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

Percentage Accurate: 93.3% → 97.1%

Time: 11.6s

Alternatives: 17

Speedup: 1.0×

• 24.5% 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: 93.3% 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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((t - z) / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

5. Taylor expanded in y around 0 95.0%

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

   1. associate-*l/ 97.1%

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

   2. *-commutative 97.1%

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

7. Simplified 97.1%

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

   1. clear-num 97.0%

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

   2. un-div-inv 97.5%

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

9. Applied egg-rr 97.5%

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

10. Final simplification 97.5%

    \[\leadsto x + \frac{t - z}{\frac{a}{y}} \]
11. Add Preprocessing

Alternative 2: 61.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.2e+108) x (* y (/ (- t z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.2e+108) {
		tmp = x;
	} else {
		tmp = y * ((t - 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 (x <= (-8.2d+108)) then
        tmp = x
    else
        tmp = y * ((t - 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 (x <= -8.2e+108) {
		tmp = x;
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.2e+108:
		tmp = x
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.2e+108)
		tmp = x;
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -8.2e+108)
		tmp = x;
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.2e+108], x, N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999998e108

   1. Initial program 97.2%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in x around inf 70.0%

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

   if -8.1999999999999998e108 < x

   1. Initial program 94.7%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around 0 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-frac-neg2 59.9%

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

      3. sub-neg 59.9%

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

      4. +-commutative 59.9%

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

      5. neg-sub0 59.9%

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

      6. associate--r- 59.9%

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

      7. neg-sub0 59.9%

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

      8. associate-*r/ 60.8%

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

      9. distribute-neg-frac 60.8%

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

      10. distribute-neg-frac2 60.8%

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

      11. remove-double-neg 60.8%

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

   7. Simplified 60.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.4e+106) x (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e+106) {
		tmp = x;
	} else {
		tmp = (y / a) * (t - 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 (a <= (-6.4d+106)) then
        tmp = x
    else
        tmp = (y / a) * (t - 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 (a <= -6.4e+106) {
		tmp = x;
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.4e+106:
		tmp = x
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.4e+106)
		tmp = x;
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.4e+106)
		tmp = x;
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.4e+106], x, N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.3999999999999996e106

   1. Initial program 83.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 64.8%

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

   if -6.3999999999999996e106 < a

   1. Initial program 97.6%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around 0 97.6%

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

      1. associate-*l/ 98.1%

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

      2. *-commutative 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in x around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r/ 62.7%

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

      4. *-commutative 62.7%

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

      5. distribute-rgt-neg-in 62.7%

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

      6. neg-sub0 62.7%

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

      7. associate--r- 62.7%

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

      8. neg-sub0 62.7%

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

      9. +-commutative 62.7%

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

      10. sub-neg 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.22:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.22) (* y (/ (- t z) a)) (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.22) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((t * y) / 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 (y <= (-0.22d0)) then
        tmp = y * ((t - z) / a)
    else
        tmp = x + ((t * y) / 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 (y <= -0.22) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.22:
		tmp = y * ((t - z) / a)
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.22)
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.22)
		tmp = y * ((t - z) / a);
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.22], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.220000000000000001

   1. Initial program 87.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. distribute-frac-neg2 68.1%

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

      3. sub-neg 68.1%

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

      4. +-commutative 68.1%

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

      5. neg-sub0 68.1%

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

      6. associate--r- 68.1%

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

      7. neg-sub0 68.1%

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

      8. associate-*r/ 80.2%

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

      9. distribute-neg-frac 80.2%

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

      10. distribute-neg-frac2 80.2%

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

      11. remove-double-neg 80.2%

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

   7. Simplified 80.2%

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

   if -0.220000000000000001 < y

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. distribute-frac-neg2 97.0%

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

      3. +-commutative 97.0%

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

      4. associate-/l* 92.4%

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

      5. fma-define 92.4%

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

      6. distribute-frac-neg2 92.4%

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

      7. distribute-neg-frac 92.4%

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

      8. sub-neg 92.4%

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

      9. distribute-neg-in 92.4%

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

      10. remove-double-neg 92.4%

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

      11. +-commutative 92.4%

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

      12. sub-neg 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 75.6%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.22:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e-80) (+ x (/ (* t y) a)) (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e-80) {
		tmp = x + ((t * y) / 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 <= (-2.2d-80)) then
        tmp = x + ((t * y) / 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 <= -2.2e-80) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.2e-80:
		tmp = x + ((t * y) / a)
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e-80)
		tmp = Float64(x + Float64(Float64(t * y) / 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 <= -2.2e-80)
		tmp = x + ((t * y) / a);
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e-80], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2000000000000001e-80

   1. Initial program 96.7%

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

      1. sub-neg 96.7%

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

      2. distribute-frac-neg2 96.7%

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

      3. +-commutative 96.7%

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

      4. associate-/l* 90.3%

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

      5. fma-define 90.3%

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

      6. distribute-frac-neg2 90.3%

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

      7. distribute-neg-frac 90.3%

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

      8. sub-neg 90.3%

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

      9. distribute-neg-in 90.3%

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

      10. remove-double-neg 90.3%

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

      11. +-commutative 90.3%

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

      12. sub-neg 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in z around 0 77.9%

