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

Percentage Accurate: 92.9% → 97.9%

Time: 7.7s

Alternatives: 14

Speedup: 1.0×

• 25.0% 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: 92.9% 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: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in z around 0 85.2%

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

   1. +-commutative 85.2%

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

   2. *-commutative 85.2%

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

   3. associate-*r/ 86.8%

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

   4. mul-1-neg 86.8%

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

   5. associate-/l* 88.8%

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

   6. distribute-lft-neg-in 88.8%

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

   7. distribute-rgt-in 98.7%

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

   8. sub-neg 98.7%

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

5. Simplified 98.7%

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

   1. *-commutative 98.7%

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

   2. clear-num 98.6%

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

   3. un-div-inv 99.2%

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

7. Applied egg-rr 99.2%

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

Alternative 2: 51.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.14e+64)
   (* z (/ y t))
   (if (<= z -1.25e-167)
     x
     (if (<= z -1.1e-296)
       (/ x (/ t (- y)))
       (if (<= z 2.15e-92)
         x
         (if (<= z 1.95e+28)
           (* x (/ y (- t)))
           (if (<= z 1.15e+39)
             x
             (if (<= z 1.35e+83)
               (/ y (/ t z))
               (if (<= z 2.05e+87) x (/ z (/ t y)))))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.14e+64) {
		tmp = z * (y / t);
	} else if (z <= -1.25e-167) {
		tmp = x;
	} else if (z <= -1.1e-296) {
		tmp = x / (t / -y);
	} else if (z <= 2.15e-92) {
		tmp = x;
	} else if (z <= 1.95e+28) {
		tmp = x * (y / -t);
	} else if (z <= 1.15e+39) {
		tmp = x;
	} else if (z <= 1.35e+83) {
		tmp = y / (t / z);
	} else if (z <= 2.05e+87) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-1.14d+64)) then
        tmp = z * (y / t)
    else if (z <= (-1.25d-167)) then
        tmp = x
    else if (z <= (-1.1d-296)) then
        tmp = x / (t / -y)
    else if (z <= 2.15d-92) then
        tmp = x
    else if (z <= 1.95d+28) then
        tmp = x * (y / -t)
    else if (z <= 1.15d+39) then
        tmp = x
    else if (z <= 1.35d+83) then
        tmp = y / (t / z)
    else if (z <= 2.05d+87) then
        tmp = x
    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 tmp;
	if (z <= -1.14e+64) {
		tmp = z * (y / t);
	} else if (z <= -1.25e-167) {
		tmp = x;
	} else if (z <= -1.1e-296) {
		tmp = x / (t / -y);
	} else if (z <= 2.15e-92) {
		tmp = x;
	} else if (z <= 1.95e+28) {
		tmp = x * (y / -t);
	} else if (z <= 1.15e+39) {
		tmp = x;
	} else if (z <= 1.35e+83) {
		tmp = y / (t / z);
	} else if (z <= 2.05e+87) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.14e+64:
		tmp = z * (y / t)
	elif z <= -1.25e-167:
		tmp = x
	elif z <= -1.1e-296:
		tmp = x / (t / -y)
	elif z <= 2.15e-92:
		tmp = x
	elif z <= 1.95e+28:
		tmp = x * (y / -t)
	elif z <= 1.15e+39:
		tmp = x
	elif z <= 1.35e+83:
		tmp = y / (t / z)
	elif z <= 2.05e+87:
		tmp = x
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.14e+64)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= -1.25e-167)
		tmp = x;
	elseif (z <= -1.1e-296)
		tmp = Float64(x / Float64(t / Float64(-y)));
	elseif (z <= 2.15e-92)
		tmp = x;
	elseif (z <= 1.95e+28)
		tmp = Float64(x * Float64(y / Float64(-t)));
	elseif (z <= 1.15e+39)
		tmp = x;
	elseif (z <= 1.35e+83)
		tmp = Float64(y / Float64(t / z));
	elseif (z <= 2.05e+87)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.14e+64)
		tmp = z * (y / t);
	elseif (z <= -1.25e-167)
		tmp = x;
	elseif (z <= -1.1e-296)
		tmp = x / (t / -y);
	elseif (z <= 2.15e-92)
		tmp = x;
	elseif (z <= 1.95e+28)
		tmp = x * (y / -t);
	elseif (z <= 1.15e+39)
		tmp = x;
	elseif (z <= 1.35e+83)
		tmp = y / (t / z);
	elseif (z <= 2.05e+87)
		tmp = x;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.14e+64], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-167], x, If[LessEqual[z, -1.1e-296], N[(x / N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-92], x, If[LessEqual[z, 1.95e+28], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+39], x, If[LessEqual[z, 1.35e+83], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+87], x, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.14e64

