Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.6% → 95.2%

Time: 16.1s

Alternatives: 20

Speedup: 0.7×

• 47.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -2 \cdot 10^{+93}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(c, \mathsf{fma}\left(b, c, a\right) \cdot \left(-i\right), x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c (+ a (* b c))) -2e+93)
   (* 2.0 (fma z t (fma c (* (fma b c a) (- i)) (* x y))))
   (* 2.0 (fma y x (- (* z t) (* (fma b c a) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * (a + (b * c))) <= -2e+93) {
		tmp = 2.0 * fma(z, t, fma(c, (fma(b, c, a) * -i), (x * y)));
	} else {
		tmp = 2.0 * fma(y, x, ((z * t) - (fma(b, c, a) * (c * i))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * Float64(a + Float64(b * c))) <= -2e+93)
		tmp = Float64(2.0 * fma(z, t, fma(c, Float64(fma(b, c, a) * Float64(-i)), Float64(x * y))));
	else
		tmp = Float64(2.0 * fma(y, x, Float64(Float64(z * t) - Float64(fma(b, c, a) * Float64(c * i)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -2e+93], N[(2.0 * N[(z * t + N[(c * N[(N[(b * c + a), $MachinePrecision] * (-i)), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * x + N[(N[(z * t), $MachinePrecision] - N[(N[(b * c + a), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -2.00000000000000009e93

   1. Initial program 78.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate--l+ 78.7%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]

      2. +-commutative 78.7%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y\right)} \]

      3. associate-+l- 78.7%

         \[\leadsto 2 \cdot \color{blue}{\left(z \cdot t - \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - x \cdot y\right)\right)} \]

      4. fma-neg 83.1%

         \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, -\left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - x \cdot y\right)\right)} \]

      5. neg-sub0 83.1%

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{0 - \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i - x \cdot y\right)}\right) \]

      6. associate-+l- 83.1%

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(0 - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) + x \cdot y}\right) \]

      7. neg-sub0 83.1%

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(-\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)} + x \cdot y\right) \]

      8. distribute-rgt-neg-in 83.1%

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot \left(-i\right)} + x \cdot y\right) \]

      9. *-commutative 83.1%

         \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot \left(-i\right) + x \cdot y\right) \]

      10. associate-*l* 91.3%

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)} + x \cdot y\right) \]

      11. fma-def 94.3%

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \color{blue}{\mathsf{fma}\left(c, \left(a + b \cdot c\right) \cdot \left(-i\right), x \cdot y\right)}\right) \]

      12. +-commutative 94.3%

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(c, \color{blue}{\left(b \cdot c + a\right)} \cdot \left(-i\right), x \cdot y\right)\right) \]

      13. fma-def 94.3%

          \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(c, \color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot \left(-i\right), x \cdot y\right)\right) \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(c, \mathsf{fma}\left(b, c, a\right) \cdot \left(-i\right), x \cdot y\right)\right)} \]

   if -2.00000000000000009e93 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 93.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 96.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 97.2%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 96.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 96.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 96.7%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]
   6. Step-by-step derivation

      1. +-commutative 96.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. associate-*r* 93.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right) \]

      3. *-commutative 93.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

      4. +-commutative 93.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \color{blue}{\left(b \cdot c + a\right)}\right) \cdot i\right) \]

      5. fma-udef 93.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \color{blue}{\mathsf{fma}\left(b, c, a\right)}\right) \cdot i\right) \]

      6. add-cube-cbrt 92.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)} \cdot \sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right) \cdot \sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)} \cdot i\right) \]

      7. unpow3 92.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)}^{3}} \cdot i\right) \]

      8. associate--l+ 92.9%

         \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - {\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)}^{3} \cdot i\right)\right)} \]

      9. *-commutative 92.9%

         \[\leadsto 2 \cdot \left(\color{blue}{y \cdot x} + \left(z \cdot t - {\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)}^{3} \cdot i\right)\right) \]

      10. fma-def 93.9%

          \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(y, x, z \cdot t - {\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)}^{3} \cdot i\right)} \]

      11. unpow3 94.0%

          \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)} \cdot \sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right) \cdot \sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)} \cdot i\right) \]

