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

Percentage Accurate: 92.7% → 98.0%

Time: 9.4s

Alternatives: 11

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% 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 95.1%

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

3. Taylor expanded in z around 0 91.6%

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

   1. +-commutative 91.6%

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

   2. *-commutative 91.6%

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

   3. associate-*r/ 91.1%

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

   4. mul-1-neg 91.1%

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

   5. associate-/l* 92.5%

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

   6. distribute-lft-neg-in 92.5%

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

   7. distribute-rgt-in 97.3%

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

   8. sub-neg 97.3%

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

5. Simplified 97.3%

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

6. Taylor expanded in y around 0 95.1%

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

   1. associate-*r/ 93.2%

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

   2. *-commutative 93.2%

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

   3. associate-/r/ 97.4%

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

8. Simplified 97.4%

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

Alternative 2: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+136} \lor \neg \left(x \leq 4.1 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.8e+136) (not (<= x 4.1e-22)))
   (* x (- 1.0 (/ y t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+136) || !(x <= 4.1e-22)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (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 <= (-3.8d+136)) .or. (.not. (x <= 4.1d-22))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (z * (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 <= -3.8e+136) || !(x <= 4.1e-22)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.8e+136) or not (x <= 4.1e-22):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.8e+136) || !(x <= 4.1e-22))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.8e+136) || ~((x <= 4.1e-22)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.8e+136], N[Not[LessEqual[x, 4.1e-22]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000015e136 or 4.0999999999999999e-22 < x

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 92.8%

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

      1. mul-1-neg 92.8%

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

      2. unsub-neg 92.8%

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

   5. Simplified 92.8%

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

   if -3.80000000000000015e136 < x < 4.0999999999999999e-22

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 92.7%

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

      1. +-commutative 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-*r/ 93.1%

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

      4. mul-1-neg 93.1%

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

      5. associate-/l* 93.1%

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

      6. distribute-lft-neg-in 93.1%

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

      7. distribute-rgt-in 95.7%

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

      8. sub-neg 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in z around inf 85.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+136} \lor \neg \left(x \leq 4.1 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+21} \lor \neg \left(x \leq 3.55 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.6e+21) (not (<= x 3.55e-22)))
   (* x (- 1.0 (/ y t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.6e+21) || !(x <= 3.55e-22)) {
		tmp = x * (1.0 - (y / t));
	} 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 ((x <= (-2.6d+21)) .or. (.not. (x <= 3.55d-22))) then
        tmp = x * (1.0d0 - (y / t))
    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 ((x <= -2.6e+21) || !(x <= 3.55e-22)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.6e+21) or not (x <= 3.55e-22):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.6e+21) || !(x <= 3.55e-22))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	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 ((x <= -2.6e+21) || ~((x <= 3.55e-22)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.6e+21], N[Not[LessEqual[x, 3.55e-22]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e21 or 3.5499999999999999e-22 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

   if -2.6e21 < x < 3.5499999999999999e-22

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 82.1%

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

      1. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+21} \lor \neg \left(x \leq 3.55 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-194} \lor \neg \left(x \leq 2.9 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.4e-194) (not (<= x 2.9e-83)))
   (* x (- 1.0 (/ y t)))
   (* z (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e-194) || !(x <= 2.9e-83)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z * (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 <= (-4.4d-194)) .or. (.not. (x <= 2.9d-83))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = z * (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 <= -4.4e-194) || !(x <= 2.9e-83)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.4e-194) or not (x <= 2.9e-83):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.4e-194) || !(x <= 2.9e-83))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.4e-194) || ~((x <= 2.9e-83)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.4e-194], N[Not[LessEqual[x, 2.9e-83]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4000000000000003e-194 or 2.8999999999999999e-83 < x

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. unsub-neg 77.9%

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

   5. Simplified 77.9%

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

   if -4.4000000000000003e-194 < x < 2.8999999999999999e-83

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0 95.1%

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

   4. Taylor expanded in x around 0 65.9%

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

      1. associate-*l/ 69.3%

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

   6. Applied egg-rr 69.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-194} \lor \neg \left(x \leq 2.9 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-106}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e-106)
   (+ x (* z (/ y t)))
   (if (<= t 2.6e-67) (/ (* (- z x) y) t) (+ x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e-106) {
		tmp = x + (z * (y / t));
	} else if (t <= 2.6e-67) {
		tmp = ((z - x) * y) / t;
	} 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 (t <= (-3.7d-106)) then
        tmp = x + (z * (y / t))
    else if (t <= 2.6d-67) then
        tmp = ((z - x) * y) / t
    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 (t <= -3.7e-106) {
		tmp = x + (z * (y / t));
	} else if (t <= 2.6e-67) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.7e-106:
		tmp = x + (z * (y / t))
	elif t <= 2.6e-67:
		tmp = ((z - x) * y) / t
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.7e-106)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (t <= 2.6e-67)
		tmp = Float64(Float64(Float64(z - x) * y) / t);
	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 (t <= -3.7e-106)
		tmp = x + (z * (y / t));
	elseif (t <= 2.6e-67)
		tmp = ((z - x) * y) / t;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.7e-106], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-67], N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999979e-106