   1. Initial program 89.2%

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

   3. Taylor expanded in y around -inf 65.0%

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

   4. Taylor expanded in z around inf 58.3%

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

      1. associate-/l* 86.8%

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

   6. Simplified 62.6%

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

      1. clear-num 86.8%

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

      2. un-div-inv 84.8%

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

   8. Applied egg-rr 60.6%

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

      1. associate-/r/ 93.1%

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

   10. Applied egg-rr 68.9%

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

   if -1.14e64 < z < -1.25000000000000005e-167 or -1.10000000000000006e-296 < z < 2.15000000000000007e-92 or 1.9499999999999999e28 < z < 1.15000000000000006e39 or 1.35000000000000003e83 < z < 2.05e87

   1. Initial program 91.0%

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

   3. Taylor expanded in y around 0 60.5%

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

   if -1.25000000000000005e-167 < z < -1.10000000000000006e-296

   1. Initial program 86.6%

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

   3. Taylor expanded in y around -inf 57.4%

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

   4. Taylor expanded in z around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. associate-/l* 58.2%

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

      3. distribute-rgt-neg-in 58.2%

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

      4. mul-1-neg 58.2%

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

      5. associate-*r/ 58.2%

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

      6. mul-1-neg 58.2%

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

   6. Simplified 58.2%

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

      1. add-sqr-sqrt 33.1%

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

      2. sqrt-unprod 23.7%

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

      3. sqr-neg 23.7%

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

      4. sqrt-unprod 0.9%

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

      5. add-sqr-sqrt 1.9%

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

      6. clear-num 1.9%

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

      7. div-inv 1.9%

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

      8. frac-2neg 1.9%

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

      9. distribute-frac-neg2 1.9%

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

      10. add-sqr-sqrt 1.0%

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

      11. sqrt-unprod 16.2%

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

      12. sqr-neg 16.2%

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

      13. sqrt-unprod 25.0%

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

      14. add-sqr-sqrt 60.6%

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

   8. Applied egg-rr 60.6%

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

   if 2.15000000000000007e-92 < z < 1.9499999999999999e28

   1. Initial program 95.9%

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

   3. Taylor expanded in y around -inf 71.6%

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

   4. Taylor expanded in z around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. associate-/l* 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