      12. add-cube-cbrt 94.3%

          \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(c \cdot \mathsf{fma}\left(b, c, a\right)\right)} \cdot i\right) \]

      13. fma-udef 94.3%

          \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \left(c \cdot \color{blue}{\left(b \cdot c + a\right)}\right) \cdot i\right) \]

      14. +-commutative 94.3%

          \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \left(c \cdot \color{blue}{\left(a + b \cdot c\right)}\right) \cdot i\right) \]

      15. *-commutative 94.3%

          \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)} \cdot i\right) \]

      16. associate-*r* 97.8%

          \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      17. +-commutative 97.8%

          \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(b \cdot c + a\right)} \cdot \left(c \cdot i\right)\right) \]

      18. fma-udef 97.8%

          \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot \left(c \cdot i\right)\right) \]

   7. Applied egg-rr 97.8%

      \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(y, x, z \cdot t - \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -2 \cdot 10^{+93}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(c, \mathsf{fma}\left(b, c, a\right) \cdot \left(-i\right), x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 2: 95.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (fma y x (- (* z t) (* (fma b c a) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * fma(y, x, ((z * t) - (fma(b, c, a) * (c * i))));
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * fma(y, x, Float64(Float64(z * t) - Float64(fma(b, c, a) * Float64(c * i)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(y * x + N[(N[(z * t), $MachinePrecision] - N[(N[(b * c + a), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.3%

   \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
2. Step-by-step derivation

   1. associate-*l* 94.4%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   2. fma-def 94.8%

      \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

3. Simplified 94.8%

   \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
4. Step-by-step derivation

   1. fma-def 94.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   2. +-commutative 94.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

5. Applied egg-rr 94.4%

   \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]
6. Step-by-step derivation

   1. +-commutative 94.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   2. associate-*r* 89.3%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i}\right) \]

   3. *-commutative 89.3%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)} \cdot i\right) \]

   4. +-commutative 89.3%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \color{blue}{\left(b \cdot c + a\right)}\right) \cdot i\right) \]

   5. fma-udef 89.3%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \color{blue}{\mathsf{fma}\left(b, c, a\right)}\right) \cdot i\right) \]

   6. add-cube-cbrt 89.1%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)} \cdot \sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right) \cdot \sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)} \cdot i\right) \]

   7. unpow3 89.0%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)}^{3}} \cdot i\right) \]

   8. associate--l+ 89.0%

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - {\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)}^{3} \cdot i\right)\right)} \]

   9. *-commutative 89.0%

      \[\leadsto 2 \cdot \left(\color{blue}{y \cdot x} + \left(z \cdot t - {\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)}^{3} \cdot i\right)\right) \]

   10. fma-def 89.8%

       \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(y, x, z \cdot t - {\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)}^{3} \cdot i\right)} \]

   11. unpow3 89.9%

       \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(\left(\sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)} \cdot \sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right) \cdot \sqrt[3]{c \cdot \mathsf{fma}\left(b, c, a\right)}\right)} \cdot i\right) \]

   12. add-cube-cbrt 90.1%

       \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(c \cdot \mathsf{fma}\left(b, c, a\right)\right)} \cdot i\right) \]

   13. fma-udef 90.1%

       \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \left(c \cdot \color{blue}{\left(b \cdot c + a\right)}\right) \cdot i\right) \]

   14. +-commutative 90.1%

       \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \left(c \cdot \color{blue}{\left(a + b \cdot c\right)}\right) \cdot i\right) \]

   15. *-commutative 90.1%

       \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(\left(a + b \cdot c\right) \cdot c\right)} \cdot i\right) \]

   16. associate-*r* 95.2%

       \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

   17. +-commutative 95.2%

       \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(b \cdot c + a\right)} \cdot \left(c \cdot i\right)\right) \]

   18. fma-udef 95.2%

       \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\mathsf{fma}\left(b, c, a\right)} \cdot \left(c \cdot i\right)\right) \]

7. Applied egg-rr 95.2%

   \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(y, x, z \cdot t - \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot i\right)\right)} \]

8. Final simplification 95.2%

   \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot i\right)\right) \]

