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

Percentage Accurate: 92.9% → 97.9%

Time: 7.9s

Alternatives: 13

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: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{elif}\;z \leq 260:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= z -5.4e+63)
     t_1
     (if (<= z -1.65e-179)
       x
       (if (<= z -1.02e-296) (/ x (/ (- t) y)) (if (<= z 260.0) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (z <= -5.4e+63) {
		tmp = t_1;
	} else if (z <= -1.65e-179) {
		tmp = x;
	} else if (z <= -1.02e-296) {
		tmp = x / (-t / y);
	} else if (z <= 260.0) {
		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 * (y / t)
    if (z <= (-5.4d+63)) then
        tmp = t_1
    else if (z <= (-1.65d-179)) then
        tmp = x
    else if (z <= (-1.02d-296)) then
        tmp = x / (-t / y)
    else if (z <= 260.0d0) 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 * (y / t);
	double tmp;
	if (z <= -5.4e+63) {
		tmp = t_1;
	} else if (z <= -1.65e-179) {
		tmp = x;
	} else if (z <= -1.02e-296) {
		tmp = x / (-t / y);
	} else if (z <= 260.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	tmp = 0
	if z <= -5.4e+63:
		tmp = t_1
	elif z <= -1.65e-179:
		tmp = x
	elif z <= -1.02e-296:
		tmp = x / (-t / y)
	elif z <= 260.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (z <= -5.4e+63)
		tmp = t_1;
	elseif (z <= -1.65e-179)
		tmp = x;
	elseif (z <= -1.02e-296)
		tmp = Float64(x / Float64(Float64(-t) / y));
	elseif (z <= 260.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (z <= -5.4e+63)
		tmp = t_1;
	elseif (z <= -1.65e-179)
		tmp = x;
	elseif (z <= -1.02e-296)
		tmp = x / (-t / y);
	elseif (z <= 260.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+63], t$95$1, If[LessEqual[z, -1.65e-179], x, If[LessEqual[z, -1.02e-296], N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 260.0], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.40000000000000035e63 or 260 < 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 69.8%

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

   4. Taylor expanded in z around inf 60.4%

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

      1. associate-/l* 81.7%

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

   6. Simplified 62.3%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.5%

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

   8. Applied egg-rr 62.1%

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

      1. associate-/r/ 89.6%

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

   10. Applied egg-rr 70.0%

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

   if -5.40000000000000035e63 < z < -1.6499999999999999e-179 or -1.02000000000000002e-296 < z < 260

