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

Percentage Accurate: 92.8% → 97.7%

Time: 8.0s

Alternatives: 10

Speedup: 1.0×

• 24.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 92.8% 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: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -8.2e-83) (- x (/ y (/ a (- z t)))) (+ x (/ (- t z) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8.2e-83) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((t - 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 (y <= (-8.2d-83)) then
        tmp = x - (y / (a / (z - t)))
    else
        tmp = x + ((t - 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 (y <= -8.2e-83) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -8.2e-83:
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + ((t - z) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -8.2e-83)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -8.2e-83)
		tmp = x - (y / (a / (z - t)));
	else
		tmp = x + ((t - z) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -8.2e-83], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999999e-83

   1. Initial program 85.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -8.1999999999999999e-83 < y

   1. Initial program 95.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around 0 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-/l* 97.4%

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

   6. Simplified 97.4%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-83}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \]

Alternative 2: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-165}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5500000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) a))))
   (if (<= a -4.4e-45)
     x
     (if (<= a 6.8e-224)
       t_1
       (if (<= a 1.36e-165)
         (/ (* y t) a)
         (if (<= a 6.5e-49) t_1 (if (<= a 5500000.0) (* t (/ y a)) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (a <= -4.4e-45) {
		tmp = x;
	} else if (a <= 6.8e-224) {
		tmp = t_1;
	} else if (a <= 1.36e-165) {
		tmp = (y * t) / a;
	} else if (a <= 6.5e-49) {
		tmp = t_1;
	} else if (a <= 5500000.0) {
		tmp = t * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = z * (-y / a)
    if (a <= (-4.4d-45)) then
        tmp = x
    else if (a <= 6.8d-224) then
        tmp = t_1
    else if (a <= 1.36d-165) then
        tmp = (y * t) / a
    else if (a <= 6.5d-49) then
        tmp = t_1
    else if (a <= 5500000.0d0) then
        tmp = t * (y / 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 t_1 = z * (-y / a);
	double tmp;
	if (a <= -4.4e-45) {
		tmp = x;
	} else if (a <= 6.8e-224) {
		tmp = t_1;
	} else if (a <= 1.36e-165) {
		tmp = (y * t) / a;
	} else if (a <= 6.5e-49) {
		tmp = t_1;
	} else if (a <= 5500000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / a)
	tmp = 0
	if a <= -4.4e-45:
		tmp = x
	elif a <= 6.8e-224:
		tmp = t_1
	elif a <= 1.36e-165:
		tmp = (y * t) / a
	elif a <= 6.5e-49:
		tmp = t_1
	elif a <= 5500000.0:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / a))
	tmp = 0.0
	if (a <= -4.4e-45)
		tmp = x;
	elseif (a <= 6.8e-224)
		tmp = t_1;
	elseif (a <= 1.36e-165)
		tmp = Float64(Float64(y * t) / a);
	elseif (a <= 6.5e-49)
		tmp = t_1;
	elseif (a <= 5500000.0)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / a);
	tmp = 0.0;
	if (a <= -4.4e-45)
		tmp = x;
	elseif (a <= 6.8e-224)
		tmp = t_1;
	elseif (a <= 1.36e-165)
		tmp = (y * t) / a;
	elseif (a <= 6.5e-49)
		tmp = t_1;
	elseif (a <= 5500000.0)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.4e-45], x, If[LessEqual[a, 6.8e-224], t$95$1, If[LessEqual[a, 1.36e-165], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 6.5e-49], t$95$1, If[LessEqual[a, 5500000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.39999999999999987e-45 or 5.5e6 < a