Alternative 3: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;t_2 - \left(c \cdot t_1\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(t_2 - t_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* x y) (* z t))))
   (if (<= (- t_2 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* 2.0 t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((t_2 - ((c * t_1) * i)) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = 2.0 * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (t_2 - ((c * t_1) * i)) <= math.inf:
		tmp = 2.0 * (t_2 - (t_1 * (c * i)))
	else:
		tmp = 2.0 * t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(t_2 - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((t_2 - ((c * t_1) * i)) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = 2.0 * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)) < +inf.0

   1. Initial program 93.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 98.3%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 98.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 98.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 98.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 98.3%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i))

   1. Initial program 0.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 58.3%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 4: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq 5 \cdot 10^{+279}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(t_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 5e+279)
     (* 2.0 (- (+ (* x y) (* z t)) t_2))
     (* 2.0 (- (* x y) (* c (* t_1 i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= 5e+279) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = (c * t_1) * i
    if (t_2 <= 5d+279) then
        tmp = 2.0d0 * (((x * y) + (z * t)) - t_2)
    else
        tmp = 2.0d0 * ((x * y) - (c * (t_1 * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= 5e+279) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= 5e+279:
		tmp = 2.0 * (((x * y) + (z * t)) - t_2)
	else:
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= 5e+279)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(t_1 * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if (t_2 <= 5e+279)
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	else
		tmp = 2.0 * ((x * y) - (c * (t_1 * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, 5e+279], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000002e279

   1. Initial program 95.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   if 5.0000000000000002e279 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 64.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 84.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+279}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -2.55 \cdot 10^{+182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(t_2 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-90} \lor \neg \left(c \leq 2.5 \cdot 10^{+19}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_2 - \frac{c \cdot i}{\frac{1}{a}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i)))))
        (t_2 (+ (* x y) (* z t))))
   (if (<= c -2.55e+182)
     t_1
     (if (<= c -2.1e+128)
       (* 2.0 (- t_2 (* c (* c (* b i)))))
       (if (or (<= c -4.5e-90) (not (<= c 2.5e+19)))
         t_1
         (* 2.0 (- t_2 (/ (* c i) (/ 1.0 a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (c <= -2.55e+182) {
		tmp = t_1;
	} else if (c <= -2.1e+128) {
		tmp = 2.0 * (t_2 - (c * (c * (b * i))));
	} else if ((c <= -4.5e-90) || !(c <= 2.5e+19)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (t_2 - ((c * i) / (1.0 / a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    t_2 = (x * y) + (z * t)
    if (c <= (-2.55d+182)) then
        tmp = t_1
    else if (c <= (-2.1d+128)) then
        tmp = 2.0d0 * (t_2 - (c * (c * (b * i))))
    else if ((c <= (-4.5d-90)) .or. (.not. (c <= 2.5d+19))) then
        tmp = t_1
    else
        tmp = 2.0d0 * (t_2 - ((c * i) / (1.0d0 / a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (c <= -2.55e+182) {
		tmp = t_1;
	} else if (c <= -2.1e+128) {
		tmp = 2.0 * (t_2 - (c * (c * (b * i))));
	} else if ((c <= -4.5e-90) || !(c <= 2.5e+19)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (t_2 - ((c * i) / (1.0 / a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	t_2 = (x * y) + (z * t)
	tmp = 0
	if c <= -2.55e+182:
		tmp = t_1
	elif c <= -2.1e+128:
		tmp = 2.0 * (t_2 - (c * (c * (b * i))))
	elif (c <= -4.5e-90) or not (c <= 2.5e+19):
		tmp = t_1
	else:
		tmp = 2.0 * (t_2 - ((c * i) / (1.0 / a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -2.55e+182)
		tmp = t_1;
	elseif (c <= -2.1e+128)
		tmp = Float64(2.0 * Float64(t_2 - Float64(c * Float64(c * Float64(b * i)))));
	elseif ((c <= -4.5e-90) || !(c <= 2.5e+19))
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(t_2 - Float64(Float64(c * i) / Float64(1.0 / a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -2.55e+182)
		tmp = t_1;
	elseif (c <= -2.1e+128)
		tmp = 2.0 * (t_2 - (c * (c * (b * i))));
	elseif ((c <= -4.5e-90) || ~((c <= 2.5e+19)))
		tmp = t_1;
	else
		tmp = 2.0 * (t_2 - ((c * i) / (1.0 / a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.55e+182], t$95$1, If[LessEqual[c, -2.1e+128], N[(2.0 * N[(t$95$2 - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, -4.5e-90], N[Not[LessEqual[c, 2.5e+19]], $MachinePrecision]], t$95$1, N[(2.0 * N[(t$95$2 - N[(N[(c * i), $MachinePrecision] / N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.55000000000000005e182 or -2.1e128 < c < -4.50000000000000009e-90 or 2.5e19 < c