      4. mul-1-neg 51.5%

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

      5. associate-*r/ 51.5%

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

      6. mul-1-neg 51.5%

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

   6. Simplified 51.5%

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

   if 1.15000000000000006e39 < z < 1.35000000000000003e83

   1. Initial program 86.7%

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

   3. Taylor expanded in y around -inf 80.0%

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

   4. Taylor expanded in z around inf 58.3%

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

      1. associate-/l* 78.4%

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

   6. Simplified 71.4%

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

      1. clear-num 78.5%

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

      2. un-div-inv 78.5%

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

   8. Applied egg-rr 71.5%

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

   if 2.05e87 < z

   1. Initial program 88.5%

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

   3. Taylor expanded in y around -inf 70.2%

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

   4. Taylor expanded in z around inf 66.1%

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

      1. associate-/l* 82.7%

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

   6. Simplified 64.9%

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

      1. clear-num 82.7%

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

      2. un-div-inv 82.7%

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

   8. Applied egg-rr 64.8%

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

      1. associate-/r/ 93.5%

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

   10. Applied egg-rr 75.3%

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

       1. *-commutative 75.3%

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

       2. clear-num 75.4%

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

       3. un-div-inv 75.4%

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

   12. Applied egg-rr 75.4%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{-t}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-223}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t)))))
   (if (<= z -1.65e+61)
     (* z (/ y t))
     (if (<= z -4e-179)
       x
       (if (<= z -1.15e-223)
         t_1
         (if (<= z 8.1e-92)
           x
           (if (<= z 5.8e+33) t_1 (if (<= z 1.45e+39) x (/ z (/ t y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / -t);
	double tmp;
	if (z <= -1.65e+61) {
		tmp = z * (y / t);
	} else if (z <= -4e-179) {
		tmp = x;
	} else if (z <= -1.15e-223) {
		tmp = t_1;
	} else if (z <= 8.1e-92) {
		tmp = x;
	} else if (z <= 5.8e+33) {
		tmp = t_1;
	} else if (z <= 1.45e+39) {
		tmp = x;
	} 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) :: tmp
    t_1 = x * (y / -t)
    if (z <= (-1.65d+61)) then
        tmp = z * (y / t)
    else if (z <= (-4d-179)) then
        tmp = x
    else if (z <= (-1.15d-223)) then
        tmp = t_1
    else if (z <= 8.1d-92) then
        tmp = x
    else if (z <= 5.8d+33) then
        tmp = t_1
    else if (z <= 1.45d+39) then
        tmp = x
    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 * (y / -t);
	double tmp;
	if (z <= -1.65e+61) {
		tmp = z * (y / t);
	} else if (z <= -4e-179) {
		tmp = x;
	} else if (z <= -1.15e-223) {
		tmp = t_1;
	} else if (z <= 8.1e-92) {
		tmp = x;
	} else if (z <= 5.8e+33) {
		tmp = t_1;
	} else if (z <= 1.45e+39) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / -t)
	tmp = 0
	if z <= -1.65e+61:
		tmp = z * (y / t)
	elif z <= -4e-179:
		tmp = x
	elif z <= -1.15e-223:
		tmp = t_1
	elif z <= 8.1e-92:
		tmp = x
	elif z <= 5.8e+33:
		tmp = t_1
	elif z <= 1.45e+39:
		tmp = x
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(-t)))
	tmp = 0.0
	if (z <= -1.65e+61)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= -4e-179)
		tmp = x;
	elseif (z <= -1.15e-223)
		tmp = t_1;
	elseif (z <= 8.1e-92)
		tmp = x;
	elseif (z <= 5.8e+33)
		tmp = t_1;
	elseif (z <= 1.45e+39)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / -t);
	tmp = 0.0;
	if (z <= -1.65e+61)
		tmp = z * (y / t);
	elseif (z <= -4e-179)
		tmp = x;
	elseif (z <= -1.15e-223)
		tmp = t_1;
	elseif (z <= 8.1e-92)
		tmp = x;
	elseif (z <= 5.8e+33)
		tmp = t_1;
	elseif (z <= 1.45e+39)
		tmp = x;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+61], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-179], x, If[LessEqual[z, -1.15e-223], t$95$1, If[LessEqual[z, 8.1e-92], x, If[LessEqual[z, 5.8e+33], t$95$1, If[LessEqual[z, 1.45e+39], x, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6499999999999999e61

   1. Initial program 89.2%

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

   3. Taylor expanded in y around -inf 65.0%

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

   4. Taylor expanded in z around inf 58.3%

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

      1. associate-/l* 86.8%

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

   6. Simplified 62.6%

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

      1. clear-num 86.8%

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

      2. un-div-inv 84.8%

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

   8. Applied egg-rr 60.6%

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

      1. associate-/r/ 93.1%

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

   10. Applied egg-rr 68.9%

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

   if -1.6499999999999999e61 < z < -4.0000000000000001e-179 or -1.15e-223 < z < 8.09999999999999951e-92 or 5.80000000000000049e33 < z < 1.45000000000000015e39

   1. Initial program 90.9%

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

   3. Taylor expanded in y around 0 55.9%

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

   if -4.0000000000000001e-179 < z < -1.15e-223 or 8.09999999999999951e-92 < z < 5.80000000000000049e33

