <= -5.5e-303) {
		tmp = x;
	} else if (z <= 1.8e-240) {
		tmp = x / -(t / y);
	} else if (z <= 3.2e-28) {
		tmp = x;
	} else if (z <= 3.4e+18) {
		tmp = y * (z / t);
	} else if (z <= 5.5e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (t / y)
    if (z <= (-1.1d+59)) then
        tmp = t_1
    else if (z <= (-2.6d-234)) then
        tmp = x
    else if (z <= (-1.85d-259)) then
        tmp = y / (-t / x)
    else if (z <= (-5.5d-303)) then
        tmp = x
    else if (z <= 1.8d-240) then
        tmp = x / -(t / y)
    else if (z <= 3.2d-28) then
        tmp = x
    else if (z <= 3.4d+18) then
        tmp = y * (z / t)
    else if (z <= 5.5d+104) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -1.1e+59) {
		tmp = t_1;
	} else if (z <= -2.6e-234) {
		tmp = x;
	} else if (z <= -1.85e-259) {
		tmp = y / (-t / x);
	} else if (z <= -5.5e-303) {
		tmp = x;
	} else if (z <= 1.8e-240) {
		tmp = x / -(t / y);
	} else if (z <= 3.2e-28) {
		tmp = x;
	} else if (z <= 3.4e+18) {
		tmp = y * (z / t);
	} else if (z <= 5.5e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (t / y)
	tmp = 0
	if z <= -1.1e+59:
		tmp = t_1
	elif z <= -2.6e-234:
		tmp = x
	elif z <= -1.85e-259:
		tmp = y / (-t / x)
	elif z <= -5.5e-303:
		tmp = x
	elif z <= 1.8e-240:
		tmp = x / -(t / y)
	elif z <= 3.2e-28:
		tmp = x
	elif z <= 3.4e+18:
		tmp = y * (z / t)
	elif z <= 5.5e+104:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(t / y))
	tmp = 0.0
	if (z <= -1.1e+59)
		tmp = t_1;
	elseif (z <= -2.6e-234)
		tmp = x;
	elseif (z <= -1.85e-259)
		tmp = Float64(y / Float64(Float64(-t) / x));
	elseif (z <= -5.5e-303)
		tmp = x;
	elseif (z <= 1.8e-240)
		tmp = Float64(x / Float64(-Float64(t / y)));
	elseif (z <= 3.2e-28)
		tmp = x;
	elseif (z <= 3.4e+18)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 5.5e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (t / y);
	tmp = 0.0;
	if (z <= -1.1e+59)
		tmp = t_1;
	elseif (z <= -2.6e-234)
		tmp = x;
	elseif (z <= -1.85e-259)
		tmp = y / (-t / x);
	elseif (z <= -5.5e-303)
		tmp = x;
	elseif (z <= 1.8e-240)
		tmp = x / -(t / y);
	elseif (z <= 3.2e-28)
		tmp = x;
	elseif (z <= 3.4e+18)
		tmp = y * (z / t);
	elseif (z <= 5.5e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+59], t$95$1, If[LessEqual[z, -2.6e-234], x, If[LessEqual[z, -1.85e-259], N[(y / N[((-t) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-303], x, If[LessEqual[z, 1.8e-240], N[(x / (-N[(t / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.2e-28], x, If[LessEqual[z, 3.4e+18], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+104], x, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1e59 or 5.50000000000000017e104 < z

   1. Initial program 92.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.4%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/r/ 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -1.1e59 < z < -2.59999999999999989e-234 or -1.84999999999999996e-259 < z < -5.50000000000000018e-303 or 1.7999999999999999e-240 < z < 3.19999999999999982e-28 or 3.4e18 < z < 5.50000000000000017e104

   1. Initial program 94.4%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 59.1%

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

   if -2.59999999999999989e-234 < z < -1.84999999999999996e-259

   1. Initial program 100.0%

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

      1. associate-*l/ 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in x around inf 84.2%

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

      1. mul-1-neg 84.2%

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

      2. unsub-neg 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in y around inf 84.2%