   1. Initial program 86.0%

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

      1. sub-neg 86.0%

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

      2. distribute-frac-neg 86.0%

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

      3. distribute-lft-neg-out 86.0%

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

      4. +-commutative 86.0%

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

      5. distribute-lft-neg-out 86.0%

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

      6. distribute-rgt-neg-in 86.0%

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

      7. associate-*l/ 97.6%

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

      8. fma-def 97.6%

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

      9. sub-neg 97.6%

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

      10. distribute-neg-in 97.6%

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

      11. remove-double-neg 97.6%

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

      12. +-commutative 97.6%

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

      13. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around 0 58.7%

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

   if -4.39999999999999987e-45 < a < 6.79999999999999984e-224 or 1.3599999999999999e-165 < a < 6.49999999999999968e-49

   1. Initial program 98.9%

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

      1. sub-neg 98.9%

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

      2. distribute-frac-neg 98.9%

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

      3. distribute-lft-neg-out 98.9%

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

      4. +-commutative 98.9%

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

      5. distribute-lft-neg-out 98.9%

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

      6. distribute-rgt-neg-in 98.9%

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

      7. associate-*l/ 95.1%

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

      8. fma-def 95.1%

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

      9. sub-neg 95.1%

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

      10. distribute-neg-in 95.1%

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

      11. remove-double-neg 95.1%

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

      12. +-commutative 95.1%

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

      13. sub-neg 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. associate-*l/ 60.6%

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

      3. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if 6.79999999999999984e-224 < a < 1.3599999999999999e-165

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. associate-*l/ 87.2%

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

      8. fma-def 87.2%

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

      9. sub-neg 87.2%

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

      10. distribute-neg-in 87.2%

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

      11. remove-double-neg 87.2%

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

      12. +-commutative 87.2%

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

      13. sub-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in t around inf 51.4%

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

   if 6.49999999999999968e-49 < a < 5.5e6

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. distribute-lft-neg-out 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. associate-*l/ 100.0%

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

      8. fma-def 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. remove-double-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 75.8%

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

      1. associate-*r/ 75.8%

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

   6. Simplified 75.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-224}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-165}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-49}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 5500000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-226}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 5800000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e+38)
   x
   (if (<= a 4.5e-226)
     (/ (- z) (/ a y))
     (if (<= a 2.65e-160)
       (/ (* y t) a)
       (if (<= a 5e-50)
         (* z (/ (- y) a))
         (if (<= a 5800000.0) (* t (/ y a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e+38) {
		tmp = x;
	} else if (a <= 4.5e-226) {
		tmp = -z / (a / y);
	} else if (a <= 2.65e-160) {
		tmp = (y * t) / a;
	} else if (a <= 5e-50) {
		tmp = z * (-y / a);
	} else if (a <= 5800000.0) {
		tmp = t * (y / 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 <= (-8d+38)) then
        tmp = x
    else if (a <= 4.5d-226) then
        tmp = -z / (a / y)
    else if (a <= 2.65d-160) then
        tmp = (y * t) / a
    else if (a <= 5d-50) then
        tmp = z * (-y / a)
    else if (a <= 5800000.0d0) then
        tmp = t * (y / 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 <= -8e+38) {
		tmp = x;
	} else if (a <= 4.5e-226) {
		tmp = -z / (a / y);
	} else if (a <= 2.65e-160) {
		tmp = (y * t) / a;
	} else if (a <= 5e-50) {
		tmp = z * (-y / a);
	} else if (a <= 5800000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e+38:
		tmp = x
	elif a <= 4.5e-226:
		tmp = -z / (a / y)
	elif a <= 2.65e-160:
		tmp = (y * t) / a
	elif a <= 5e-50:
		tmp = z * (-y / a)
	elif a <= 5800000.0:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e+38)
		tmp = x;
	elseif (a <= 4.5e-226)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (a <= 2.65e-160)
		tmp = Float64(Float64(y * t) / a);
	elseif (a <= 5e-50)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (a <= 5800000.0)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8e+38)
		tmp = x;
	elseif (a <= 4.5e-226)
		tmp = -z / (a / y);
	elseif (a <= 2.65e-160)
		tmp = (y * t) / a;
	elseif (a <= 5e-50)
		tmp = z * (-y / a);
	elseif (a <= 5800000.0)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e+38], x, If[LessEqual[a, 4.5e-226], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.65e-160], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 5e-50], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5800000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.99999999999999982e38 or 5.8e6 < a