   1. Initial program 93.8%

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

   3. Taylor expanded in y around -inf 72.7%

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

   4. Taylor expanded in z around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 55.3%

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

      3. distribute-rgt-neg-in 55.3%

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

      4. mul-1-neg 55.3%

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

      5. associate-*r/ 55.3%

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

      6. mul-1-neg 55.3%

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

   6. Simplified 55.3%

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

   if 1.45000000000000015e39 < z

   1. Initial program 86.8%

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

   3. Taylor expanded in y around -inf 71.2%

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

   4. Taylor expanded in z around inf 63.4%

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

      1. associate-/l* 82.1%

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

   6. Simplified 65.3%

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

      1. clear-num 82.1%

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

      2. un-div-inv 82.0%

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

   8. Applied egg-rr 65.3%

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

      1. associate-/r/ 90.3%

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

   10. Applied egg-rr 73.3%

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

       1. *-commutative 73.3%

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

       2. clear-num 73.4%

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

       3. un-div-inv 73.4%

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

   12. Applied egg-rr 73.4%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-223}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ t_2 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 45000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))) (t_2 (+ x (* z (/ y t)))))
   (if (<= z -8.2e+40)
     t_2
     (if (<= z -3.6e-282)
       t_1
       (if (<= z -3.5e-282)
         (* y (/ z t))
         (if (<= z 45000000.0)
           t_1
           (if (<= z 7.8e+50) (/ (* (- z x) y) t) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double t_2 = x + (z * (y / t));
	double tmp;
	if (z <= -8.2e+40) {
		tmp = t_2;
	} else if (z <= -3.6e-282) {
		tmp = t_1;
	} else if (z <= -3.5e-282) {
		tmp = y * (z / t);
	} else if (z <= 45000000.0) {
		tmp = t_1;
	} else if (z <= 7.8e+50) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    t_2 = x + (z * (y / t))
    if (z <= (-8.2d+40)) then
        tmp = t_2
    else if (z <= (-3.6d-282)) then
        tmp = t_1
    else if (z <= (-3.5d-282)) then
        tmp = y * (z / t)
    else if (z <= 45000000.0d0) then
        tmp = t_1
    else if (z <= 7.8d+50) then
        tmp = ((z - x) * y) / t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double t_2 = x + (z * (y / t));
	double tmp;
	if (z <= -8.2e+40) {
		tmp = t_2;
	} else if (z <= -3.6e-282) {
		tmp = t_1;
	} else if (z <= -3.5e-282) {
		tmp = y * (z / t);
	} else if (z <= 45000000.0) {
		tmp = t_1;
	} else if (z <= 7.8e+50) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	t_2 = x + (z * (y / t))
	tmp = 0
	if z <= -8.2e+40:
		tmp = t_2
	elif z <= -3.6e-282:
		tmp = t_1
	elif z <= -3.5e-282:
		tmp = y * (z / t)
	elif z <= 45000000.0:
		tmp = t_1
	elif z <= 7.8e+50:
		tmp = ((z - x) * y) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	t_2 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (z <= -8.2e+40)
		tmp = t_2;
	elseif (z <= -3.6e-282)
		tmp = t_1;
	elseif (z <= -3.5e-282)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 45000000.0)
		tmp = t_1;
	elseif (z <= 7.8e+50)
		tmp = Float64(Float64(Float64(z - x) * y) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	t_2 = x + (z * (y / t));
	tmp = 0.0;
	if (z <= -8.2e+40)
		tmp = t_2;
	elseif (z <= -3.6e-282)
		tmp = t_1;
	elseif (z <= -3.5e-282)
		tmp = y * (z / t);
	elseif (z <= 45000000.0)
		tmp = t_1;
	elseif (z <= 7.8e+50)
		tmp = ((z - x) * y) / t;
	else
		tmp = t_2;
	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[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+40], t$95$2, If[LessEqual[z, -3.6e-282], t$95$1, If[LessEqual[z, -3.5e-282], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 45000000.0], t$95$1, If[LessEqual[z, 7.8e+50], N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.2000000000000003e40 or 7.79999999999999935e50 < z

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 81.6%

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

      1. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

      1. clear-num 84.2%

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

      2. un-div-inv 83.4%

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

   7. Applied egg-rr 83.4%

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

      1. associate-/r/ 91.8%

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

   9. Applied egg-rr 91.8%

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

   if -8.2000000000000003e40 < z < -3.5999999999999998e-282 or -3.50000000000000006e-282 < z < 4.5e7

