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

Percentage Accurate: 93.6% → 96.9%

Time: 8.3s

Alternatives: 9

Speedup: 1.0×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 2: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+142} \lor \neg \left(z \leq 4 \cdot 10^{+160}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+142) (not (<= z 4e+160)))
   (* (/ y a) (- t z))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+142) || !(z <= 4e+160)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+142)) .or. (.not. (z <= 4d+160))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+142) || !(z <= 4e+160)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+142) or not (z <= 4e+160):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+142) || !(z <= 4e+160))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+142) || ~((z <= 4e+160)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+142], N[Not[LessEqual[z, 4e+160]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000001e142 or 4.00000000000000003e160 < z

   1. Initial program 89.1%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 72.2%

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

      1. associate-*r/ 68.9%

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

      2. *-commutative 68.9%

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

      3. associate-*r* 68.9%

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

      4. neg-mul-1 68.9%

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

      5. neg-sub0 68.9%

         \[\leadsto \color{blue}{\left(0 - \frac{z - t}{a}\right)} \cdot y \]

      6. div-sub 62.2%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \cdot y \]

      7. associate-+l- 62.2%

         \[\leadsto \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \cdot y \]

      8. neg-sub0 62.2%

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

      9. +-commutative 62.2%

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

      10. sub-neg 62.2%

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

      11. div-sub 68.9%

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

      12. *-rgt-identity 68.9%

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

      13. associate-*r/ 68.8%

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

      14. associate-*l* 81.2%

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

      15. associate-*l/ 81.3%

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

      16. associate-*r/ 81.3%

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

      17. *-lft-identity 81.3%

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

   6. Simplified 81.3%

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

   if -9.50000000000000001e142 < z < 4.00000000000000003e160

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. +-commutative 95.7%

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

      3. distribute-neg-frac 95.7%

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

      4. distribute-rgt-neg-in 95.7%

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

      5. associate-*r/ 95.0%

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

      6. distribute-frac-neg 95.0%

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

      7. fma-def 95.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -\frac{z - t}{a}, x\right)} \]

      8. distribute-frac-neg 95.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{-\left(z - t\right)}{a}}, x\right) \]

      9. sub-neg 95.0%

         \[\leadsto \mathsf{fma}\left(y, \frac{-\color{blue}{\left(z + \left(-t\right)\right)}}{a}, x\right) \]

      10. +-commutative 95.0%

          \[\leadsto \mathsf{fma}\left(y, \frac{-\color{blue}{\left(\left(-t\right) + z\right)}}{a}, x\right) \]

      11. distribute-neg-in 95.0%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\left(-\left(-t\right)\right) + \left(-z\right)}}{a}, x\right) \]

      12. unsub-neg 95.0%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\left(-\left(-t\right)\right) - z}}{a}, x\right) \]

      13. remove-double-neg 95.0%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{t} - z}{a}, x\right) \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - z}{a}, x\right)} \]

   4. Taylor expanded in z around 0 83.8%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+142} \lor \neg \left(z \leq 4 \cdot 10^{+160}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 3: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+86} \lor \neg \left(t \leq 1.06 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e+86) (not (<= t 1.06e+15)))
   (+ x (/ (* y t) a))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e+86) || !(t <= 1.06e+15)) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1d+86)) .or. (.not. (t <= 1.06d+15))) then
        tmp = x + ((y * t) / a)
    else
        tmp = x - (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e+86) || !(t <= 1.06e+15)) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1e+86) or not (t <= 1.06e+15):
		tmp = x + ((y * t) / a)
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1e+86) || !(t <= 1.06e+15))
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1e+86) || ~((t <= 1.06e+15)))
		tmp = x + ((y * t) / a);
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1e+86], N[Not[LessEqual[t, 1.06e+15]], $MachinePrecision]], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1e86 or 1.06e15 < t

   1. Initial program 93.5%

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

      1. sub-neg 93.5%

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

      2. +-commutative 93.5%

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

      3. distribute-neg-frac 93.5%

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

      4. distribute-rgt-neg-in 93.5%

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

      5. associate-*r/ 90.1%

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

      6. distribute-frac-neg 90.1%

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

      7. fma-def 90.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -\frac{z - t}{a}, x\right)} \]