   1. Initial program 85.5%

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

      1. sub-neg 85.5%

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

      2. distribute-frac-neg 85.5%

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

      3. distribute-lft-neg-out 85.5%

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

      4. +-commutative 85.5%

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

      5. distribute-lft-neg-out 85.5%

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

      6. distribute-rgt-neg-in 85.5%

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

      7. associate-*l/ 97.5%

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

      8. fma-def 97.5%

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

      9. sub-neg 97.5%

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

      10. distribute-neg-in 97.5%

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

      11. remove-double-neg 97.5%

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

      12. +-commutative 97.5%

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

      13. sub-neg 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 60.6%

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

   if -7.99999999999999982e38 < a < 4.50000000000000011e-226

   1. Initial program 97.8%

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

      1. sub-neg 97.8%

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

      2. distribute-frac-neg 97.8%

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

      3. distribute-lft-neg-out 97.8%

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

      4. +-commutative 97.8%

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

      5. distribute-lft-neg-out 97.8%

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

      6. distribute-rgt-neg-in 97.8%

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

      7. associate-*l/ 94.6%

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

      8. fma-def 94.6%

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

      9. sub-neg 94.6%

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

      10. distribute-neg-in 94.6%

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

      11. remove-double-neg 94.6%

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

      12. +-commutative 94.6%

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

      13. sub-neg 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. mul-1-neg 57.7%

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

      2. *-commutative 57.7%

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

      3. associate-/l* 57.5%

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

      4. associate-/r/ 50.3%

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

   6. Simplified 50.3%

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

      1. associate-/r/ 57.5%

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

   8. Applied egg-rr 57.5%

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

   if 4.50000000000000011e-226 < a < 2.6500000000000001e-160

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. associate-*l/ 87.2%

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

      8. fma-def 87.2%

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

      9. sub-neg 87.2%

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

      10. distribute-neg-in 87.2%

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

      11. remove-double-neg 87.2%

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

      12. +-commutative 87.2%

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

      13. sub-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in t around inf 51.4%

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

   if 2.6500000000000001e-160 < a < 4.99999999999999968e-50

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. associate-*l/ 99.9%

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

      8. fma-def 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. remove-double-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. associate-*l/ 66.0%

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

      3. *-commutative 66.0%

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

   6. Simplified 66.0%

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

   if 4.99999999999999968e-50 < a < 5.8e6

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. distribute-lft-neg-out 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. associate-*l/ 100.0%

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

      8. fma-def 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. remove-double-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 75.8%