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

   if -2.2000000000000001e-80 < t

   1. Initial program 94.5%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in z around inf 77.0%

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

      1. associate-/l* 77.8%

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

   7. Simplified 77.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.3e+101) (+ x (/ (* t y) a)) (- x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.3e+101) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - (z / (a / y));
	}
	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 <= (-4.3d+101)) then
        tmp = x + ((t * y) / a)
    else
        tmp = x - (z / (a / y))
    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 <= -4.3e+101) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.3e+101:
		tmp = x + ((t * y) / a)
	else:
		tmp = x - (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.3e+101)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(x - Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.3e+101)
		tmp = x + ((t * y) / a);
	else
		tmp = x - (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.3e+101], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3000000000000001e101

   1. Initial program 96.6%

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

      1. sub-neg 96.6%

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

      2. distribute-frac-neg2 96.6%

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

      3. +-commutative 96.6%

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

      4. associate-/l* 87.4%

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

      5. fma-define 87.4%

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

      6. distribute-frac-neg2 87.4%

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

      7. distribute-neg-frac 87.4%

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

      8. sub-neg 87.4%

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

      9. distribute-neg-in 87.4%

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

      10. remove-double-neg 87.4%

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

      11. +-commutative 87.4%

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

      12. sub-neg 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in z around 0 83.8%

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

   if -4.3000000000000001e101 < t

   1. Initial program 94.8%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in z around inf 76.3%

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

      1. associate-/l* 76.5%

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

   7. Simplified 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-/r/ 78.0%

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

   9. Applied egg-rr 78.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+31) (+ x (/ (* t y) a)) (- x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+31) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - ((z * y) / 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 <= (-1.5d+31)) then
        tmp = x + ((t * y) / a)
    else
        tmp = x - ((z * y) / 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 <= -1.5e+31) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+31:
		tmp = x + ((t * y) / a)
	else:
		tmp = x - ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+31)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(x - Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+31)
		tmp = x + ((t * y) / a);
	else
		tmp = x - ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+31], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999995e31

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. distribute-frac-neg2 95.4%

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

      3. +-commutative 95.4%

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

      4. associate-/l* 91.0%

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

      5. fma-define 91.1%

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

      6. distribute-frac-neg2 91.1%

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

      7. distribute-neg-frac 91.1%

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

      8. sub-neg 91.1%

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

      9. distribute-neg-in 91.1%

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

      10. remove-double-neg 91.1%

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

      11. +-commutative 91.1%

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

      12. sub-neg 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 79.8%

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

   if -1.49999999999999995e31 < t

   1. Initial program 95.0%

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

      1. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around inf 77.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{+156}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.2e+156) (- x (/ z (/ a y))) (/ (* y (- t z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.2e+156) {
		tmp = x - (z / (a / y));
	} else {
		tmp = (y * (t - 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 <= 1.2d+156) then
        tmp = x - (z / (a / y))
    else
        tmp = (y * (t - 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 <= 1.2e+156) {
		tmp = x - (z / (a / y));
	} else {
		tmp = (y * (t - z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.2e+156:
		tmp = x - (z / (a / y))
	else:
		tmp = (y * (t - z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.2e+156)
		tmp = Float64(x - Float64(z / Float64(a / y)));
	else
		tmp = Float64(Float64(y * Float64(t - z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.2e+156)
		tmp = x - (z / (a / y));
	else
		tmp = (y * (t - z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.2e+156], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.2000000000000001e156

   1. Initial program 95.6%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 78.0%

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

      1. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-/r/ 80.4%

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

   9. Applied egg-rr 80.4%

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

   if 1.2000000000000001e156 < t

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. distribute-frac-neg2 91.3%

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

      3. +-commutative 91.3%

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

      4. associate-/l* 86.2%

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

      5. fma-define 86.2%

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

      6. distribute-frac-neg2 86.2%

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

      7. distribute-neg-frac 86.2%

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

      8. sub-neg 86.2%

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

      9. distribute-neg-in 86.2%

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

      10. remove-double-neg 86.2%

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

      11. +-commutative 86.2%

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

      12. sub-neg 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in y around -inf 80.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.2 \cdot 10^{+156}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{+90}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.05e+90) (- x (/ z (/ a y))) (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.05e+90) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + (y / (a / t));
	}
	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 <= 1.05d+90) then
        tmp = x - (z / (a / y))
    else
        tmp = x + (y / (a / t))
    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 <= 1.05e+90) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.05e+90:
		tmp = x - (z / (a / y))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.05e+90)
		tmp = Float64(x - Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.05e+90)
		tmp = x - (z / (a / y));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.05e+90], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.0499999999999999e90