      8. distribute-frac-neg 90.1%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{-\left(z - t\right)}{a}}, x\right) \]

      9. sub-neg 90.1%

         \[\leadsto \mathsf{fma}\left(y, \frac{-\color{blue}{\left(z + \left(-t\right)\right)}}{a}, x\right) \]

      10. +-commutative 90.1%

          \[\leadsto \mathsf{fma}\left(y, \frac{-\color{blue}{\left(\left(-t\right) + z\right)}}{a}, x\right) \]

      11. distribute-neg-in 90.1%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\left(-\left(-t\right)\right) + \left(-z\right)}}{a}, x\right) \]

      12. unsub-neg 90.1%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\left(-\left(-t\right)\right) - z}}{a}, x\right) \]

      13. remove-double-neg 90.1%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{t} - z}{a}, x\right) \]

   3. Simplified 90.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - z}{a}, x\right)} \]

   4. Taylor expanded in z around 0 86.0%

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

   if -1e86 < t < 1.06e15

   1. Initial program 94.6%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around inf 88.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+86} \lor \neg \left(t \leq 1.06 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 4: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+86} \lor \neg \left(t \leq 5.8 \cdot 10^{+45}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -7.5e+86) (not (<= t 5.8e+45)))
   (+ x (/ (* y t) a))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e+86) || !(t <= 5.8e+45)) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-7.5d+86)) .or. (.not. (t <= 5.8d+45))) then
        tmp = x + ((y * t) / a)
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -7.5e+86) || !(t <= 5.8e+45)) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -7.5e+86) or not (t <= 5.8e+45):
		tmp = x + ((y * t) / a)
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -7.5e+86) || !(t <= 5.8e+45))
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -7.5e+86) || ~((t <= 5.8e+45)))
		tmp = x + ((y * t) / a);
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -7.5e+86], N[Not[LessEqual[t, 5.8e+45]], $MachinePrecision]], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4999999999999997e86 or 5.7999999999999994e45 < t

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. +-commutative 93.2%

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

      3. distribute-neg-frac 93.2%

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

      4. distribute-rgt-neg-in 93.2%

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

      5. associate-*r/ 89.6%

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

      6. distribute-frac-neg 89.6%

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

      7. fma-def 89.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -\frac{z - t}{a}, x\right)} \]

      8. distribute-frac-neg 89.6%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{-\left(z - t\right)}{a}}, x\right) \]

      9. sub-neg 89.6%

         \[\leadsto \mathsf{fma}\left(y, \frac{-\color{blue}{\left(z + \left(-t\right)\right)}}{a}, x\right) \]

      10. +-commutative 89.6%

          \[\leadsto \mathsf{fma}\left(y, \frac{-\color{blue}{\left(\left(-t\right) + z\right)}}{a}, x\right) \]

      11. distribute-neg-in 89.6%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\left(-\left(-t\right)\right) + \left(-z\right)}}{a}, x\right) \]

      12. unsub-neg 89.6%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{\left(-\left(-t\right)\right) - z}}{a}, x\right) \]

      13. remove-double-neg 89.6%

          \[\leadsto \mathsf{fma}\left(y, \frac{\color{blue}{t} - z}{a}, x\right) \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - z}{a}, x\right)} \]

   4. Taylor expanded in z around 0 87.0%

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

   if -7.4999999999999997e86 < t < 5.7999999999999994e45

   1. Initial program 94.8%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around inf 87.7%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+86} \lor \neg \left(t \leq 5.8 \cdot 10^{+45}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 5: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.25e+20) x (if (<= a 3.2e+32) (* y (/ (- t z) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.25e+20) {
		tmp = x;
	} else if (a <= 3.2e+32) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.25d+20)) then
        tmp = x
    else if (a <= 3.2d+32) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.25e+20) {
		tmp = x;
	} else if (a <= 3.2e+32) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.25e+20:
		tmp = x
	elif a <= 3.2e+32:
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.25e+20)
		tmp = x;
	elseif (a <= 3.2e+32)
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.25e+20)
		tmp = x;
	elseif (a <= 3.2e+32)
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.25e+20], x, If[LessEqual[a, 3.2e+32], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.25e20 or 3.1999999999999999e32 < a