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

   5. Simplified 87.4%

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

   if -3.5999999999999998e-282 < z < -3.50000000000000006e-282

   1. Initial program 4.0%

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

   3. Taylor expanded in y around -inf 4.1%

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

   4. Taylor expanded in z around inf 4.1%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if 4.5e7 < z < 7.79999999999999935e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 85.5%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+40}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 45000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ t_2 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 155:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+47}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))) (t_2 (+ x (* z (/ y t)))))
   (if (<= z -6.4e+40)
     t_2
     (if (<= z -3.6e-282)
       t_1
       (if (<= z -3.5e-282)
         (* y (/ z t))
         (if (<= z 155.0) t_1 (if (<= z 6.9e+47) (* (- z x) (/ y t)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double t_2 = x + (z * (y / t));
	double tmp;
	if (z <= -6.4e+40) {
		tmp = t_2;
	} else if (z <= -3.6e-282) {
		tmp = t_1;
	} else if (z <= -3.5e-282) {
		tmp = y * (z / t);
	} else if (z <= 155.0) {
		tmp = t_1;
	} else if (z <= 6.9e+47) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    t_2 = x + (z * (y / t))
    if (z <= (-6.4d+40)) then
        tmp = t_2
    else if (z <= (-3.6d-282)) then
        tmp = t_1
    else if (z <= (-3.5d-282)) then
        tmp = y * (z / t)
    else if (z <= 155.0d0) then
        tmp = t_1
    else if (z <= 6.9d+47) then
        tmp = (z - x) * (y / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double t_2 = x + (z * (y / t));
	double tmp;
	if (z <= -6.4e+40) {
		tmp = t_2;
	} else if (z <= -3.6e-282) {
		tmp = t_1;
	} else if (z <= -3.5e-282) {
		tmp = y * (z / t);
	} else if (z <= 155.0) {
		tmp = t_1;
	} else if (z <= 6.9e+47) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	t_2 = x + (z * (y / t))
	tmp = 0
	if z <= -6.4e+40:
		tmp = t_2
	elif z <= -3.6e-282:
		tmp = t_1
	elif z <= -3.5e-282:
		tmp = y * (z / t)
	elif z <= 155.0:
		tmp = t_1
	elif z <= 6.9e+47:
		tmp = (z - x) * (y / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	t_2 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (z <= -6.4e+40)
		tmp = t_2;
	elseif (z <= -3.6e-282)
		tmp = t_1;
	elseif (z <= -3.5e-282)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 155.0)
		tmp = t_1;
	elseif (z <= 6.9e+47)
		tmp = Float64(Float64(z - x) * Float64(y / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	t_2 = x + (z * (y / t));
	tmp = 0.0;
	if (z <= -6.4e+40)
		tmp = t_2;
	elseif (z <= -3.6e-282)
		tmp = t_1;
	elseif (z <= -3.5e-282)
		tmp = y * (z / t);
	elseif (z <= 155.0)
		tmp = t_1;
	elseif (z <= 6.9e+47)
		tmp = (z - x) * (y / t);
	else
		tmp = t_2;
	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[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+40], t$95$2, If[LessEqual[z, -3.6e-282], t$95$1, If[LessEqual[z, -3.5e-282], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 155.0], t$95$1, If[LessEqual[z, 6.9e+47], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.39999999999999961e40 or 6.9000000000000004e47 < z

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 81.6%

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

      1. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

      1. clear-num 84.2%

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

      2. un-div-inv 83.4%

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

   7. Applied egg-rr 83.4%

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

      1. associate-/r/ 91.8%

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

   9. Applied egg-rr 91.8%

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

   if -6.39999999999999961e40 < z < -3.5999999999999998e-282 or -3.50000000000000006e-282 < z < 155

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

   5. Simplified 87.4%

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

   if -3.5999999999999998e-282 < z < -3.50000000000000006e-282

   1. Initial program 4.0%

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

   3. Taylor expanded in y around -inf 4.1%

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

   4. Taylor expanded in z around inf 4.1%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if 155 < z < 6.9000000000000004e47