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 57.0%

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

   if -1.6499999999999999e-179 < z < -1.02000000000000002e-296

   1. Initial program 85.1%

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

   3. Taylor expanded in y around -inf 59.8%

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

   4. Taylor expanded in z around 0 53.3%

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

      1. mul-1-neg 78.6%

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

      2. associate-/l* 86.1%

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

      3. distribute-rgt-neg-in 86.1%

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

      4. mul-1-neg 86.1%

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

      5. associate-*r/ 86.1%

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

      6. mul-1-neg 86.1%

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

   6. Simplified 60.8%

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

      1. add-sqr-sqrt 37.0%

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

      2. sqrt-unprod 26.1%

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

      3. sqr-neg 26.1%

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

      4. sqrt-unprod 0.7%

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

      5. add-sqr-sqrt 1.8%

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

      6. clear-num 1.8%

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

      7. div-inv 1.8%

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

      8. frac-2neg 1.8%

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

      9. distribute-frac-neg2 1.8%

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

      10. add-sqr-sqrt 1.1%

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

      11. sqrt-unprod 13.9%

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

      12. sqr-neg 13.9%

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

      13. sqrt-unprod 23.8%

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

      14. add-sqr-sqrt 63.4%

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

   8. Applied egg-rr 63.4%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{elif}\;z \leq 260:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-180}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= z -3.7e+62)
     t_1
     (if (<= z -7e-180)
       x
       (if (<= z -1.1e-296) (* x (/ y (- t))) (if (<= z 2.2) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (z <= -3.7e+62) {
		tmp = t_1;
	} else if (z <= -7e-180) {
		tmp = x;
	} else if (z <= -1.1e-296) {
		tmp = x * (y / -t);
	} else if (z <= 2.2) {
		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 * (y / t)
    if (z <= (-3.7d+62)) then
        tmp = t_1
    else if (z <= (-7d-180)) then
        tmp = x
    else if (z <= (-1.1d-296)) then
        tmp = x * (y / -t)
    else if (z <= 2.2d0) 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 * (y / t);
	double tmp;
	if (z <= -3.7e+62) {
		tmp = t_1;
	} else if (z <= -7e-180) {
		tmp = x;
	} else if (z <= -1.1e-296) {
		tmp = x * (y / -t);
	} else if (z <= 2.2) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	tmp = 0
	if z <= -3.7e+62:
		tmp = t_1
	elif z <= -7e-180:
		tmp = x
	elif z <= -1.1e-296:
		tmp = x * (y / -t)
	elif z <= 2.2:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (z <= -3.7e+62)
		tmp = t_1;
	elseif (z <= -7e-180)
		tmp = x;
	elseif (z <= -1.1e-296)
		tmp = Float64(x * Float64(y / Float64(-t)));
	elseif (z <= 2.2)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (z <= -3.7e+62)
		tmp = t_1;
	elseif (z <= -7e-180)
		tmp = x;
	elseif (z <= -1.1e-296)
		tmp = x * (y / -t);
	elseif (z <= 2.2)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+62], t$95$1, If[LessEqual[z, -7e-180], x, If[LessEqual[z, -1.1e-296], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.70000000000000014e62 or 2.2000000000000002 < 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 69.8%

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

   4. Taylor expanded in z around inf 60.4%

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

      1. associate-/l* 81.7%

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

   6. Simplified 62.3%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.5%

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

   8. Applied egg-rr 62.1%

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

      1. associate-/r/ 89.6%

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

   10. Applied egg-rr 70.0%

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

   if -3.70000000000000014e62 < z < -7.0000000000000001e-180 or -1.10000000000000006e-296 < z < 2.2000000000000002

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 57.0%

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

   if -7.0000000000000001e-180 < z < -1.10000000000000006e-296

   1. Initial program 85.1%

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

   3. Taylor expanded in y around -inf 59.8%

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

   4. Taylor expanded in z around 0 53.3%

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

      1. mul-1-neg 78.6%

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

      2. associate-/l* 86.1%

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

      3. distribute-rgt-neg-in 86.1%

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

      4. mul-1-neg 86.1%

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

      5. associate-*r/ 86.1%

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

      6. mul-1-neg 86.1%

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

   6. Simplified 60.8%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-180}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 2.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))))
   (if (<= z -8.5e-6)
     t_1
     (if (<= z 0.5)
       (- x (* x (/ y t)))
       (if (<= z 5.5e+150) (/ (- z x) (/ t y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (z <= -8.5e-6) {
		tmp = t_1;
	} else if (z <= 0.5) {
		tmp = x - (x * (y / t));
	} else if (z <= 5.5e+150) {
		tmp = (z - x) / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / t))
    if (z <= (-8.5d-6)) then
        tmp = t_1
    else if (z <= 0.5d0) then
        tmp = x - (x * (y / t))
    else if (z <= 5.5d+150) then
        tmp = (z - x) / (t / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (z <= -8.5e-6) {
		tmp = t_1;
	} else if (z <= 0.5) {
		tmp = x - (x * (y / t));
	} else if (z <= 5.5e+150) {
		tmp = (z - x) / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (y / t))
	tmp = 0
	if z <= -8.5e-6:
		tmp = t_1
	elif z <= 0.5:
		tmp = x - (x * (y / t))
	elif z <= 5.5e+150:
		tmp = (z - x) / (t / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (z <= -8.5e-6)
		tmp = t_1;
	elseif (z <= 0.5)
		tmp = Float64(x - Float64(x * Float64(y / t)));
	elseif (z <= 5.5e+150)
		tmp = Float64(Float64(z - x) / Float64(t / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * (y / t));
	tmp = 0.0;
	if (z <= -8.5e-6)
		tmp = t_1;
	elseif (z <= 0.5)
		tmp = x - (x * (y / t));
	elseif (z <= 5.5e+150)
		tmp = (z - x) / (t / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e-6], t$95$1, If[LessEqual[z, 0.5], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+150], N[(N[(z - x), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999999e-6 or 5.50000000000000017e150 < z

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 85.1%

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

      1. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

      1. clear-num 87.1%

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

      2. un-div-inv 86.2%

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

   7. Applied egg-rr 86.2%

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

      1. associate-/r/ 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -8.4999999999999999e-6 < z < 0.5