   1. Initial program 89.1%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 71.6%

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

   if -2.25e20 < a < 3.1999999999999999e32

   1. Initial program 98.5%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

      1. *-commutative 97.7%

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

      2. clear-num 97.7%

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

      3. un-div-inv 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in x around 0 82.7%

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

      1. associate-/l* 82.6%

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

      2. associate-*r/ 82.6%

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

      3. neg-mul-1 82.6%

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

      4. neg-sub0 82.6%

         \[\leadsto \frac{\color{blue}{0 - \left(z - t\right)}}{\frac{a}{y}} \]

      5. associate--r- 82.6%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right) + t}}{\frac{a}{y}} \]

      6. neg-sub0 82.6%

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

      7. +-commutative 82.6%

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

      8. sub-neg 82.6%

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

      9. associate-/r/ 74.3%

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

      10. div-sub 69.9%

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

      11. *-commutative 69.9%

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

      12. div-sub 74.3%

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

   8. Simplified 74.3%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+20) x (if (<= a 5.2e+32) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+20) {
		tmp = x;
	} else if (a <= 5.2e+32) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6d+20)) then
        tmp = x
    else if (a <= 5.2d+32) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+20) {
		tmp = x;
	} else if (a <= 5.2e+32) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+20:
		tmp = x
	elif a <= 5.2e+32:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+20)
		tmp = x;
	elseif (a <= 5.2e+32)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6e+20)
		tmp = x;
	elseif (a <= 5.2e+32)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+20], x, If[LessEqual[a, 5.2e+32], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6e20 or 5.2000000000000004e32 < a

   1. Initial program 89.1%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 71.6%

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

   if -6e20 < a < 5.2000000000000004e32

   1. Initial program 98.5%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around 0 82.7%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*r* 74.3%

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

      4. neg-mul-1 74.3%

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

      5. neg-sub0 74.3%

         \[\leadsto \color{blue}{\left(0 - \frac{z - t}{a}\right)} \cdot y \]

      6. div-sub 69.9%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \cdot y \]

      7. associate-+l- 69.9%

         \[\leadsto \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \cdot y \]

      8. neg-sub0 69.9%

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

      9. +-commutative 69.9%

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

      10. sub-neg 69.9%

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

      11. div-sub 74.3%

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

      12. *-rgt-identity 74.3%

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

      13. associate-*r/ 74.3%

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

      14. associate-*l* 82.5%

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

      15. associate-*l/ 82.6%

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

      16. associate-*r/ 82.6%

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

      17. *-lft-identity 82.6%

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

   6. Simplified 82.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.1 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-74}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.1e+18) x (if (<= a 1.08e-74) (* (/ y a) t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.1e+18) {
		tmp = x;
	} else if (a <= 1.08e-74) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.1d+18)) then
        tmp = x
    else if (a <= 1.08d-74) then
        tmp = (y / a) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.1e+18) {
		tmp = x;
	} else if (a <= 1.08e-74) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.1e+18:
		tmp = x
	elif a <= 1.08e-74:
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.1e+18)
		tmp = x;
	elseif (a <= 1.08e-74)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.1e+18)
		tmp = x;
	elseif (a <= 1.08e-74)
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.1e+18], x, If[LessEqual[a, 1.08e-74], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.1e18 or 1.0799999999999999e-74 < a

   1. Initial program 90.3%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 68.1%

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

   if -9.1e18 < a < 1.0799999999999999e-74

   1. Initial program 98.3%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around inf 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-*r/ 59.5%

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

   6. Simplified 59.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.1 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-74}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. associate-*r/ 93.2%

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

3. Simplified 93.2%

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

4. Final simplification 93.2%

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

Alternative 9: 38.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. associate-*l/ 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in x around inf 43.0%

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

5. Final simplification 43.0%

   \[\leadsto x \]

Developer target: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (- x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (- x (/ (* y (- z t)) a))
       (- x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x - (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x - (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x - (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x - (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x - Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x - Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x - (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x - (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x - N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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