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

Percentage Accurate: 92.9% → 97.9%

Time: 7.6s

Alternatives: 10

Speedup: 1.0×

• 25.8% 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 93.2%

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

   1. associate-*l/ 96.2%

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

3. Simplified 96.2%

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

   1. *-commutative 96.2%

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

   2. clear-num 96.2%

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

   3. un-div-inv 96.3%

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

5. Applied egg-rr 96.3%

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

6. Final simplification 96.3%

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

Alternative 2: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-54} \lor \neg \left(z \leq 1.45 \cdot 10^{-82}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e-54) (not (<= z 1.45e-82)))
   (+ x (* z (/ y t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e-54) || !(z <= 1.45e-82)) {
		tmp = x + (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 <= (-1.25d-54)) .or. (.not. (z <= 1.45d-82))) then
        tmp = x + (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 <= -1.25e-54) || !(z <= 1.45e-82)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e-54) or not (z <= 1.45e-82):
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e-54) || !(z <= 1.45e-82))
		tmp = Float64(x + 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 <= -1.25e-54) || ~((z <= 1.45e-82)))
		tmp = x + (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, -1.25e-54], N[Not[LessEqual[z, 1.45e-82]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000004e-54 or 1.44999999999999989e-82 < z

   1. Initial program 91.6%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around inf 85.6%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   if -1.25000000000000004e-54 < z < 1.44999999999999989e-82

   1. Initial program 95.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 90.1%

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

      1. associate-*r/ 91.9%

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

      2. neg-mul-1 91.9%

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

      3. distribute-rgt-neg-in 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in x around 0 91.9%

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

      1. mul-1-neg 91.9%

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

      2. sub-neg 91.9%

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

   9. Simplified 91.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-54} \lor \neg \left(z \leq 1.45 \cdot 10^{-82}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]

Alternative 3: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-63} \lor \neg \left(z \leq 1.3 \cdot 10^{-83}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.2e-63) (not (<= z 1.3e-83)))
   (+ x (/ y (/ t z)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-63) || !(z <= 1.3e-83)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.2d-63)) .or. (.not. (z <= 1.3d-83))) then
        tmp = x + (y / (t / z))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-63) || !(z <= 1.3e-83)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.2e-63) or not (z <= 1.3e-83):
		tmp = x + (y / (t / z))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.2e-63) || !(z <= 1.3e-83))
		tmp = Float64(x + Float64(y / Float64(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 <= -9.2e-63) || ~((z <= 1.3e-83)))
		tmp = x + (y / (t / z));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.2e-63], N[Not[LessEqual[z, 1.3e-83]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2e-63 or 1.30000000000000004e-83 < z

   1. Initial program 91.6%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around inf 88.2%

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

   if -9.2e-63 < z < 1.30000000000000004e-83

   1. Initial program 95.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 90.1%

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

      1. associate-*r/ 91.9%

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

      2. neg-mul-1 91.9%

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

      3. distribute-rgt-neg-in 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in x around 0 91.9%

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

      1. mul-1-neg 91.9%

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

      2. sub-neg 91.9%

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

   9. Simplified 91.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-63} \lor \neg \left(z \leq 1.3 \cdot 10^{-83}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]

Alternative 4: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.5e-52)
   (+ x (/ y (/ t z)))
   (if (<= z 1.12e-82) (* x (- 1.0 (/ y t))) (+ x (/ (* z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.5e-52) {
		tmp = x + (y / (t / z));
	} else if (z <= 1.12e-82) {
		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 (z <= (-7.5d-52)) then
        tmp = x + (y / (t / z))
    else if (z <= 1.12d-82) 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 (z <= -7.5e-52) {
		tmp = x + (y / (t / z));
	} else if (z <= 1.12e-82) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.5e-52:
		tmp = x + (y / (t / z))
	elif z <= 1.12e-82:
		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 (z <= -7.5e-52)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 1.12e-82)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.5e-52)
		tmp = x + (y / (t / z));
	elseif (z <= 1.12e-82)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.5e-52], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e-82], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.50000000000000006e-52