   1. Initial program 80.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 87.3%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   if -2.55000000000000005e182 < c < -2.1e128

   1. Initial program 90.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around 0 81.8%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{c}^{2} \cdot \left(i \cdot b\right)}\right) \]
   3. Step-by-step derivation

      1. unpow2 81.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. associate-*r* 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   4. Simplified 100.0%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   if -4.50000000000000009e-90 < c < 2.5e19

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*r* 99.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. *-commutative 99.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)}\right) \]

      3. flip-+ 78.5%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot i\right) \cdot \color{blue}{\frac{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}{a - b \cdot c}}\right) \]

      4. associate-*r/ 72.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{\left(c \cdot i\right) \cdot \left(a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)\right)}{a - b \cdot c}}\right) \]

      5. pow2 72.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{\left(c \cdot i\right) \cdot \left(a \cdot a - \color{blue}{{\left(b \cdot c\right)}^{2}}\right)}{a - b \cdot c}\right) \]

   3. Applied egg-rr 72.8%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{\left(c \cdot i\right) \cdot \left(a \cdot a - {\left(b \cdot c\right)}^{2}\right)}{a - b \cdot c}}\right) \]
   4. Step-by-step derivation

      1. associate-/l* 78.5%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot i}{\frac{a - b \cdot c}{a \cdot a - {\left(b \cdot c\right)}^{2}}}}\right) \]

      2. *-commutative 78.5%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{a - \color{blue}{c \cdot b}}{a \cdot a - {\left(b \cdot c\right)}^{2}}}\right) \]

      3. *-commutative 78.5%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{a - c \cdot b}{a \cdot a - {\color{blue}{\left(c \cdot b\right)}}^{2}}}\right) \]

   5. Simplified 78.5%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot i}{\frac{a - c \cdot b}{a \cdot a - {\left(c \cdot b\right)}^{2}}}}\right) \]

   6. Taylor expanded in a around inf 91.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.55 \cdot 10^{+182}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-90} \lor \neg \left(c \leq 2.5 \cdot 10^{+19}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{1}{a}}\right)\\ \end{array} \]