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 85.5%

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

   4. Taylor expanded in z around 0 85.5%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 99.8%

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

      4. mul-1-neg 99.8%

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

      5. associate-/l* 92.1%

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

      6. distribute-lft-neg-in 92.1%

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

      7. distribute-rgt-in 99.8%

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

      8. sub-neg 99.8%

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

   6. Simplified 85.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+40}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 155:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+47}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1250:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 10^{+114} \lor \neg \left(z \leq 3.6 \cdot 10^{+114}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z x) (/ y t))))
   (if (<= z -2.45e+69)
     t_1
     (if (<= z 1250.0)
       (* x (- 1.0 (/ y t)))
       (if (or (<= z 1e+114) (not (<= z 3.6e+114))) t_1 x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z - x) * (y / t);
	double tmp;
	if (z <= -2.45e+69) {
		tmp = t_1;
	} else if (z <= 1250.0) {
		tmp = x * (1.0 - (y / t));
	} else if ((z <= 1e+114) || !(z <= 3.6e+114)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - x) * (y / t)
    if (z <= (-2.45d+69)) then
        tmp = t_1
    else if (z <= 1250.0d0) then
        tmp = x * (1.0d0 - (y / t))
    else if ((z <= 1d+114) .or. (.not. (z <= 3.6d+114))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z - x) * (y / t);
	double tmp;
	if (z <= -2.45e+69) {
		tmp = t_1;
	} else if (z <= 1250.0) {
		tmp = x * (1.0 - (y / t));
	} else if ((z <= 1e+114) || !(z <= 3.6e+114)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z - x) * (y / t)
	tmp = 0
	if z <= -2.45e+69:
		tmp = t_1
	elif z <= 1250.0:
		tmp = x * (1.0 - (y / t))
	elif (z <= 1e+114) or not (z <= 3.6e+114):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z - x) * Float64(y / t))
	tmp = 0.0
	if (z <= -2.45e+69)
		tmp = t_1;
	elseif (z <= 1250.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif ((z <= 1e+114) || !(z <= 3.6e+114))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z - x) * (y / t);
	tmp = 0.0;
	if (z <= -2.45e+69)
		tmp = t_1;
	elseif (z <= 1250.0)
		tmp = x * (1.0 - (y / t));
	elseif ((z <= 1e+114) || ~((z <= 3.6e+114)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e+69], t$95$1, If[LessEqual[z, 1250.0], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1e+114], N[Not[LessEqual[z, 3.6e+114]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45e69 or 1250 < z < 1e114 or 3.6000000000000001e114 < z

   1. Initial program 88.4%

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

   3. Taylor expanded in y around -inf 70.4%

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

   4. Taylor expanded in z around 0 62.4%

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

      1. +-commutative 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*r/ 89.3%

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

      4. mul-1-neg 89.3%

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

      5. associate-/l* 86.6%

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

      6. distribute-lft-neg-in 86.6%

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

      7. distribute-rgt-in 99.6%

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

      8. sub-neg 99.6%

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

   6. Simplified 80.8%

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

   if -2.45e69 < z < 1250

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

   5. Simplified 86.5%

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

   if 1e114 < z < 3.6000000000000001e114

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+69}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 1250:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 10^{+114} \lor \neg \left(z \leq 3.6 \cdot 10^{+114}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3600:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= z -9e+73)
     t_1
     (if (<= z 3600.0)
       (* x (- 1.0 (/ y t)))
       (if (<= z 5e+108) (* (- z x) (/ y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (z <= -9e+73) {
		tmp = t_1;
	} else if (z <= 3600.0) {
		tmp = x * (1.0 - (y / t));
	} else if (z <= 5e+108) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (z <= (-9d+73)) then
        tmp = t_1
    else if (z <= 3600.0d0) then
        tmp = x * (1.0d0 - (y / t))
    else if (z <= 5d+108) then
        tmp = (z - x) * (y / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (z <= -9e+73) {
		tmp = t_1;
	} else if (z <= 3600.0) {
		tmp = x * (1.0 - (y / t));
	} else if (z <= 5e+108) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	tmp = 0
	if z <= -9e+73:
		tmp = t_1
	elif z <= 3600.0:
		tmp = x * (1.0 - (y / t))
	elif z <= 5e+108:
		tmp = (z - x) * (y / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (z <= -9e+73)
		tmp = t_1;
	elseif (z <= 3600.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (z <= 5e+108)
		tmp = Float64(Float64(z - x) * Float64(y / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (z <= -9e+73)
		tmp = t_1;
	elseif (z <= 3600.0)
		tmp = x * (1.0 - (y / t));
	elseif (z <= 5e+108)
		tmp = (z - x) * (y / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+73], t$95$1, If[LessEqual[z, 3600.0], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+108], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.99999999999999969e73 or 4.99999999999999991e108 < z

   1. Initial program 88.2%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 84.9%

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

   5. Simplified 84.9%

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

   if -8.99999999999999969e73 < z < 3600

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if 3600 < z < 4.99999999999999991e108