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

      1. associate-*r/ 84.2%

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

      2. neg-mul-1 84.2%

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

   10. Simplified 84.2%

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

       1. *-commutative 84.2%

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

       2. frac-2neg 84.2%

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

       3. remove-double-neg 84.2%

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

       4. associate-*l/ 100.0%

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

   12. Applied egg-rr 100.0%

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

       1. neg-mul-1 100.0%

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

       2. times-frac 99.2%

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

   14. Applied egg-rr 99.2%

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

       1. *-commutative 99.2%

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

       2. times-frac 100.0%

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

       3. *-commutative 100.0%

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

       4. associate-/l* 99.7%

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

       5. *-commutative 99.7%

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

       6. neg-mul-1 99.7%

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

   16. Simplified 99.7%

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

   if -5.50000000000000018e-303 < z < 1.7999999999999999e-240

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   10. Simplified 72.3%

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

       1. *-commutative 72.3%

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

       2. frac-2neg 72.3%

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

       3. remove-double-neg 72.3%

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

       4. associate-*l/ 72.3%

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

   12. Applied egg-rr 72.3%

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

       1. neg-mul-1 72.3%

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

       2. times-frac 58.6%

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

   14. Applied egg-rr 58.6%

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

       1. *-commutative 58.6%

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

       2. times-frac 72.3%

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

       3. associate-/l* 72.4%

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

       4. *-commutative 72.4%

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

       5. neg-mul-1 72.4%

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

   16. Simplified 72.4%

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

   if 3.19999999999999982e-28 < z < 3.4e18

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+59}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-259}:\\ \;\;\;\;\frac{y}{\frac{-t}{x}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-240}:\\ \;\;\;\;\frac{x}{-\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot y}{-t}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-304}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{-\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ t y))))
   (if (<= z -7.2e+59)
     t_1
     (if (<= z -1.8e-215)
       x
       (if (<= z -1.6e-259)
         (/ (* x y) (- t))
         (if (<= z -6e-304)
           x
           (if (<= z 1.2e-239)
             (/ x (- (/ t y)))
             (if (<= z 2.5e-28)
               x
               (if (<= z 4.3e+17)
                 (* y (/ z t))
                 (if (<= z 7e+104) x t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -7.2e+59) {
		tmp = t_1;
	} else if (z <= -1.8e-215) {
		tmp = x;
	} else if (z <= -1.6e-259) {
		tmp = (x * y) / -t;
	} else if (z <= -6e-304) {
		tmp = x;
	} else if (z <= 1.2e-239) {
		tmp = x / -(t / y);
	} else if (z <= 2.5e-28) {
		tmp = x;
	} else if (z <= 4.3e+17) {
		tmp = y * (z / t);
	} else if (z <= 7e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (t / y)
    if (z <= (-7.2d+59)) then
        tmp = t_1
    else if (z <= (-1.8d-215)) then
        tmp = x
    else if (z <= (-1.6d-259)) then
        tmp = (x * y) / -t
    else if (z <= (-6d-304)) then
        tmp = x
    else if (z <= 1.2d-239) then
        tmp = x / -(t / y)
    else if (z <= 2.5d-28) then
        tmp = x
    else if (z <= 4.3d+17) then
        tmp = y * (z / t)
    else if (z <= 7d+104) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -7.2e+59) {
		tmp = t_1;
	} else if (z <= -1.8e-215) {
		tmp = x;
	} else if (z <= -1.6e-259) {
		tmp = (x * y) / -t;
	} else if (z <= -6e-304) {
		tmp = x;
	} else if (z <= 1.2e-239) {
		tmp = x / -(t / y);
	} else if (z <= 2.5e-28) {
		tmp = x;
	} else if (z <= 4.3e+17) {
		tmp = y * (z / t);
	} else if (z <= 7e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (t / y)
	tmp = 0
	if z <= -7.2e+59:
		tmp = t_1
	elif z <= -1.8e-215:
		tmp = x
	elif z <= -1.6e-259:
		tmp = (x * y) / -t
	elif z <= -6e-304:
		tmp = x
	elif z <= 1.2e-239:
		tmp = x / -(t / y)
	elif z <= 2.5e-28:
		tmp = x
	elif z <= 4.3e+17:
		tmp = y * (z / t)
	elif z <= 7e+104:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(t / y))
	tmp = 0.0
	if (z <= -7.2e+59)
		tmp = t_1;
	elseif (z <= -1.8e-215)
		tmp = x;
	elseif (z <= -1.6e-259)
		tmp = Float64(Float64(x * y) / Float64(-t));
	elseif (z <= -6e-304)
		tmp = x;
	elseif (z <= 1.2e-239)
		tmp = Float64(x / Float64(-Float64(t / y)));
	elseif (z <= 2.5e-28)
		tmp = x;
	elseif (z <= 4.3e+17)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 7e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (t / y);
	tmp = 0.0;
	if (z <= -7.2e+59)
		tmp = t_1;
	elseif (z <= -1.8e-215)
		tmp = x;
	elseif (z <= -1.6e-259)
		tmp = (x * y) / -t;
	elseif (z <= -6e-304)
		tmp = x;
	elseif (z <= 1.2e-239)
		tmp = x / -(t / y);
	elseif (z <= 2.5e-28)
		tmp = x;
	elseif (z <= 4.3e+17)
		tmp = y * (z / t);
	elseif (z <= 7e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+59], t$95$1, If[LessEqual[z, -1.8e-215], x, If[LessEqual[z, -1.6e-259], N[(N[(x * y), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, -6e-304], x, If[LessEqual[z, 1.2e-239], N[(x / (-N[(t / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 2.5e-28], x, If[LessEqual[z, 4.3e+17], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+104], x, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.1999999999999997e59 or 7.0000000000000003e104 < z