Alternative 6: 66.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + z \cdot t\right)\\ t_2 := c \cdot \left(a \cdot i\right)\\ t_3 := 2 \cdot \left(x \cdot y - t_2\right)\\ \mathbf{if}\;c \leq -4.35 \cdot 10^{+158}:\\ \;\;\;\;\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq -5.7 \cdot 10^{+125}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_2\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{+99}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{-90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1300000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* x y) (* z t))))
        (t_2 (* c (* a i)))
        (t_3 (* 2.0 (- (* x y) t_2))))
   (if (<= c -4.35e+158)
     (* (* b (* c i)) (* c -2.0))
     (if (<= c -5.7e+125)
       (* 2.0 (- (* z t) t_2))
       (if (<= c -3.4e+99)
         (* -2.0 (* (* b i) (* c c)))
         (if (<= c -2.95e-90)
           t_3
           (if (<= c 1300000.0)
             t_1
             (if (<= c 1.1e+76)
               t_3
               (if (<= c 3.25e+186) t_1 (* i (* (* b c) (* c -2.0))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = c * (a * i);
	double t_3 = 2.0 * ((x * y) - t_2);
	double tmp;
	if (c <= -4.35e+158) {
		tmp = (b * (c * i)) * (c * -2.0);
	} else if (c <= -5.7e+125) {
		tmp = 2.0 * ((z * t) - t_2);
	} else if (c <= -3.4e+99) {
		tmp = -2.0 * ((b * i) * (c * c));
	} else if (c <= -2.95e-90) {
		tmp = t_3;
	} else if (c <= 1300000.0) {
		tmp = t_1;
	} else if (c <= 1.1e+76) {
		tmp = t_3;
	} else if (c <= 3.25e+186) {
		tmp = t_1;
	} else {
		tmp = i * ((b * c) * (c * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) + (z * t))
    t_2 = c * (a * i)
    t_3 = 2.0d0 * ((x * y) - t_2)
    if (c <= (-4.35d+158)) then
        tmp = (b * (c * i)) * (c * (-2.0d0))
    else if (c <= (-5.7d+125)) then
        tmp = 2.0d0 * ((z * t) - t_2)
    else if (c <= (-3.4d+99)) then
        tmp = (-2.0d0) * ((b * i) * (c * c))
    else if (c <= (-2.95d-90)) then
        tmp = t_3
    else if (c <= 1300000.0d0) then
        tmp = t_1
    else if (c <= 1.1d+76) then
        tmp = t_3
    else if (c <= 3.25d+186) then
        tmp = t_1
    else
        tmp = i * ((b * c) * (c * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) + (z * t));
	double t_2 = c * (a * i);
	double t_3 = 2.0 * ((x * y) - t_2);
	double tmp;
	if (c <= -4.35e+158) {
		tmp = (b * (c * i)) * (c * -2.0);
	} else if (c <= -5.7e+125) {
		tmp = 2.0 * ((z * t) - t_2);
	} else if (c <= -3.4e+99) {
		tmp = -2.0 * ((b * i) * (c * c));
	} else if (c <= -2.95e-90) {
		tmp = t_3;
	} else if (c <= 1300000.0) {
		tmp = t_1;
	} else if (c <= 1.1e+76) {
		tmp = t_3;
	} else if (c <= 3.25e+186) {
		tmp = t_1;
	} else {
		tmp = i * ((b * c) * (c * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) + (z * t))
	t_2 = c * (a * i)
	t_3 = 2.0 * ((x * y) - t_2)
	tmp = 0
	if c <= -4.35e+158:
		tmp = (b * (c * i)) * (c * -2.0)
	elif c <= -5.7e+125:
		tmp = 2.0 * ((z * t) - t_2)
	elif c <= -3.4e+99:
		tmp = -2.0 * ((b * i) * (c * c))
	elif c <= -2.95e-90:
		tmp = t_3
	elif c <= 1300000.0:
		tmp = t_1
	elif c <= 1.1e+76:
		tmp = t_3
	elif c <= 3.25e+186:
		tmp = t_1
	else:
		tmp = i * ((b * c) * (c * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(c * Float64(a * i))
	t_3 = Float64(2.0 * Float64(Float64(x * y) - t_2))
	tmp = 0.0
	if (c <= -4.35e+158)
		tmp = Float64(Float64(b * Float64(c * i)) * Float64(c * -2.0));
	elseif (c <= -5.7e+125)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	elseif (c <= -3.4e+99)
		tmp = Float64(-2.0 * Float64(Float64(b * i) * Float64(c * c)));
	elseif (c <= -2.95e-90)
		tmp = t_3;
	elseif (c <= 1300000.0)
		tmp = t_1;
	elseif (c <= 1.1e+76)
		tmp = t_3;
	elseif (c <= 3.25e+186)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(b * c) * Float64(c * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) + (z * t));
	t_2 = c * (a * i);
	t_3 = 2.0 * ((x * y) - t_2);
	tmp = 0.0;
	if (c <= -4.35e+158)
		tmp = (b * (c * i)) * (c * -2.0);
	elseif (c <= -5.7e+125)
		tmp = 2.0 * ((z * t) - t_2);
	elseif (c <= -3.4e+99)
		tmp = -2.0 * ((b * i) * (c * c));
	elseif (c <= -2.95e-90)
		tmp = t_3;
	elseif (c <= 1300000.0)
		tmp = t_1;
	elseif (c <= 1.1e+76)
		tmp = t_3;
	elseif (c <= 3.25e+186)
		tmp = t_1;
	else
		tmp = i * ((b * c) * (c * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.35e+158], N[(N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.7e+125], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.4e+99], N[(-2.0 * N[(N[(b * i), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.95e-90], t$95$3, If[LessEqual[c, 1300000.0], t$95$1, If[LessEqual[c, 1.1e+76], t$95$3, If[LessEqual[c, 3.25e+186], t$95$1, N[(i * N[(N[(b * c), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -4.35000000000000012e158