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 82.1%

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

      1. mul-1-neg 82.1%

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

      2. associate-/l* 86.7%

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

      3. distribute-rgt-neg-in 86.7%

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

      4. mul-1-neg 86.7%

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

      5. associate-*r/ 86.7%

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

      6. mul-1-neg 86.7%

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

   5. Simplified 86.7%

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

   if 0.5 < z < 5.50000000000000017e150

   1. Initial program 89.1%

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

   3. Taylor expanded in y around -inf 81.1%

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

      1. associate-/l* 81.0%

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

      2. *-commutative 81.0%

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

   5. Applied egg-rr 81.0%

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

      1. associate-/r/ 89.0%

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

   7. Applied egg-rr 89.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-6}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -0.012:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))))
   (if (<= z -0.012)
     t_1
     (if (<= z 2600000.0)
       (* x (- 1.0 (/ y t)))
       (if (<= z 5.5e+150) (/ (- z x) (/ t y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (z <= -0.012) {
		tmp = t_1;
	} else if (z <= 2600000.0) {
		tmp = x * (1.0 - (y / t));
	} else if (z <= 5.5e+150) {
		tmp = (z - x) / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / t))
    if (z <= (-0.012d0)) then
        tmp = t_1
    else if (z <= 2600000.0d0) then
        tmp = x * (1.0d0 - (y / t))
    else if (z <= 5.5d+150) then
        tmp = (z - x) / (t / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (z <= -0.012) {
		tmp = t_1;
	} else if (z <= 2600000.0) {
		tmp = x * (1.0 - (y / t));
	} else if (z <= 5.5e+150) {
		tmp = (z - x) / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (y / t))
	tmp = 0
	if z <= -0.012:
		tmp = t_1
	elif z <= 2600000.0:
		tmp = x * (1.0 - (y / t))
	elif z <= 5.5e+150:
		tmp = (z - x) / (t / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (z <= -0.012)
		tmp = t_1;
	elseif (z <= 2600000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (z <= 5.5e+150)
		tmp = Float64(Float64(z - x) / Float64(t / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * (y / t));
	tmp = 0.0;
	if (z <= -0.012)
		tmp = t_1;
	elseif (z <= 2600000.0)
		tmp = x * (1.0 - (y / t));
	elseif (z <= 5.5e+150)
		tmp = (z - x) / (t / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.012], t$95$1, If[LessEqual[z, 2600000.0], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+150], N[(N[(z - x), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.012 or 5.50000000000000017e150 < z

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 85.1%

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

      1. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

      1. clear-num 87.1%

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

      2. un-div-inv 86.2%

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

   7. Applied egg-rr 86.2%

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

      1. associate-/r/ 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -0.012 < z < 2.6e6

   1. Initial program 92.5%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. mul-1-neg 86.7%

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

      2. unsub-neg 86.7%

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

   5. Simplified 86.7%

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

   if 2.6e6 < z < 5.50000000000000017e150

   1. Initial program 89.1%

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

   3. Taylor expanded in y around -inf 81.1%

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

      1. associate-/l* 81.0%

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

      2. *-commutative 81.0%

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

   5. Applied egg-rr 81.0%

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

      1. associate-/r/ 89.0%

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

   7. Applied egg-rr 89.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.012:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 52000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+150}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))))
   (if (<= z -3.6e-5)
     t_1
     (if (<= z 52000000.0)
       (* x (- 1.0 (/ y t)))
       (if (<= z 5.5e+150) (* (- z x) (/ y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (z <= -3.6e-5) {
		tmp = t_1;
	} else if (z <= 52000000.0) {
		tmp = x * (1.0 - (y / t));
	} else if (z <= 5.5e+150) {
		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 + (z * (y / t))
    if (z <= (-3.6d-5)) then
        tmp = t_1
    else if (z <= 52000000.0d0) then
        tmp = x * (1.0d0 - (y / t))
    else if (z <= 5.5d+150) 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 + (z * (y / t));
	double tmp;
	if (z <= -3.6e-5) {
		tmp = t_1;
	} else if (z <= 52000000.0) {
		tmp = x * (1.0 - (y / t));
	} else if (z <= 5.5e+150) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (y / t))
	tmp = 0
	if z <= -3.6e-5:
		tmp = t_1
	elif z <= 52000000.0:
		tmp = x * (1.0 - (y / t))
	elif z <= 5.5e+150:
		tmp = (z - x) * (y / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (z <= -3.6e-5)
		tmp = t_1;
	elseif (z <= 52000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (z <= 5.5e+150)
		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 + (z * (y / t));
	tmp = 0.0;
	if (z <= -3.6e-5)
		tmp = t_1;
	elseif (z <= 52000000.0)
		tmp = x * (1.0 - (y / t));
	elseif (z <= 5.5e+150)
		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[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e-5], t$95$1, If[LessEqual[z, 52000000.0], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+150], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.60000000000000009e-5 or 5.50000000000000017e150 < z