   1. Initial program 92.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.4%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/r/ 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -7.1999999999999997e59 < z < -1.7999999999999999e-215 or -1.59999999999999994e-259 < z < -6.0000000000000002e-304 or 1.19999999999999996e-239 < z < 2.5000000000000001e-28 or 4.3e17 < z < 7.0000000000000003e104

   1. Initial program 94.1%

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

      1. associate-*l/ 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 60.6%

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

   if -1.7999999999999999e-215 < z < -1.59999999999999994e-259

   1. Initial program 99.6%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in x around inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in y around inf 61.2%

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

      1. associate-*r/ 61.2%

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

      2. neg-mul-1 61.2%

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

   10. Simplified 61.2%

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

       1. *-commutative 61.2%

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

       2. frac-2neg 61.2%

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

       3. remove-double-neg 61.2%

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

       4. associate-*l/ 67.5%

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

   12. Applied egg-rr 67.5%

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

   if -6.0000000000000002e-304 < z < 1.19999999999999996e-239

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. neg-mul-1 72.3%

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

   10. Simplified 72.3%

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

       1. *-commutative 72.3%

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

       2. frac-2neg 72.3%

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

       3. remove-double-neg 72.3%

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

       4. associate-*l/ 72.3%

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

   12. Applied egg-rr 72.3%

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

       1. neg-mul-1 72.3%

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

       2. times-frac 58.6%

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

   14. Applied egg-rr 58.6%

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

       1. *-commutative 58.6%

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

       2. times-frac 72.3%

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

       3. associate-/l* 72.4%

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

       4. *-commutative 72.4%

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

       5. neg-mul-1 72.4%

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

   16. Simplified 72.4%

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

   if 2.5000000000000001e-28 < z < 4.3e17

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-215}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;\frac{x \cdot y}{-t}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-304}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{-\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{y}}\\ t_2 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ t y))) (t_2 (* x (- 1.0 (/ y t)))))
   (if (<= z -5.6e+94)
     t_1
     (if (<= z 3.8e-14)
       t_2
       (if (<= z 1.8e+17) (* y (/ z t)) (if (<= z 3.3e+152) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double t_2 = x * (1.0 - (y / t));
	double tmp;
	if (z <= -5.6e+94) {
		tmp = t_1;
	} else if (z <= 3.8e-14) {
		tmp = t_2;
	} else if (z <= 1.8e+17) {
		tmp = y * (z / t);
	} else if (z <= 3.3e+152) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z / (t / y)
    t_2 = x * (1.0d0 - (y / t))
    if (z <= (-5.6d+94)) then
        tmp = t_1
    else if (z <= 3.8d-14) then
        tmp = t_2
    else if (z <= 1.8d+17) then
        tmp = y * (z / t)
    else if (z <= 3.3d+152) then
        tmp = t_2
    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 = z / (t / y);
	double t_2 = x * (1.0 - (y / t));