   1. Initial program 65.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf 64.7%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 64.7%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 64.7%

         \[\leadsto 2 \cdot \color{blue}{\left({c}^{2} \cdot \left(-i \cdot b\right)\right)} \]

      3. unpow2 64.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(-i \cdot b\right)\right) \]

   4. Simplified 64.7%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot c\right) \cdot \left(-i \cdot b\right)\right)} \]

   5. Taylor expanded in c around 0 64.7%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 64.7%

         \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

      2. unpow2 64.7%

         \[\leadsto \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \cdot -2 \]

      3. *-commutative 64.7%

         \[\leadsto \left(\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \cdot -2 \]

      4. associate-*r* 72.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)} \cdot -2 \]

      5. *-commutative 72.5%

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(b \cdot i\right)\right) \cdot c\right)} \cdot -2 \]

      6. associate-*l* 72.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(b \cdot i\right)\right) \cdot \left(c \cdot -2\right)} \]

      7. associate-*r* 72.9%

         \[\leadsto \color{blue}{\left(\left(c \cdot b\right) \cdot i\right)} \cdot \left(c \cdot -2\right) \]

      8. *-commutative 72.9%

         \[\leadsto \left(\color{blue}{\left(b \cdot c\right)} \cdot i\right) \cdot \left(c \cdot -2\right) \]

      9. associate-*l* 76.5%

         \[\leadsto \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)} \cdot \left(c \cdot -2\right) \]

   7. Simplified 76.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)} \]

   if -4.35000000000000012e158 < c < -5.6999999999999996e125

   1. Initial program 100.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. *-commutative 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)}\right) \]

      3. flip-+ 75.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot i\right) \cdot \color{blue}{\frac{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}{a - b \cdot c}}\right) \]

      4. associate-*r/ 75.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{\left(c \cdot i\right) \cdot \left(a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)\right)}{a - b \cdot c}}\right) \]

      5. pow2 75.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{\left(c \cdot i\right) \cdot \left(a \cdot a - \color{blue}{{\left(b \cdot c\right)}^{2}}\right)}{a - b \cdot c}\right) \]

   3. Applied egg-rr 75.0%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{\left(c \cdot i\right) \cdot \left(a \cdot a - {\left(b \cdot c\right)}^{2}\right)}{a - b \cdot c}}\right) \]
   4. Step-by-step derivation

      1. associate-/l* 75.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot i}{\frac{a - b \cdot c}{a \cdot a - {\left(b \cdot c\right)}^{2}}}}\right) \]

      2. *-commutative 75.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{a - \color{blue}{c \cdot b}}{a \cdot a - {\left(b \cdot c\right)}^{2}}}\right) \]

      3. *-commutative 75.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{a - c \cdot b}{a \cdot a - {\color{blue}{\left(c \cdot b\right)}}^{2}}}\right) \]

   5. Simplified 75.0%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot i}{\frac{a - c \cdot b}{a \cdot a - {\left(c \cdot b\right)}^{2}}}}\right) \]

   6. Taylor expanded in a around inf 87.5%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\color{blue}{\frac{1}{a}}}\right) \]

   7. Taylor expanded in x around 0 87.5%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot a\right)\right)} \]

   if -5.6999999999999996e125 < c < -3.39999999999999984e99

   1. Initial program 91.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf 61.3%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 61.3%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 61.3%

         \[\leadsto 2 \cdot \color{blue}{\left({c}^{2} \cdot \left(-i \cdot b\right)\right)} \]

      3. unpow2 61.3%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(-i \cdot b\right)\right) \]

   4. Simplified 61.3%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot c\right) \cdot \left(-i \cdot b\right)\right)} \]