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

      1. associate-*r/ 75.8%

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

   6. Simplified 75.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-226}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 5800000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-224}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 6800000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.05e-43)
   x
   (if (<= a 7.6e-224)
     (/ (* z (- y)) a)
     (if (<= a 5.2e-158)
       (/ (* y t) a)
       (if (<= a 9.5e-50)
         (* z (/ (- y) a))
         (if (<= a 6800000.0) (* t (/ y a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e-43) {
		tmp = x;
	} else if (a <= 7.6e-224) {
		tmp = (z * -y) / a;
	} else if (a <= 5.2e-158) {
		tmp = (y * t) / a;
	} else if (a <= 9.5e-50) {
		tmp = z * (-y / a);
	} else if (a <= 6800000.0) {
		tmp = t * (y / 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 <= (-1.05d-43)) then
        tmp = x
    else if (a <= 7.6d-224) then
        tmp = (z * -y) / a
    else if (a <= 5.2d-158) then
        tmp = (y * t) / a
    else if (a <= 9.5d-50) then
        tmp = z * (-y / a)
    else if (a <= 6800000.0d0) then
        tmp = t * (y / 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 <= -1.05e-43) {
		tmp = x;
	} else if (a <= 7.6e-224) {
		tmp = (z * -y) / a;
	} else if (a <= 5.2e-158) {
		tmp = (y * t) / a;
	} else if (a <= 9.5e-50) {
		tmp = z * (-y / a);
	} else if (a <= 6800000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.05e-43:
		tmp = x
	elif a <= 7.6e-224:
		tmp = (z * -y) / a
	elif a <= 5.2e-158:
		tmp = (y * t) / a
	elif a <= 9.5e-50:
		tmp = z * (-y / a)
	elif a <= 6800000.0:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.05e-43)
		tmp = x;
	elseif (a <= 7.6e-224)
		tmp = Float64(Float64(z * Float64(-y)) / a);
	elseif (a <= 5.2e-158)
		tmp = Float64(Float64(y * t) / a);
	elseif (a <= 9.5e-50)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (a <= 6800000.0)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.05e-43)
		tmp = x;
	elseif (a <= 7.6e-224)
		tmp = (z * -y) / a;
	elseif (a <= 5.2e-158)
		tmp = (y * t) / a;
	elseif (a <= 9.5e-50)
		tmp = z * (-y / a);
	elseif (a <= 6800000.0)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.05e-43], x, If[LessEqual[a, 7.6e-224], N[(N[(z * (-y)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 5.2e-158], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 9.5e-50], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6800000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.05e-43 or 6.8e6 < a

   1. Initial program 86.0%

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

      1. sub-neg 86.0%

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

      2. distribute-frac-neg 86.0%

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

      3. distribute-lft-neg-out 86.0%

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

      4. +-commutative 86.0%

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

      5. distribute-lft-neg-out 86.0%

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

      6. distribute-rgt-neg-in 86.0%

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

      7. associate-*l/ 97.6%

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

      8. fma-def 97.6%

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

      9. sub-neg 97.6%

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

      10. distribute-neg-in 97.6%

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

      11. remove-double-neg 97.6%

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

      12. +-commutative 97.6%

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

      13. sub-neg 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around 0 58.7%

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

   if -1.05e-43 < a < 7.60000000000000005e-224

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. distribute-frac-neg 98.7%

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

      3. distribute-lft-neg-out 98.7%

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

      4. +-commutative 98.7%

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

      5. distribute-lft-neg-out 98.7%

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

      6. distribute-rgt-neg-in 98.7%

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

      7. associate-*l/ 93.9%

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

      8. fma-def 93.9%

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

      9. sub-neg 93.9%

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

      10. distribute-neg-in 93.9%

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

      11. remove-double-neg 93.9%

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

      12. +-commutative 93.9%

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

      13. sub-neg 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-/l* 60.3%

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

      4. associate-/r/ 52.1%

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

   6. Simplified 52.1%

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

      1. associate-*l/ 61.6%

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

   8. Applied egg-rr 61.6%

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

   if 7.60000000000000005e-224 < a < 5.2000000000000001e-158

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-out 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. associate-*l/ 87.2%

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

      8. fma-def 87.2%

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

      9. sub-neg 87.2%

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

      10. distribute-neg-in 87.2%

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

      11. remove-double-neg 87.2%

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

      12. +-commutative 87.2%

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

      13. sub-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in t around inf 51.4%

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

   if 5.2000000000000001e-158 < a < 9.4999999999999993e-50

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-frac-neg 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-neg-out 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. associate-*l/ 99.9%

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

      8. fma-def 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. remove-double-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. associate-*l/ 66.0%

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

      3. *-commutative 66.0%

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

   6. Simplified 66.0%

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

   if 9.4999999999999993e-50 < a < 6.8e6

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. distribute-lft-neg-out 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. associate-*l/ 100.0%

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

      8. fma-def 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. remove-double-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 75.8%