   1. Initial program 87.8%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around inf 90.1%

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

   if -7.50000000000000006e-52 < z < 1.12e-82

   1. Initial program 95.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 90.1%

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

      1. associate-*r/ 91.9%

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

      2. neg-mul-1 91.9%

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

      3. distribute-rgt-neg-in 91.9%

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

   6. Simplified 91.9%

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

   7. Taylor expanded in x around 0 91.9%

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

      1. mul-1-neg 91.9%

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

      2. sub-neg 91.9%

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

   9. Simplified 91.9%

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

   if 1.12e-82 < z

   1. Initial program 95.0%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 87.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]

Alternative 5: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-84}:\\ \;\;\;\;x - y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.1e-57)
   (+ x (/ y (/ t z)))
   (if (<= z 9.5e-84) (- x (* y (/ x t))) (+ x (/ (* z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e-57) {
		tmp = x + (y / (t / z));
	} else if (z <= 9.5e-84) {
		tmp = x - (y * (x / 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 (z <= (-3.1d-57)) then
        tmp = x + (y / (t / z))
    else if (z <= 9.5d-84) then
        tmp = x - (y * (x / 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 (z <= -3.1e-57) {
		tmp = x + (y / (t / z));
	} else if (z <= 9.5e-84) {
		tmp = x - (y * (x / t));
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.1e-57:
		tmp = x + (y / (t / z))
	elif z <= 9.5e-84:
		tmp = x - (y * (x / t))
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.1e-57)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 9.5e-84)
		tmp = Float64(x - Float64(y * Float64(x / t)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.1e-57)
		tmp = x + (y / (t / z));
	elseif (z <= 9.5e-84)
		tmp = x - (y * (x / t));
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.1e-57], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-84], N[(x - N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999976e-57

   1. Initial program 87.8%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around inf 90.1%

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

   if -3.09999999999999976e-57 < z < 9.49999999999999941e-84

   1. Initial program 95.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 90.1%

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

      1. associate-*r/ 91.9%

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

      2. neg-mul-1 91.9%

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

      3. distribute-rgt-neg-in 91.9%

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

   6. Simplified 91.9%

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

      1. *-commutative 91.9%

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

      2. *-commutative 91.9%

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

      3. distribute-rgt-neg-out 91.9%

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

      4. clear-num 91.8%

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

      5. div-inv 91.9%

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

      6. unsub-neg 91.9%

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

      7. associate-/r/ 91.9%

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

   8. Applied egg-rr 91.9%

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

   if 9.49999999999999941e-84 < z

   1. Initial program 95.0%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 87.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-84}:\\ \;\;\;\;x - y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]

Alternative 6: 83.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e-52)
   (+ x (/ y (/ t z)))
   (if (<= z 1.35e-83) (- x (/ x (/ t y))) (+ x (/ (* z y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e-52) {
		tmp = x + (y / (t / z));
	} else if (z <= 1.35e-83) {
		tmp = x - (x / (t / y));
	} 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 (z <= (-2.8d-52)) then
        tmp = x + (y / (t / z))
    else if (z <= 1.35d-83) then
        tmp = x - (x / (t / y))
    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 (z <= -2.8e-52) {
		tmp = x + (y / (t / z));
	} else if (z <= 1.35e-83) {
		tmp = x - (x / (t / y));
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e-52:
		tmp = x + (y / (t / z))
	elif z <= 1.35e-83:
		tmp = x - (x / (t / y))
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e-52)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 1.35e-83)
		tmp = Float64(x - Float64(x / Float64(t / y)));
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e-52)
		tmp = x + (y / (t / z));
	elseif (z <= 1.35e-83)
		tmp = x - (x / (t / y));
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e-52], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-83], N[(x - N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999995e-52