	double tmp;
	if (z <= -5.6e+94) {
		tmp = t_1;
	} else if (z <= 3.8e-14) {
		tmp = t_2;
	} else if (z <= 1.8e+17) {
		tmp = y * (z / t);
	} else if (z <= 3.3e+152) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (t / y)
	t_2 = x * (1.0 - (y / t))
	tmp = 0
	if z <= -5.6e+94:
		tmp = t_1
	elif z <= 3.8e-14:
		tmp = t_2
	elif z <= 1.8e+17:
		tmp = y * (z / t)
	elif z <= 3.3e+152:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(t / y))
	t_2 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (z <= -5.6e+94)
		tmp = t_1;
	elseif (z <= 3.8e-14)
		tmp = t_2;
	elseif (z <= 1.8e+17)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 3.3e+152)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (t / y);
	t_2 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (z <= -5.6e+94)
		tmp = t_1;
	elseif (z <= 3.8e-14)
		tmp = t_2;
	elseif (z <= 1.8e+17)
		tmp = y * (z / t);
	elseif (z <= 3.3e+152)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+94], t$95$1, If[LessEqual[z, 3.8e-14], t$95$2, If[LessEqual[z, 1.8e+17], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+152], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999997e94 or 3.3000000000000001e152 < z

   1. Initial program 92.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 68.2%

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

   6. Taylor expanded in z around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-/r/ 78.2%

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

   8. Applied egg-rr 78.2%

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

   if -5.59999999999999997e94 < z < 3.8000000000000002e-14 or 1.8e17 < z < 3.3000000000000001e152

   1. Initial program 94.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. unsub-neg 86.1%

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

   7. Simplified 86.1%

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

   if 3.8000000000000002e-14 < z < 1.8e17

   1. Initial program 99.2%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   6. Taylor expanded in z around inf 75.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+94}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ t_2 := y \cdot \frac{z - x}{t}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))) (t_2 (* y (/ (- z x) t))))
   (if (<= z -1.6e+108)
     t_2
     (if (<= z 7.6e-31)
       t_1
       (if (<= z 1.05e+18) t_2 (if (<= z 4.6e+152) t_1 (/ z (/ t y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double t_2 = y * ((z - x) / t);
	double tmp;
	if (z <= -1.6e+108) {
		tmp = t_2;
	} else if (z <= 7.6e-31) {
		tmp = t_1;
	} else if (z <= 1.05e+18) {
		tmp = t_2;
	} else if (z <= 4.6e+152) {
		tmp = t_1;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    t_2 = y * ((z - x) / t)
    if (z <= (-1.6d+108)) then
        tmp = t_2
    else if (z <= 7.6d-31) then
        tmp = t_1
    else if (z <= 1.05d+18) then
        tmp = t_2
    else if (z <= 4.6d+152) then
        tmp = t_1
    else
        tmp = z / (t / y)
    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 / t));
	double t_2 = y * ((z - x) / t);
	double tmp;
	if (z <= -1.6e+108) {
		tmp = t_2;
	} else if (z <= 7.6e-31) {
		tmp = t_1;
	} else if (z <= 1.05e+18) {
		tmp = t_2;
	} else if (z <= 4.6e+152) {
		tmp = t_1;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	t_2 = y * ((z - x) / t)
	tmp = 0
	if z <= -1.6e+108:
		tmp = t_2
	elif z <= 7.6e-31:
		tmp = t_1
	elif z <= 1.05e+18:
		tmp = t_2
	elif z <= 4.6e+152:
		tmp = t_1
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	t_2 = Float64(y * Float64(Float64(z - x) / t))
	tmp = 0.0
	if (z <= -1.6e+108)
		tmp = t_2;
	elseif (z <= 7.6e-31)
		tmp = t_1;
	elseif (z <= 1.05e+18)
		tmp = t_2;
	elseif (z <= 4.6e+152)
		tmp = t_1;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	t_2 = y * ((z - x) / t);
	tmp = 0.0;
	if (z <= -1.6e+108)
		tmp = t_2;
	elseif (z <= 7.6e-31)
		tmp = t_1;
	elseif (z <= 1.05e+18)
		tmp = t_2;
	elseif (z <= 4.6e+152)
		tmp = t_1;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+108], t$95$2, If[LessEqual[z, 7.6e-31], t$95$1, If[LessEqual[z, 1.05e+18], t$95$2, If[LessEqual[z, 4.6e+152], t$95$1, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e108 or 7.5999999999999999e-31 < z < 1.05e18