   1. Initial program 88.6%

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

   3. Taylor expanded in y around -inf 81.1%

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

   4. Taylor expanded in z around 0 73.1%

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

      1. +-commutative 80.6%

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

      2. *-commutative 80.6%

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

      3. associate-*r/ 87.8%

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

      4. mul-1-neg 87.8%

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

      5. associate-/l* 83.8%

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

      6. distribute-lft-neg-in 83.8%

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

      7. distribute-rgt-in 99.8%

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

      8. sub-neg 99.8%

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

   6. Simplified 88.3%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 3600:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+66}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e+104)
   (* y (/ (- z x) t))
   (if (<= y 1.52e+66) (+ x (* z (/ y t))) (/ (- z x) (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e+104) {
		tmp = y * ((z - x) / t);
	} else if (y <= 1.52e+66) {
		tmp = x + (z * (y / t));
	} else {
		tmp = (z - 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 (y <= (-6d+104)) then
        tmp = y * ((z - x) / t)
    else if (y <= 1.52d+66) then
        tmp = x + (z * (y / t))
    else
        tmp = (z - 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 (y <= -6e+104) {
		tmp = y * ((z - x) / t);
	} else if (y <= 1.52e+66) {
		tmp = x + (z * (y / t));
	} else {
		tmp = (z - x) / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e+104:
		tmp = y * ((z - x) / t)
	elif y <= 1.52e+66:
		tmp = x + (z * (y / t))
	else:
		tmp = (z - x) / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6e+104)
		tmp = Float64(y * Float64(Float64(z - x) / t));
	elseif (y <= 1.52e+66)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(Float64(z - x) / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6e+104)
		tmp = y * ((z - x) / t);
	elseif (y <= 1.52e+66)
		tmp = x + (z * (y / t));
	else
		tmp = (z - x) / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6e+104], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e+66], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - x), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.99999999999999937e104

   1. Initial program 86.2%

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

   3. Taylor expanded in y around -inf 80.6%

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

      1. associate-/l* 91.8%

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

      2. *-commutative 91.8%

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

   5. Applied egg-rr 91.8%

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

   if -5.99999999999999937e104 < y < 1.52000000000000004e66

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 82.6%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

      1. clear-num 78.8%

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

      2. un-div-inv 78.7%

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

   7. Applied egg-rr 78.7%

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

      1. associate-/r/ 84.8%

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

   9. Applied egg-rr 84.8%

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

   if 1.52000000000000004e66 < y

   1. Initial program 80.6%

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

   3. Taylor expanded in y around -inf 78.9%

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

      1. associate-/l* 89.7%

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

      2. *-commutative 89.7%

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

   5. Applied egg-rr 89.7%

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

      1. associate-/r/ 92.6%

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

   7. Applied egg-rr 92.6%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+66}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+231}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 110000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e+231)
   (* z (/ y t))
   (if (<= z 110000000.0) (* x (- 1.0 (/ y t))) (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+231) {
		tmp = z * (y / t);
	} else if (z <= 110000000.0) {
		tmp = x * (1.0 - (y / t));
	} 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) :: tmp
    if (z <= (-3.5d+231)) then
        tmp = z * (y / t)
    else if (z <= 110000000.0d0) then
        tmp = x * (1.0d0 - (y / t))
    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 tmp;
	if (z <= -3.5e+231) {
		tmp = z * (y / t);
	} else if (z <= 110000000.0) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e+231:
		tmp = z * (y / t)
	elif z <= 110000000.0:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e+231)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 110000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e+231)
		tmp = z * (y / t);
	elseif (z <= 110000000.0)
		tmp = x * (1.0 - (y / t));
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e+231], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 110000000.0], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999999e231

   1. Initial program 85.6%

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

   3. Taylor expanded in y around -inf 78.2%

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

   4. Taylor expanded in z around inf 78.2%

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

      1. associate-/l* 78.6%

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

   6. Simplified 71.2%

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

      1. clear-num 78.7%

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

      2. un-div-inv 78.7%

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

   8. Applied egg-rr 71.3%

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

      1. associate-/r/ 99.8%

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

   10. Applied egg-rr 92.4%

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

   if -3.4999999999999999e231 < z < 1.1e8

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

   5. Simplified 80.7%

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

   if 1.1e8 < z

   1. Initial program 88.1%

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

   3. Taylor expanded in y around -inf 72.7%

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

   4. Taylor expanded in z around inf 61.7%

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

      1. associate-/l* 78.6%

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

   6. Simplified 62.1%

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

      1. clear-num 78.6%

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

      2. un-div-inv 79.5%

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

   8. Applied egg-rr 63.0%

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

      1. associate-/r/ 87.4%

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

   10. Applied egg-rr 70.7%

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

       1. *-commutative 70.7%

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

       2. clear-num 70.8%

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

       3. un-div-inv 70.7%

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

   12. Applied egg-rr 70.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+231}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 110000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+63} \lor \neg \left(z \leq 2.45 \cdot 10^{-39}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e+63) (not (<= z 2.45e-39))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+63) || !(z <= 2.45e-39)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4d+63)) .or. (.not. (z <= 2.45d-39))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+63) || !(z <= 2.45e-39)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4e+63) or not (z <= 2.45e-39):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e+63) || !(z <= 2.45e-39))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e+63) || ~((z <= 2.45e-39)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e+63], N[Not[LessEqual[z, 2.45e-39]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000023e63 or 2.44999999999999987e-39 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in y around -inf 69.4%