   1. Initial program 87.8%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around inf 90.1%

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

   if -2.79999999999999995e-52 < z < 1.34999999999999996e-83

   1. Initial program 95.3%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 90.1%

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

      1. mul-1-neg 90.1%

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

      2. associate-/l* 91.9%

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

   6. Simplified 91.9%

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

   if 1.34999999999999996e-83 < z

   1. Initial program 95.0%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around inf 87.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]

Alternative 7: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+32} \lor \neg \left(y \leq 1650000000000\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+32) (not (<= y 1650000000000.0))) (* x (/ (- y) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+32) || !(y <= 1650000000000.0)) {
		tmp = x * (-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 <= (-7.5d+32)) .or. (.not. (y <= 1650000000000.0d0))) then
        tmp = x * (-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 <= -7.5e+32) || !(y <= 1650000000000.0)) {
		tmp = x * (-y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+32) or not (y <= 1650000000000.0):
		tmp = x * (-y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+32) || !(y <= 1650000000000.0))
		tmp = Float64(x * Float64(Float64(-y) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e+32) || ~((y <= 1650000000000.0)))
		tmp = x * (-y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+32], N[Not[LessEqual[y, 1650000000000.0]], $MachinePrecision]], N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999959e32 or 1.65e12 < y

   1. Initial program 87.1%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around 0 53.1%

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

      1. associate-*r/ 60.1%

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

      2. neg-mul-1 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

   6. Simplified 60.1%

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

      1. *-commutative 60.1%

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

      2. *-commutative 60.1%

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

      3. distribute-rgt-neg-out 60.1%

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

      4. clear-num 60.0%

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

      5. div-inv 60.1%

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

      6. unsub-neg 60.1%

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

      7. associate-/r/ 59.3%

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

   8. Applied egg-rr 59.3%

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

   9. Taylor expanded in x around 0 53.1%

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

       1. *-commutative 53.1%

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

       2. associate-/l* 59.2%

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

   11. Simplified 59.2%

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

   12. Taylor expanded in y around inf 48.8%

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

       1. mul-1-neg 48.8%

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

       2. associate-*r/ 51.3%

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

       3. distribute-rgt-neg-in 51.3%

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

       4. distribute-neg-frac 51.3%

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

   14. Simplified 51.3%

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

   if -7.49999999999999959e32 < y < 1.65e12

   1. Initial program 97.8%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around 0 69.6%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

      3. distribute-rgt-neg-in 71.0%

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

   6. Simplified 71.0%

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

   7. Taylor expanded in y around 0 56.8%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+32} \lor \neg \left(y \leq 1650000000000\right):\\ \;\;\;\;x \cdot \frac{-y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 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 93.2%

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

   1. associate-*l/ 96.2%

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

3. Simplified 96.2%

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

4. Final simplification 96.2%

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

Alternative 9: 66.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{y}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ y t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (y / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (y / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (y / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(y / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (y / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.2%

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

   1. associate-*l/ 96.2%

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

3. Simplified 96.2%

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

4. Taylor expanded in z around 0 62.5%

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

   1. associate-*r/ 66.2%

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

   2. neg-mul-1 66.2%

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

   3. distribute-rgt-neg-in 66.2%

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

6. Simplified 66.2%

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

7. Taylor expanded in x around 0 66.2%

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

   1. mul-1-neg 66.2%

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

   2. sub-neg 66.2%

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

9. Simplified 66.2%

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

10. Final simplification 66.2%

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

Alternative 10: 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 93.2%

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

   1. associate-*l/ 96.2%

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

3. Simplified 96.2%

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

4. Taylor expanded in z around 0 62.5%

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

   1. associate-*r/ 66.2%

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

   2. neg-mul-1 66.2%

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

   3. distribute-rgt-neg-in 66.2%

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

6. Simplified 66.2%

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

7. Taylor expanded in y around 0 37.2%

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

8. Final simplification 37.2%

   \[\leadsto x \]

Developer target: 91.1% 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 2023318 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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