   1. Initial program 93.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 76.8%

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

   6. Taylor expanded in z around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-frac-neg 76.8%

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

      3. +-commutative 76.8%

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

      4. distribute-frac-neg 76.8%

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

      5. sub-neg 76.8%

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

      6. div-sub 84.1%

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

   8. Simplified 84.1%

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

   if -1.6e108 < z < 7.5999999999999999e-31 or 1.05e18 < z < 4.5999999999999997e152

   1. Initial program 94.8%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

   7. Simplified 86.4%

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

   if 4.5999999999999997e152 < z

   1. Initial program 93.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.2%

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

   6. Taylor expanded in z around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-/r/ 81.7%

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

   8. Applied egg-rr 81.7%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+67} \lor \neg \left(z \leq 2.8 \cdot 10^{-28}\right) \land \left(z \leq 3.5 \cdot 10^{+18} \lor \neg \left(z \leq 5.4 \cdot 10^{+104}\right)\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.4e+67)
         (and (not (<= z 2.8e-28)) (or (<= z 3.5e+18) (not (<= z 5.4e+104)))))
   (* y (/ z t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4e+67) || (!(z <= 2.8e-28) && ((z <= 3.5e+18) || !(z <= 5.4e+104)))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.4d+67)) .or. (.not. (z <= 2.8d-28)) .and. (z <= 3.5d+18) .or. (.not. (z <= 5.4d+104))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4e+67) || (!(z <= 2.8e-28) && ((z <= 3.5e+18) || !(z <= 5.4e+104)))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.4e+67) or (not (z <= 2.8e-28) and ((z <= 3.5e+18) or not (z <= 5.4e+104))):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.4e+67) || (!(z <= 2.8e-28) && ((z <= 3.5e+18) || !(z <= 5.4e+104))))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.4e+67) || (~((z <= 2.8e-28)) && ((z <= 3.5e+18) || ~((z <= 5.4e+104)))))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.4e+67], And[N[Not[LessEqual[z, 2.8e-28]], $MachinePrecision], Or[LessEqual[z, 3.5e+18], N[Not[LessEqual[z, 5.4e+104]], $MachinePrecision]]]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e67 or 2.7999999999999998e-28 < z < 3.5e18 or 5.39999999999999969e104 < z