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0 92.8%

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

      1. +-commutative 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*r/ 97.7%

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

      4. mul-1-neg 97.7%

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

      5. associate-/l* 98.7%

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

      6. distribute-lft-neg-in 98.7%

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

      7. distribute-rgt-in 99.8%

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

      8. sub-neg 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 84.6%

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

   if -3.69999999999999979e-106 < t < 2.5999999999999999e-67

   1. Initial program 98.8%

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

   3. Taylor expanded in y around -inf 93.6%

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

   if 2.5999999999999999e-67 < t

   1. Initial program 90.8%

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

   3. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 87.7%

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

   5. Simplified 87.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-106}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-107} \lor \neg \left(y \leq 9.4 \cdot 10^{+27}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-107) (not (<= y 9.4e+27))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-107) || !(y <= 9.4e+27)) {
		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 ((y <= (-5.2d-107)) .or. (.not. (y <= 9.4d+27))) 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 ((y <= -5.2e-107) || !(y <= 9.4e+27)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e-107) or not (y <= 9.4e+27):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e-107) || !(y <= 9.4e+27))
		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 ((y <= -5.2e-107) || ~((y <= 9.4e+27)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e-107], N[Not[LessEqual[y, 9.4e+27]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000001e-107 or 9.39999999999999952e27 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in t around 0 90.7%

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

   4. Taylor expanded in x around 0 50.2%

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

      1. associate-*l/ 55.8%

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

   6. Applied egg-rr 55.8%

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

   if -5.2000000000000001e-107 < y < 9.39999999999999952e27

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 66.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-107} \lor \neg \left(y \leq 9.4 \cdot 10^{+27}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-106} \lor \neg \left(y \leq 1.95 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e-106) (not (<= y 1.95e+28))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-106) || !(y <= 1.95e+28)) {
		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 ((y <= (-1.02d-106)) .or. (.not. (y <= 1.95d+28))) 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 ((y <= -1.02e-106) || !(y <= 1.95e+28)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e-106) or not (y <= 1.95e+28):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e-106) || !(y <= 1.95e+28))
		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 ((y <= -1.02e-106) || ~((y <= 1.95e+28)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e-106], N[Not[LessEqual[y, 1.95e+28]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e-106 or 1.9499999999999999e28 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in y around -inf 81.4%

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

   4. Taylor expanded in z around inf 50.2%

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

      1. associate-/l* 65.1%

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

   6. Simplified 52.4%

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

   if -1.02e-106 < y < 1.9499999999999999e28

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 66.1%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-106} \lor \neg \left(y \leq 1.95 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e-106) (* z (/ y t)) (if (<= y 1.32e+28) x (/ z (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e-106) {
		tmp = z * (y / t);
	} else if (y <= 1.32e+28) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.02d-106)) then
        tmp = z * (y / t)
    else if (y <= 1.32d+28) then
        tmp = x
    else
        tmp = z / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e-106) {
		tmp = z * (y / t);
	} else if (y <= 1.32e+28) {
		tmp = x;
	} else {
		tmp = z / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e-106:
		tmp = z * (y / t)
	elif y <= 1.32e+28:
		tmp = x
	else:
		tmp = z / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e-106)
		tmp = Float64(z * Float64(y / t));
	elseif (y <= 1.32e+28)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.02e-106)
		tmp = z * (y / t);
	elseif (y <= 1.32e+28)
		tmp = x;
	else
		tmp = z / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e-106], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e+28], x, N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02e-106

   1. Initial program 90.9%

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

   3. Taylor expanded in t around 0 89.6%

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

   4. Taylor expanded in x around 0 47.4%

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

      1. associate-*l/ 52.6%

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

   6. Applied egg-rr 52.6%

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

   if -1.02e-106 < y < 1.3199999999999999e28

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 66.1%

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

   if 1.3199999999999999e28 < y

   1. Initial program 92.1%

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

   3. Taylor expanded in t around 0 92.1%

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

   4. Taylor expanded in x around 0 53.6%

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

      1. associate-*l/ 59.5%

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

   6. Applied egg-rr 59.5%

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

      1. *-commutative 59.5%

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

      2. clear-num 59.5%

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

      3. div-inv 59.9%

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

   8. Applied egg-rr 59.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-106}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+189}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x 4.1e+189) x (* t (/ x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 4.1e+189) {
		tmp = x;
	} else {
		tmp = t * (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 <= 4.1d+189) then
        tmp = x
    else
        tmp = t * (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 <= 4.1e+189) {
		tmp = x;
	} else {
		tmp = t * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 4.1e+189:
		tmp = x
	else:
		tmp = t * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 4.1e+189)
		tmp = x;
	else
		tmp = Float64(t * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 4.1e+189)
		tmp = x;
	else
		tmp = t * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 4.1e+189], x, N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.1000000000000002e189

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 38.8%

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

   if 4.1000000000000002e189 < x

   1. Initial program 96.4%

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

   3. Taylor expanded in t around 0 86.3%

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

   4. Taylor expanded in t around inf 25.3%

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

      1. *-commutative 25.3%

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

   6. Simplified 25.3%

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

      1. *-commutative 25.3%

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

      2. associate-/l* 51.8%

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

   8. Applied egg-rr 51.8%

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

Alternative 10: 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 95.1%

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

3. Taylor expanded in z around 0 91.6%

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

   1. +-commutative 91.6%

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

   2. *-commutative 91.6%

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

   3. associate-*r/ 91.1%

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

   4. mul-1-neg 91.1%

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

   5. associate-/l* 92.5%

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

   6. distribute-lft-neg-in 92.5%

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

   7. distribute-rgt-in 97.3%

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

   8. sub-neg 97.3%

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

5. Simplified 97.3%

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

6. Final simplification 97.3%

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

Alternative 11: 38.9% 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 95.1%

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

3. Taylor expanded in y around 0 38.4%

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

Developer Target 1: 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 2024186 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (+ (* x (/ y t)) (* (- z) (/ y t)))))

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