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

Percentage Accurate: 92.4% → 97.8%

Time: 8.3s

Alternatives: 13

Speedup: 1.0×

• 25.4% 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: 92.4% 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: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

3. Taylor expanded in z around 0 91.7%

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

   1. +-commutative 91.7%

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

   2. *-commutative 91.7%

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

   3. associate-*r/ 92.3%

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

   4. mul-1-neg 92.3%

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

   5. associate-/l* 91.8%

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

   6. distribute-lft-neg-in 91.8%

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

   7. distribute-rgt-in 98.1%

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

   8. sub-neg 98.1%

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

5. Simplified 98.1%

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

6. Final simplification 98.1%

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

Alternative 2: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+156}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e+156) (* (/ y t) z) (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+156) {
		tmp = (y / t) * z;
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.5d+156)) then
        tmp = (y / t) * z
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+156) {
		tmp = (y / t) * z;
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e+156:
		tmp = (y / t) * z
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e+156)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.5e+156)
		tmp = (y / t) * z;
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e+156], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.49999999999999996e156

   1. Initial program 90.9%

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

   3. Taylor expanded in y around -inf 71.9%

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

   4. Taylor expanded in z around inf 71.5%

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

      1. add-log-exp 44.3%

         \[\leadsto \color{blue}{\log \left(e^{\frac{y \cdot z}{t}}\right)} \]

      2. *-un-lft-identity 44.3%

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

      3. log-prod 44.3%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{y \cdot z}{t}}\right)} \]

      4. metadata-eval 44.3%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{y \cdot z}{t}}\right) \]

      5. add-log-exp 71.5%

         \[\leadsto 0 + \color{blue}{\frac{y \cdot z}{t}} \]

      6. associate-/l* 65.3%

         \[\leadsto 0 + \color{blue}{y \cdot \frac{z}{t}} \]

   6. Applied egg-rr 65.3%

      \[\leadsto \color{blue}{0 + y \cdot \frac{z}{t}} \]
   7. Step-by-step derivation

      1. +-lft-identity 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-*l/ 71.5%

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

      4. associate-*r/ 77.5%

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

   8. Simplified 77.5%

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

   if -2.49999999999999996e156 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+156}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.45 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.45e+73) (* x (- 1.0 (/ y t))) (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.45e+73) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - 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 <= 1.45d+73) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.45e+73) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.45e+73:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.45e+73)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.45e+73)
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.45e+73], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.4500000000000001e73

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

   5. Simplified 71.5%

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

   if 1.4500000000000001e73 < z

   1. Initial program 96.2%

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

   3. Taylor expanded in y around -inf 78.3%

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

   4. Taylor expanded in z around 0 68.7%

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

      1. +-commutative 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*r/ 88.9%

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

      4. mul-1-neg 88.9%

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

      5. associate-/l* 87.0%

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

      6. distribute-lft-neg-in 87.0%

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

      7. distribute-rgt-in 98.5%

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

      8. sub-neg 98.5%

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

   6. Simplified 80.5%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.45 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e+119) (* (/ y t) (- z x)) (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+119) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d+119)) then
        tmp = (y / t) * (z - x)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+119) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e+119:
		tmp = (y / t) * (z - x)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e+119)
		tmp = Float64(Float64(y / t) * Float64(z - x));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e+119)
		tmp = (y / t) * (z - x);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e+119], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000014e119

   1. Initial program 94.6%

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

   3. Taylor expanded in y around -inf 92.6%

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

   4. Taylor expanded in z around 0 84.3%

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

      1. +-commutative 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*r/ 77.9%

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

      4. mul-1-neg 77.9%

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

      5. associate-/l* 80.4%

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

      6. distribute-lft-neg-in 80.4%

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

      7. distribute-rgt-in 89.4%

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

      8. sub-neg 89.4%

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

   6. Simplified 87.4%

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

   if -5.80000000000000014e119 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. associate-/l* 37.4%

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

   5. Simplified 76.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+119}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e+119) (* (/ y t) (- z x)) (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+119) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.5d+119)) then
        tmp = (y / t) * (z - x)
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+119) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e+119:
		tmp = (y / t) * (z - x)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e+119)
		tmp = Float64(Float64(y / t) * Float64(z - x));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e+119)
		tmp = (y / t) * (z - x);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+119], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999997e119