   1. Initial program 93.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 70.8%

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

   6. Taylor expanded in z around inf 67.8%

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

   if -4.4e67 < z < 2.7999999999999998e-28 or 3.5e18 < z < 5.39999999999999969e104

   1. Initial program 95.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 54.5%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+67} \lor \neg \left(z \leq 2.8 \cdot 10^{-28}\right) \land \left(z \leq 3.5 \cdot 10^{+18} \lor \neg \left(z \leq 5.4 \cdot 10^{+104}\right)\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ t z))))
   (if (<= z -1.35e+63)
     t_1
     (if (<= z 8.6e-29)
       x
       (if (<= z 2.75e+17) (* y (/ z t)) (if (<= z 2.35e+104) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if (z <= -1.35e+63) {
		tmp = t_1;
	} else if (z <= 8.6e-29) {
		tmp = x;
	} else if (z <= 2.75e+17) {
		tmp = y * (z / t);
	} else if (z <= 2.35e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (t / z)
    if (z <= (-1.35d+63)) then
        tmp = t_1
    else if (z <= 8.6d-29) then
        tmp = x
    else if (z <= 2.75d+17) then
        tmp = y * (z / t)
    else if (z <= 2.35d+104) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if (z <= -1.35e+63) {
		tmp = t_1;
	} else if (z <= 8.6e-29) {
		tmp = x;
	} else if (z <= 2.75e+17) {
		tmp = y * (z / t);
	} else if (z <= 2.35e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t / z)
	tmp = 0
	if z <= -1.35e+63:
		tmp = t_1
	elif z <= 8.6e-29:
		tmp = x
	elif z <= 2.75e+17:
		tmp = y * (z / t)
	elif z <= 2.35e+104:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (z <= -1.35e+63)
		tmp = t_1;
	elseif (z <= 8.6e-29)
		tmp = x;
	elseif (z <= 2.75e+17)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 2.35e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t / z);
	tmp = 0.0;
	if (z <= -1.35e+63)
		tmp = t_1;
	elseif (z <= 8.6e-29)
		tmp = x;
	elseif (z <= 2.75e+17)
		tmp = y * (z / t);
	elseif (z <= 2.35e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+63], t$95$1, If[LessEqual[z, 8.6e-29], x, If[LessEqual[z, 2.75e+17], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+104], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000009e63 or 2.35000000000000008e104 < z

   1. Initial program 92.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.4%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. clear-num 67.5%

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

      2. un-div-inv 68.1%

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

   8. Applied egg-rr 68.1%

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

   if -1.35000000000000009e63 < z < 8.5999999999999996e-29 or 2.75e17 < z < 2.35000000000000008e104

   1. Initial program 95.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 54.5%

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

   if 8.5999999999999996e-29 < z < 2.75e17

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ t y))))
   (if (<= z -1.8e+63)
     t_1
     (if (<= z 1.65e-29)
       x
       (if (<= z 2.8e+17) (* y (/ z t)) (if (<= z 8.2e+104) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -1.8e+63) {
		tmp = t_1;
	} else if (z <= 1.65e-29) {
		tmp = x;
	} else if (z <= 2.8e+17) {
		tmp = y * (z / t);
	} else if (z <= 8.2e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (t / y)
    if (z <= (-1.8d+63)) then
        tmp = t_1
    else if (z <= 1.65d-29) then
        tmp = x
    else if (z <= 2.8d+17) then
        tmp = y * (z / t)
    else if (z <= 8.2d+104) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (t / y);
	double tmp;
	if (z <= -1.8e+63) {
		tmp = t_1;
	} else if (z <= 1.65e-29) {
		tmp = x;
	} else if (z <= 2.8e+17) {
		tmp = y * (z / t);
	} else if (z <= 8.2e+104) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (t / y)
	tmp = 0
	if z <= -1.8e+63:
		tmp = t_1
	elif z <= 1.65e-29:
		tmp = x
	elif z <= 2.8e+17:
		tmp = y * (z / t)
	elif z <= 8.2e+104:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(t / y))
	tmp = 0.0
	if (z <= -1.8e+63)
		tmp = t_1;
	elseif (z <= 1.65e-29)
		tmp = x;
	elseif (z <= 2.8e+17)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 8.2e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (t / y);
	tmp = 0.0;
	if (z <= -1.8e+63)
		tmp = t_1;
	elseif (z <= 1.65e-29)
		tmp = x;
	elseif (z <= 2.8e+17)
		tmp = y * (z / t);
	elseif (z <= 8.2e+104)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+63], t$95$1, If[LessEqual[z, 1.65e-29], x, If[LessEqual[z, 2.8e+17], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+104], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999999e63 or 8.1999999999999997e104 < z