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

      1. associate-*r/ 75.8%

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

   6. Simplified 75.8%

      \[\leadsto \color{blue}{t \cdot \frac{y}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-224}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 6800000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+177} \lor \neg \left(z \leq 6 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+177) (not (<= z 6e+28)))
   (/ (- z) (/ a y))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+177) || !(z <= 6e+28)) {
		tmp = -z / (a / y);
	} 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 <= (-7.2d+177)) .or. (.not. (z <= 6d+28))) then
        tmp = -z / (a / y)
    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 <= -7.2e+177) || !(z <= 6e+28)) {
		tmp = -z / (a / y);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+177) or not (z <= 6e+28):
		tmp = -z / (a / y)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+177) || !(z <= 6e+28))
		tmp = Float64(Float64(-z) / Float64(a / y));
	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 <= -7.2e+177) || ~((z <= 6e+28)))
		tmp = -z / (a / y);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+177], N[Not[LessEqual[z, 6e+28]], $MachinePrecision]], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000005e177 or 6.0000000000000002e28 < z

   1. Initial program 86.4%

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

      1. sub-neg 86.4%

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

      2. distribute-frac-neg 86.4%

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

      3. distribute-lft-neg-out 86.4%

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

      4. +-commutative 86.4%

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

      5. distribute-lft-neg-out 86.4%

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

      6. distribute-rgt-neg-in 86.4%

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

      7. associate-*l/ 96.6%

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

      8. fma-def 96.6%

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

      9. sub-neg 96.6%

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

      10. distribute-neg-in 96.6%

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

      11. remove-double-neg 96.6%

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

      12. +-commutative 96.6%

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

      13. sub-neg 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. *-commutative 60.8%

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

      3. associate-/l* 66.9%

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

      4. associate-/r/ 57.6%

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

   6. Simplified 57.6%

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

      1. associate-/r/ 66.9%

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

   8. Applied egg-rr 66.9%

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

   if -7.20000000000000005e177 < z < 6.0000000000000002e28

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. distribute-frac-neg 95.3%

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

      3. distribute-lft-neg-out 95.3%

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

      4. +-commutative 95.3%

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

      5. distribute-lft-neg-out 95.3%

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

      6. distribute-rgt-neg-in 95.3%

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

      7. associate-*l/ 95.9%

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

      8. fma-def 95.9%

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

      9. sub-neg 95.9%

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

      10. distribute-neg-in 95.9%

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

      11. remove-double-neg 95.9%

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

      12. +-commutative 95.9%

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

      13. sub-neg 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 79.2%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+177} \lor \neg \left(z \leq 6 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 6: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+39} \lor \neg \left(t \leq 2.2 \cdot 10^{-61}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.4e+39) (not (<= t 2.2e-61)))
   (+ 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 <= -3.4e+39) || !(t <= 2.2e-61)) {
		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 <= (-3.4d+39)) .or. (.not. (t <= 2.2d-61))) 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 <= -3.4e+39) || !(t <= 2.2e-61)) {
		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 <= -3.4e+39) or not (t <= 2.2e-61):
		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 <= -3.4e+39) || !(t <= 2.2e-61))
		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 <= -3.4e+39) || ~((t <= 2.2e-61)))
		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, -3.4e+39], N[Not[LessEqual[t, 2.2e-61]], $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 < -3.3999999999999999e39 or 2.20000000000000009e-61 < t