   1. Initial program 94.6%

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

   3. Taylor expanded in y around -inf 92.6%

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

   4. Taylor expanded in z around 0 84.3%

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

      1. +-commutative 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*r/ 77.9%

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

      4. mul-1-neg 77.9%

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

      5. associate-/l* 80.4%

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

      6. distribute-lft-neg-in 80.4%

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

      7. distribute-rgt-in 89.4%

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

      8. sub-neg 89.4%

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

   6. Simplified 87.4%

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

   if -6.4999999999999997e119 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf 78.1%

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

      1. associate-/l* 37.4%

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

   5. Simplified 76.0%

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

      1. clear-num 37.5%

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

      2. un-div-inv 37.5%

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

   7. Applied egg-rr 76.1%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+119}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 11500000:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 11500000.0) (+ x (* y (/ z t))) (/ (* y (- z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 11500000.0) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y * (z - x)) / 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 (y <= 11500000.0d0) then
        tmp = x + (y * (z / t))
    else
        tmp = (y * (z - x)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 11500000.0) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y * (z - x)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 11500000.0:
		tmp = x + (y * (z / t))
	else:
		tmp = (y * (z - x)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 11500000.0)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 11500000.0)
		tmp = x + (y * (z / t));
	else
		tmp = (y * (z - x)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 11500000.0], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.15e7

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 37.6%

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

   5. Simplified 77.9%

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

   if 1.15e7 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in y around -inf 81.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 11500000:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1.5e+95) (* (/ y t) z) (* x (/ (- y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.5e+95) {
		tmp = (y / t) * z;
	} else {
		tmp = x * (-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 (x <= 1.5d+95) then
        tmp = (y / t) * z
    else
        tmp = x * (-y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1.5e+95) {
		tmp = (y / t) * z;
	} else {
		tmp = x * (-y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1.5e+95:
		tmp = (y / t) * z
	else:
		tmp = x * (-y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1.5e+95)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = Float64(x * Float64(Float64(-y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 1.5e+95)
		tmp = (y / t) * z;
	else
		tmp = x * (-y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1.5e+95], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.49999999999999996e95

   1. Initial program 97.0%

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

   3. Taylor expanded in y around -inf 64.2%

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

   4. Taylor expanded in z around inf 46.9%

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

      1. add-log-exp 25.9%

         \[\leadsto \color{blue}{\log \left(e^{\frac{y \cdot z}{t}}\right)} \]

      2. *-un-lft-identity 25.9%

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

      3. log-prod 25.9%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{y \cdot z}{t}}\right)} \]

      4. metadata-eval 25.9%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{y \cdot z}{t}}\right) \]

      5. add-log-exp 46.9%

         \[\leadsto 0 + \color{blue}{\frac{y \cdot z}{t}} \]

      6. associate-/l* 44.8%

         \[\leadsto 0 + \color{blue}{y \cdot \frac{z}{t}} \]

   6. Applied egg-rr 44.8%

      \[\leadsto \color{blue}{0 + y \cdot \frac{z}{t}} \]
   7. Step-by-step derivation

      1. +-lft-identity 44.8%

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

      2. *-commutative 44.8%

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

      3. associate-*l/ 46.9%

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

      4. associate-*r/ 48.5%

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

   8. Simplified 48.5%

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

   if 1.49999999999999996e95 < x

   1. Initial program 92.8%

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

   3. Taylor expanded in y around -inf 54.2%

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

   4. Taylor expanded in z around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. associate-/l* 54.1%

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

      3. distribute-rgt-neg-in 54.1%

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

      4. mul-1-neg 54.1%

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

      5. associate-*r/ 54.1%

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

      6. mul-1-neg 54.1%

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

   6. Simplified 54.1%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 5.8e+94) (* (/ y t) z) (/ (* y (- x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5.8e+94) {
		tmp = (y / t) * z;
	} else {
		tmp = (y * -x) / 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 (x <= 5.8d+94) then
        tmp = (y / t) * z
    else
        tmp = (y * -x) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 5.8e+94) {
		tmp = (y / t) * z;
	} else {
		tmp = (y * -x) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 5.8e+94:
		tmp = (y / t) * z
	else:
		tmp = (y * -x) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 5.8e+94)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = Float64(Float64(y * Float64(-x)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 5.8e+94)
		tmp = (y / t) * z;
	else
		tmp = (y * -x) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 5.8e+94], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(y * (-x)), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.7999999999999997e94

   1. Initial program 97.0%

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

   3. Taylor expanded in y around -inf 64.2%

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

   4. Taylor expanded in z around inf 46.9%

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

      1. add-log-exp 25.9%

         \[\leadsto \color{blue}{\log \left(e^{\frac{y \cdot z}{t}}\right)} \]