   1. Initial program 95.7%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in z around inf 78.3%

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

      1. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

      1. *-commutative 78.2%

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

      2. associate-/r/ 81.0%

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

   9. Applied egg-rr 81.0%

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

   if 1.0499999999999999e90 < t

   1. Initial program 92.7%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. clear-num 91.4%

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

      2. un-div-inv 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in z around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   9. Simplified 81.3%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{+90}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 21500000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 21500000.0) x (* y (- (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 21500000.0) {
		tmp = x;
	} else {
		tmp = 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 (z <= 21500000.0d0) then
        tmp = x
    else
        tmp = 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 (z <= 21500000.0) {
		tmp = x;
	} else {
		tmp = y * -(z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 21500000.0:
		tmp = x
	else:
		tmp = y * -(z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 21500000.0)
		tmp = x;
	else
		tmp = Float64(y * Float64(-Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 21500000.0)
		tmp = x;
	else
		tmp = y * -(z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 21500000.0], x, N[(y * (-N[(z / a), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.15e7

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 47.3%

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

   if 2.15e7 < z

   1. Initial program 93.5%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in z around inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   6. Step-by-step derivation

      1. mul-1-neg 53.2%

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

      2. associate-/l* 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

      4. distribute-neg-frac2 51.5%

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

   7. Simplified 51.5%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 21500000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 45.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z 5000.0) x (* z (/ y (- a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 5000.0) {
		tmp = x;
	} else {
		tmp = z * (y / -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 <= 5000.0d0) then
        tmp = x
    else
        tmp = z * (y / -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 <= 5000.0) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 5000.0:
		tmp = x
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 5000.0)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 5000.0)
		tmp = x;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 5000.0], x, N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5e3

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 47.3%

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

   if 5e3 < z

   1. Initial program 93.5%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in y around 0 93.5%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 53.2%

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

      2. associate-*l/ 56.2%

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

      3. distribute-rgt-neg-in 56.2%

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

   10. Simplified 56.2%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 44:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z 44.0) x (* y (- (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 44.0) {
		tmp = x;
	} else {
		tmp = 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 (z <= 44.0d0) then
        tmp = x
    else
        tmp = 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 (z <= 44.0) {
		tmp = x;
	} else {
		tmp = y * -(z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 44.0:
		tmp = x
	else:
		tmp = y * -(z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 44.0)
		tmp = x;
	else
		tmp = Float64(y * Float64(-Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 44.0)
		tmp = x;
	else
		tmp = y * -(z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 44.0], x, N[(y * (-N[(z / a), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 44

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 47.3%

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

   if 44 < z

   1. Initial program 93.5%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in y around 0 93.5%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 53.2%

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

      2. mul-1-neg 53.2%

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

      3. distribute-rgt-neg-out 53.2%

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

   10. Simplified 53.2%

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

       1. distribute-rgt-neg-out 53.2%

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

       2. distribute-lft-neg-in 53.2%

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

       3. associate-*r/ 51.5%

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

       4. *-commutative 51.5%

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

   12. Applied egg-rr 51.5%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 44:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 25.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z 25.5) x (/ (* z y) (- a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 25.5) {
		tmp = x;
	} else {
		tmp = (z * y) / -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 <= 25.5d0) then
        tmp = x
    else
        tmp = (z * y) / -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 <= 25.5) {
		tmp = x;
	} else {
		tmp = (z * y) / -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 25.5:
		tmp = x
	else:
		tmp = (z * y) / -a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 25.5)
		tmp = x;
	else
		tmp = Float64(Float64(z * y) / Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 25.5)
		tmp = x;
	else
		tmp = (z * y) / -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 25.5], x, N[(N[(z * y), $MachinePrecision] / (-a)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 25.5

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 47.3%

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

   if 25.5 < z

   1. Initial program 93.5%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in y around 0 93.5%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 53.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 53.2%

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

      2. mul-1-neg 53.2%

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

      3. distribute-rgt-neg-out 53.2%

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

   10. Simplified 53.2%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 25.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3200000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 3200000000000.0) x (/ (* t y) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 3200000000000.0) {
		tmp = x;
	} else {
		tmp = (t * y) / 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 (y <= 3200000000000.0d0) then
        tmp = x
    else
        tmp = (t * y) / 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 (y <= 3200000000000.0) {
		tmp = x;
	} else {
		tmp = (t * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 3200000000000.0:
		tmp = x
	else:
		tmp = (t * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 3200000000000.0)
		tmp = x;
	else
		tmp = Float64(Float64(t * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 3200000000000.0)
		tmp = x;
	else
		tmp = (t * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 3200000000000.0], x, N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.2e12

   1. Initial program 96.4%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in x around inf 50.2%

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

   if 3.2e12 < y

   1. Initial program 90.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 57.9%

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

      1. *-commutative 57.9%

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

   7. Simplified 57.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3200000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 93.5% 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 95.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

5. Final simplification 94.0%

   \[\leadsto x + y \cdot \frac{t - z}{a} \]
6. Add Preprocessing

Alternative 16: 97.0% 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 95.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

5. Taylor expanded in y around 0 95.0%

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

   1. associate-*l/ 97.1%

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

   2. *-commutative 97.1%

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

7. Simplified 97.1%

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

8. Final simplification 97.1%

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

Alternative 17: 39.7% 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 95.0%

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

   1. associate-/l* 94.0%

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

3. Simplified 94.0%

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

5. Taylor expanded in x around inf 41.7%

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

6. Final simplification 41.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.4% accurate, 0.5× 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 2024066 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (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)))