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf 85.1%

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

      1. associate-/l* 87.1%

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

   5. Simplified 87.1%

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

      1. clear-num 87.1%

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

      2. un-div-inv 86.2%

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

   7. Applied egg-rr 86.2%

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

      1. associate-/r/ 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -3.60000000000000009e-5 < z < 5.2e7

   1. Initial program 92.5%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. mul-1-neg 86.7%

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

      2. unsub-neg 86.7%

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

   5. Simplified 86.7%

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

   if 5.2e7 < z < 5.50000000000000017e150

   1. Initial program 89.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   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 75.2%

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

      1. +-commutative 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*r/ 88.5%

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

      4. mul-1-neg 88.5%

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

      5. associate-/l* 85.4%

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

      6. distribute-lft-neg-in 85.4%

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

      7. distribute-rgt-in 99.7%

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

      8. sub-neg 99.7%

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

   6. Simplified 88.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 52000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+150}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+159}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= z -6.4e+40)
     t_1
     (if (<= z 0.5)
       (* x (- 1.0 (/ y t)))
       (if (<= z 9e+159) (* (- 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 <= -6.4e+40) {
		tmp = t_1;
	} else if (z <= 0.5) {
		tmp = x * (1.0 - (y / t));
	} else if (z <= 9e+159) {
		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 <= (-6.4d+40)) then
        tmp = t_1
    else if (z <= 0.5d0) then
        tmp = x * (1.0d0 - (y / t))
    else if (z <= 9d+159) 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 <= -6.4e+40) {
		tmp = t_1;
	} else if (z <= 0.5) {
		tmp = x * (1.0 - (y / t));
	} else if (z <= 9e+159) {
		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 <= -6.4e+40:
		tmp = t_1
	elif z <= 0.5:
		tmp = x * (1.0 - (y / t))
	elif z <= 9e+159:
		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 <= -6.4e+40)
		tmp = t_1;
	elseif (z <= 0.5)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (z <= 9e+159)
		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 <= -6.4e+40)
		tmp = t_1;
	elseif (z <= 0.5)
		tmp = x * (1.0 - (y / t));
	elseif (z <= 9e+159)
		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, -6.4e+40], t$95$1, If[LessEqual[z, 0.5], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+159], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.39999999999999961e40 or 9.00000000000000053e159 < z

   1. Initial program 88.7%

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

   3. Taylor expanded in z around inf 85.6%

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

      1. associate-/l* 87.9%

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

   5. Simplified 87.9%

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

   if -6.39999999999999961e40 < z < 0.5

   1. Initial program 91.5%

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

   3. Taylor expanded in x around inf 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

   5. Simplified 86.8%

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

   if 0.5 < z < 9.00000000000000053e159

   1. Initial program 87.1%

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

   3. Taylor expanded in y around -inf 79.5%

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

   4. Taylor expanded in z around 0 73.9%

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

      1. +-commutative 81.5%

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

      2. *-commutative 81.5%

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

      3. associate-*r/ 89.1%

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

      4. mul-1-neg 89.1%

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

      5. associate-/l* 86.2%

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

      6. distribute-lft-neg-in 86.2%

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

      7. distribute-rgt-in 99.7%

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

      8. sub-neg 99.7%

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

   6. Simplified 89.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+40}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+159}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+60} \lor \neg \left(z \leq 0.8\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.8e+60) (not (<= z 0.8)))
   (* (- z x) (/ y t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.8e+60) || !(z <= 0.8)) {
		tmp = (z - x) * (y / 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 <= (-9.8d+60)) .or. (.not. (z <= 0.8d0))) then
        tmp = (z - x) * (y / 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 <= -9.8e+60) || !(z <= 0.8)) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.8e+60) or not (z <= 0.8):
		tmp = (z - x) * (y / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.8e+60) || !(z <= 0.8))
		tmp = Float64(Float64(z - x) * Float64(y / 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 <= -9.8e+60) || ~((z <= 0.8)))
		tmp = (z - x) * (y / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.8e+60], N[Not[LessEqual[z, 0.8]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8000000000000005e60 or 0.80000000000000004 < 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 69.8%