   1. Initial program 92.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 67.4%

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

   6. Taylor expanded in z around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-/r/ 75.1%

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

   8. Applied egg-rr 75.1%

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

   if -1.79999999999999999e63 < z < 1.65000000000000014e-29 or 2.8e17 < z < 8.1999999999999997e104

   1. Initial program 95.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 54.5%

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

   if 1.65000000000000014e-29 < z < 2.8e17

   1. Initial program 99.4%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+63}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-41} \lor \neg \left(z \leq 2.05 \cdot 10^{-22}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.2e-41) (not (<= z 2.05e-22)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-41) || !(z <= 2.05e-22)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.2d-41)) .or. (.not. (z <= 2.05d-22))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-41) || !(z <= 2.05e-22)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.2e-41) or not (z <= 2.05e-22):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.2e-41) || !(z <= 2.05e-22))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.2e-41) || ~((z <= 2.05e-22)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.2e-41], N[Not[LessEqual[z, 2.05e-22]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.20000000000000041e-41 or 2.05e-22 < z

   1. Initial program 92.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 87.4%

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

      1. associate-*r/ 86.8%

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

   9. Simplified 86.8%

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

   if -9.20000000000000041e-41 < z < 2.05e-22

   1. Initial program 96.0%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf 91.1%

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

      1. mul-1-neg 91.1%

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

      2. unsub-neg 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-41} \lor \neg \left(z \leq 2.05 \cdot 10^{-22}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-44} \lor \neg \left(z \leq 1.85 \cdot 10^{-25}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e-44) (not (<= z 1.85e-25)))
   (+ x (* (/ y t) z))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e-44) || !(z <= 1.85e-25)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.4d-44)) .or. (.not. (z <= 1.85d-25))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e-44) || !(z <= 1.85e-25)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e-44) or not (z <= 1.85e-25):
		tmp = x + ((y / t) * z)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e-44) || !(z <= 1.85e-25))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e-44) || ~((z <= 1.85e-25)))
		tmp = x + ((y / t) * z);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e-44], N[Not[LessEqual[z, 1.85e-25]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e-44 or 1.85000000000000004e-25 < z

   1. Initial program 92.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.4%

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

      1. associate-*l/ 91.7%

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

      2. *-commutative 91.7%

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

   7. Simplified 91.7%

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

   if -1.4e-44 < z < 1.85000000000000004e-25

   1. Initial program 96.0%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf 91.1%

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

      1. mul-1-neg 91.1%

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

      2. unsub-neg 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-44} \lor \neg \left(z \leq 1.85 \cdot 10^{-25}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-44} \lor \neg \left(z \leq 2.7 \cdot 10^{-26}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e-44) (not (<= z 2.7e-26)))
   (+ x (* (/ y t) z))
   (- x (/ x (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-44) || !(z <= 2.7e-26)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (x / (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.2d-44)) .or. (.not. (z <= 2.7d-26))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x - (x / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-44) || !(z <= 2.7e-26)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (x / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e-44) or not (z <= 2.7e-26):
		tmp = x + ((y / t) * z)
	else:
		tmp = x - (x / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e-44) || !(z <= 2.7e-26))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x - Float64(x / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e-44) || ~((z <= 2.7e-26)))
		tmp = x + ((y / t) * z);
	else
		tmp = x - (x / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-44], N[Not[LessEqual[z, 2.7e-26]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999996e-44 or 2.69999999999999982e-26 < z

   1. Initial program 92.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 87.4%

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

      1. associate-*l/ 91.7%

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

      2. *-commutative 91.7%

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

   7. Simplified 91.7%

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

   if -5.1999999999999996e-44 < z < 2.69999999999999982e-26

   1. Initial program 96.0%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. associate-/l* 91.1%

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

      3. distribute-neg-frac 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-44} \lor \neg \left(z \leq 2.7 \cdot 10^{-26}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.5% 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 94.3%

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

   1. associate-*l/ 98.8%

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

3. Simplified 98.8%

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

5. Taylor expanded in y around 0 41.3%

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

6. Final simplification 41.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 90.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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 - ((x * (y / t)) + (-z * (y / t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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