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

   4. Taylor expanded in z around inf 58.8%

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

      1. associate-/l* 80.9%

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

   6. Simplified 60.6%

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

      1. clear-num 80.9%

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

      2. un-div-inv 80.7%

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

   8. Applied egg-rr 60.4%

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

      1. associate-/r/ 88.4%

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

   10. Applied egg-rr 68.0%

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

   if -4.00000000000000023e63 < z < 2.44999999999999987e-39

   1. Initial program 90.8%

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

   3. Taylor expanded in y around 0 51.7%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+63} \lor \neg \left(z \leq 2.45 \cdot 10^{-39}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+74} \lor \neg \left(z \leq 0.07\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.2e+74) (not (<= z 0.07))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.2e+74) || !(z <= 0.07)) {
		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 <= (-1.2d+74)) .or. (.not. (z <= 0.07d0))) 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 <= -1.2e+74) || !(z <= 0.07)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.2e+74) or not (z <= 0.07):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.2e+74) || !(z <= 0.07))
		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 <= -1.2e+74) || ~((z <= 0.07)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.2e+74], N[Not[LessEqual[z, 0.07]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000004e74 or 0.070000000000000007 < z

   1. Initial program 88.3%

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

   3. Taylor expanded in y around -inf 69.3%

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

   4. Taylor expanded in z around inf 59.8%

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

      1. associate-/l* 81.4%

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

   6. Simplified 61.6%

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

   if -1.20000000000000004e74 < z < 0.070000000000000007

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 50.8%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+74} \lor \neg \left(z \leq 0.07\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 500:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+62) (* z (/ y t)) (if (<= z 500.0) x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+62) {
		tmp = z * (y / t);
	} else if (z <= 500.0) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-5.2d+62)) then
        tmp = z * (y / t)
    else if (z <= 500.0d0) then
        tmp = x
    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 tmp;
	if (z <= -5.2e+62) {
		tmp = z * (y / t);
	} else if (z <= 500.0) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+62:
		tmp = z * (y / t)
	elif z <= 500.0:
		tmp = x
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+62)
		tmp = Float64(z * Float64(y / t));
	elseif (z <= 500.0)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+62)
		tmp = z * (y / t);
	elseif (z <= 500.0)
		tmp = x;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+62], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 500.0], x, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.19999999999999968e62

   1. Initial program 89.2%

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

   3. Taylor expanded in y around -inf 65.0%

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

   4. Taylor expanded in z around inf 58.3%

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

      1. associate-/l* 86.8%

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

   6. Simplified 62.6%

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

      1. clear-num 86.8%

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

      2. un-div-inv 84.8%

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

   8. Applied egg-rr 60.6%

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

      1. associate-/r/ 93.1%

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

   10. Applied egg-rr 68.9%

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

   if -5.19999999999999968e62 < z < 500

   1. Initial program 91.1%

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

   3. Taylor expanded in y around 0 51.4%

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

   if 500 < z

   1. Initial program 88.1%

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

   3. Taylor expanded in y around -inf 72.7%

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

   4. Taylor expanded in z around inf 61.7%

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

      1. associate-/l* 78.6%

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

   6. Simplified 62.1%

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

      1. clear-num 78.6%

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

      2. un-div-inv 79.5%

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

   8. Applied egg-rr 63.0%

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

      1. associate-/r/ 87.4%

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

   10. Applied egg-rr 70.7%

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

       1. *-commutative 70.7%

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

       2. clear-num 70.8%

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

       3. un-div-inv 70.7%

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

   12. Applied egg-rr 70.7%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 500:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in z around 0 85.2%

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

   1. +-commutative 85.2%

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

   2. *-commutative 85.2%

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

   3. associate-*r/ 86.8%

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

   4. mul-1-neg 86.8%

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

   5. associate-/l* 88.8%

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

   6. distribute-lft-neg-in 88.8%

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

   7. distribute-rgt-in 98.7%

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

   8. sub-neg 98.7%

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

5. Simplified 98.7%

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

6. Final simplification 98.7%

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

Alternative 14: 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 89.9%

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

3. Taylor expanded in y around 0 37.8%

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

Developer target: 91.2% 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 2024107 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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