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

   4. Taylor expanded in z around 0 61.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{t} + \frac{y \cdot z}{t}} \]
   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/ 89.4%

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

      4. mul-1-neg 89.4%

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

      5. associate-/l* 86.7%

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

      6. distribute-lft-neg-in 86.7%

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

      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 80.2%

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

   if -9.8000000000000005e60 < z < 0.80000000000000004

   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%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+60} \lor \neg \left(z \leq 0.8\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+184} \lor \neg \left(z \leq 4.2 \cdot 10^{+40}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e+184) (not (<= z 4.2e+40)))
   (* z (/ y t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+184) || !(z <= 4.2e+40)) {
		tmp = z * (y / 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 <= (-1.4d+184)) .or. (.not. (z <= 4.2d+40))) then
        tmp = z * (y / 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 <= -1.4e+184) || !(z <= 4.2e+40)) {
		tmp = z * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e+184) or not (z <= 4.2e+40):
		tmp = z * (y / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e+184) || !(z <= 4.2e+40))
		tmp = Float64(z * Float64(y / 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 <= -1.4e+184) || ~((z <= 4.2e+40)))
		tmp = z * (y / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e+184], N[Not[LessEqual[z, 4.2e+40]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999995e184 or 4.2000000000000002e40 < z

   1. Initial program 86.9%

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

   3. Taylor expanded in y around -inf 69.7%

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

   4. Taylor expanded in z around inf 63.8%

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

      1. associate-/l* 82.3%

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

   6. Simplified 64.2%

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

      1. clear-num 82.3%

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

      2. un-div-inv 82.3%

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

   8. Applied egg-rr 64.2%

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

      1. associate-/r/ 92.7%

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

   10. Applied egg-rr 74.4%

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

   if -1.39999999999999995e184 < z < 4.2000000000000002e40

   1. Initial program 91.5%

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

   3. Taylor expanded in x around inf 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+184} \lor \neg \left(z \leq 4.2 \cdot 10^{+40}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+66} \lor \neg \left(z \leq 0.082\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.5e+66) (not (<= z 0.082))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.5e+66) || !(z <= 0.082)) {
		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 <= (-4.5d+66)) .or. (.not. (z <= 0.082d0))) 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 <= -4.5e+66) || !(z <= 0.082)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.5e+66) or not (z <= 0.082):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.5e+66) || !(z <= 0.082))
		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 <= -4.5e+66) || ~((z <= 0.082)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.5e+66], N[Not[LessEqual[z, 0.082]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e66 or 0.0820000000000000034 < 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 69.8%

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

   4. Taylor expanded in z around inf 60.4%

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

      1. associate-/l* 81.7%

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

   6. Simplified 62.3%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.5%

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

   8. Applied egg-rr 62.1%

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

      1. associate-/r/ 89.6%

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

   10. Applied egg-rr 70.0%

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

   if -4.4999999999999998e66 < z < 0.0820000000000000034

   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%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+66} \lor \neg \left(z \leq 0.082\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+62} \lor \neg \left(z \leq 14000\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+62) (not (<= z 14000.0))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+62) || !(z <= 14000.0)) {
		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 <= (-6.2d+62)) .or. (.not. (z <= 14000.0d0))) 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 <= -6.2e+62) || !(z <= 14000.0)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+62) or not (z <= 14000.0):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+62) || !(z <= 14000.0))
		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 <= -6.2e+62) || ~((z <= 14000.0)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+62], N[Not[LessEqual[z, 14000.0]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000029e62 or 14000 < 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 69.8%

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

   4. Taylor expanded in z around inf 60.4%

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

      1. associate-/l* 81.7%

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

   6. Simplified 62.3%

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

   if -6.20000000000000029e62 < z < 14000

   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%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+62} \lor \neg \left(z \leq 14000\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 13: 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)))