   1. Initial program 91.6%

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

      1. sub-neg 91.6%

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

      2. distribute-frac-neg 91.6%

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

      3. distribute-lft-neg-out 91.6%

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

      4. +-commutative 91.6%

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

      5. distribute-lft-neg-out 91.6%

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

      6. distribute-rgt-neg-in 91.6%

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

      7. associate-*l/ 99.2%

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

      8. fma-def 99.2%

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

      9. sub-neg 99.2%

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

      10. distribute-neg-in 99.2%

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

      11. remove-double-neg 99.2%

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

      12. +-commutative 99.2%

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

      13. sub-neg 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 79.7%

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

   if -3.3999999999999999e39 < t < 2.20000000000000009e-61

   1. Initial program 92.7%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around inf 89.1%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+39} \lor \neg \left(t \leq 2.2 \cdot 10^{-61}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 7: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.5e-95) (- x (/ y (/ a (- z t)))) (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.5e-95) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((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 (y <= (-4.5d-95)) then
        tmp = x - (y / (a / (z - t)))
    else
        tmp = x + ((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 (y <= -4.5e-95) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.5e-95:
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.5e-95)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + 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 (y <= -4.5e-95)
		tmp = x - (y / (a / (z - t)));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.5e-95], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e-95

   1. Initial program 85.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -4.5e-95 < y

   1. Initial program 95.4%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 8: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 17000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.5e-95) x (if (<= a 17000000.0) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.5e-95) {
		tmp = x;
	} else if (a <= 17000000.0) {
		tmp = t * (y / 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 <= (-4.5d-95)) then
        tmp = x
    else if (a <= 17000000.0d0) then
        tmp = t * (y / 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 <= -4.5e-95) {
		tmp = x;
	} else if (a <= 17000000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.5e-95:
		tmp = x
	elif a <= 17000000.0:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.5e-95)
		tmp = x;
	elseif (a <= 17000000.0)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.5e-95)
		tmp = x;
	elseif (a <= 17000000.0)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.5e-95], x, If[LessEqual[a, 17000000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5e-95 or 1.7e7 < a

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. distribute-frac-neg 86.8%

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

      3. distribute-lft-neg-out 86.8%

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

      4. +-commutative 86.8%

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

      5. distribute-lft-neg-out 86.8%

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

      6. distribute-rgt-neg-in 86.8%

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

      7. associate-*l/ 97.1%

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

      8. fma-def 97.1%

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

      9. sub-neg 97.1%

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

      10. distribute-neg-in 97.1%

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

      11. remove-double-neg 97.1%

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

      12. +-commutative 97.1%

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

      13. sub-neg 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around 0 56.9%

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

   if -4.5e-95 < a < 1.7e7

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. distribute-frac-neg 99.0%

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

      3. distribute-lft-neg-out 99.0%

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

      4. +-commutative 99.0%

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

      5. distribute-lft-neg-out 99.0%

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

      6. distribute-rgt-neg-in 99.0%

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

      7. associate-*l/ 95.0%

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

      8. fma-def 95.0%

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

      9. sub-neg 95.0%

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

      10. distribute-neg-in 95.0%

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

      11. remove-double-neg 95.0%

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

      12. +-commutative 95.0%

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

      13. sub-neg 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around inf 40.9%

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

      1. associate-*r/ 43.3%

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

   6. Simplified 43.3%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 17000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 97.3% 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 92.2%

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

   1. associate-*l/ 96.2%

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

3. Simplified 96.2%

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

4. Final simplification 96.2%

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

Alternative 10: 39.4% 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 92.2%

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

   1. sub-neg 92.2%

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

   2. distribute-frac-neg 92.2%

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

   3. distribute-lft-neg-out 92.2%

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

   4. +-commutative 92.2%

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

   5. distribute-lft-neg-out 92.2%

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

   6. distribute-rgt-neg-in 92.2%

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

   7. associate-*l/ 96.2%

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

   8. fma-def 96.2%

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

   9. sub-neg 96.2%

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

   10. distribute-neg-in 96.2%

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

   11. remove-double-neg 96.2%

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

   12. +-commutative 96.2%

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

   13. sub-neg 96.2%

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

3. Simplified 96.2%

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

4. Taylor expanded in y around 0 39.4%

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

5. Final simplification 39.4%

   \[\leadsto x \]

Developer target: 99.3% 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 2023271 
(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)))