      2. *-un-lft-identity 25.9%

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

      3. log-prod 25.9%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{y \cdot z}{t}}\right)} \]

      4. metadata-eval 25.9%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{y \cdot z}{t}}\right) \]

      5. add-log-exp 46.9%

         \[\leadsto 0 + \color{blue}{\frac{y \cdot z}{t}} \]

      6. associate-/l* 44.8%

         \[\leadsto 0 + \color{blue}{y \cdot \frac{z}{t}} \]

   6. Applied egg-rr 44.8%

      \[\leadsto \color{blue}{0 + y \cdot \frac{z}{t}} \]
   7. Step-by-step derivation

      1. +-lft-identity 44.8%

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

      2. *-commutative 44.8%

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

      3. associate-*l/ 46.9%

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

      4. associate-*r/ 48.5%

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

   8. Simplified 48.5%

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

   if 5.7999999999999997e94 < x

   1. Initial program 92.8%

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

   3. Taylor expanded in y around -inf 54.2%

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

   4. Taylor expanded in z around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. distribute-lft-neg-out 51.9%

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

      3. *-commutative 51.9%

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

   6. Simplified 51.9%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(-x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -2.7e-68) x (* y (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.7e-68) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.7d-68)) then
        tmp = x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.7e-68) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.7e-68:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.7e-68)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.7e-68)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.7e-68], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000002e-68

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 45.7%

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

   if -2.7000000000000002e-68 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in y around -inf 66.1%

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

   4. Taylor expanded in z around inf 49.3%

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

      1. associate-/l* 47.8%

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

   6. Simplified 47.8%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -7e-70) x (* (/ y t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-70) {
		tmp = x;
	} else {
		tmp = (y / t) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-7d-70)) then
        tmp = x
    else
        tmp = (y / t) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-70) {
		tmp = x;
	} else {
		tmp = (y / t) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7e-70:
		tmp = x
	else:
		tmp = (y / t) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7e-70)
		tmp = x;
	else
		tmp = Float64(Float64(y / t) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7e-70)
		tmp = x;
	else
		tmp = (y / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7e-70], x, N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.99999999999999949e-70

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 45.7%

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

   if -6.99999999999999949e-70 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in y around -inf 66.1%

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

   4. Taylor expanded in z around inf 49.3%

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

      1. add-log-exp 25.8%

         \[\leadsto \color{blue}{\log \left(e^{\frac{y \cdot z}{t}}\right)} \]

      2. *-un-lft-identity 25.8%

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

      3. log-prod 25.8%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{y \cdot z}{t}}\right)} \]

      4. metadata-eval 25.8%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{y \cdot z}{t}}\right) \]

      5. add-log-exp 49.3%

         \[\leadsto 0 + \color{blue}{\frac{y \cdot z}{t}} \]

      6. associate-/l* 47.8%

         \[\leadsto 0 + \color{blue}{y \cdot \frac{z}{t}} \]

   6. Applied egg-rr 47.8%

      \[\leadsto \color{blue}{0 + y \cdot \frac{z}{t}} \]
   7. Step-by-step derivation

      1. +-lft-identity 47.8%

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

      2. *-commutative 47.8%

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

      3. associate-*l/ 49.3%

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

      4. associate-*r/ 51.7%

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

   8. Simplified 51.7%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -3.3e-71) x (/ y (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3e-71) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.3d-71)) then
        tmp = x
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.3e-71) {
		tmp = x;
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.3e-71:
		tmp = x
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.3e-71)
		tmp = x;
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.3e-71)
		tmp = x;
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.3e-71], x, N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3000000000000002e-71

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 45.7%

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

   if -3.3000000000000002e-71 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in y around -inf 66.1%

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

   4. Taylor expanded in z around inf 49.3%

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

      1. associate-/l* 47.8%

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

   6. Simplified 47.8%

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

      1. clear-num 47.4%

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

      2. un-div-inv 47.4%

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

   8. Applied egg-rr 47.4%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -9.5e-69) x (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e-69) {
		tmp = x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-9.5d-69)) then
        tmp = x
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e-69) {
		tmp = x;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e-69:
		tmp = x
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.5e-69)
		tmp = x;
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.5e-69)
		tmp = x;
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e-69], x, N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000094e-69

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 45.7%

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

   if -9.50000000000000094e-69 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in y around -inf 66.1%

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

   4. Taylor expanded in z around inf 49.3%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 96.4%

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

3. Taylor expanded in y around 0 36.7%

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

4. Final simplification 36.7%

   \[\leadsto x \]
5. 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 2024066 
(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)))