   5. Taylor expanded in c around 0 61.3%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 61.3%

         \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

   7. Simplified 61.3%

      \[\leadsto \color{blue}{-2 \cdot \left(\left(c \cdot c\right) \cdot \left(i \cdot b\right)\right)} \]

   if -3.39999999999999984e99 < c < -2.95000000000000002e-90 or 1.3e6 < c < 1.1e76

   1. Initial program 86.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*r* 89.6%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. *-commutative 89.6%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)}\right) \]

      3. flip-+ 57.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot i\right) \cdot \color{blue}{\frac{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}{a - b \cdot c}}\right) \]

      4. associate-*r/ 54.5%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{\left(c \cdot i\right) \cdot \left(a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)\right)}{a - b \cdot c}}\right) \]

      5. pow2 54.5%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{\left(c \cdot i\right) \cdot \left(a \cdot a - \color{blue}{{\left(b \cdot c\right)}^{2}}\right)}{a - b \cdot c}\right) \]

   3. Applied egg-rr 54.5%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{\left(c \cdot i\right) \cdot \left(a \cdot a - {\left(b \cdot c\right)}^{2}\right)}{a - b \cdot c}}\right) \]
   4. Step-by-step derivation

      1. associate-/l* 57.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot i}{\frac{a - b \cdot c}{a \cdot a - {\left(b \cdot c\right)}^{2}}}}\right) \]

      2. *-commutative 57.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{a - \color{blue}{c \cdot b}}{a \cdot a - {\left(b \cdot c\right)}^{2}}}\right) \]

      3. *-commutative 57.7%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{a - c \cdot b}{a \cdot a - {\color{blue}{\left(c \cdot b\right)}}^{2}}}\right) \]

   5. Simplified 57.7%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot i}{\frac{a - c \cdot b}{a \cdot a - {\left(c \cdot b\right)}^{2}}}}\right) \]

   6. Taylor expanded in a around inf 62.6%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\color{blue}{\frac{1}{a}}}\right) \]

   7. Taylor expanded in z around 0 57.7%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot a\right)\right)} \]

   if -2.95000000000000002e-90 < c < 1.3e6 or 1.1e76 < c < 3.2499999999999998e186

   1. Initial program 96.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 74.5%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 3.2499999999999998e186 < c

   1. Initial program 79.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around 0 66.2%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{c}^{2} \cdot \left(i \cdot b\right)}\right) \]
   3. Step-by-step derivation

      1. unpow2 66.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. associate-*r* 78.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   4. Simplified 78.9%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   5. Taylor expanded in z around 0 70.6%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - {c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 70.6%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. *-commutative 70.6%

         \[\leadsto 2 \cdot \left(y \cdot x - \left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      3. associate-*r* 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c \cdot \left(c \cdot \left(b \cdot i\right)\right)}\right) \]

      4. associate-*r* 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(\left(c \cdot b\right) \cdot i\right)}\right) \]

      5. *-commutative 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \left(\color{blue}{\left(b \cdot c\right)} \cdot i\right)\right) \]

      6. associate-*l* 78.9%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]

   7. Simplified 78.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)} \]

   8. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

      2. *-commutative 70.6%

         \[\leadsto \color{blue}{\left(\left(i \cdot b\right) \cdot {c}^{2}\right)} \cdot -2 \]

      3. associate-*l* 70.6%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left({c}^{2} \cdot -2\right)} \]

      4. unpow2 70.6%

         \[\leadsto \left(i \cdot b\right) \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot -2\right) \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(\left(c \cdot c\right) \cdot -2\right)} \]

   11. Taylor expanded in i around 0 70.6%

       \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   12. Step-by-step derivation

       1. unpow2 70.6%

          \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

       2. associate-*r* 70.6%

          \[\leadsto \color{blue}{\left(-2 \cdot \left(c \cdot c\right)\right) \cdot \left(i \cdot b\right)} \]

       3. *-commutative 70.6%

          \[\leadsto \color{blue}{\left(\left(c \cdot c\right) \cdot -2\right)} \cdot \left(i \cdot b\right) \]

       4. associate-*r* 70.6%

          \[\leadsto \color{blue}{\left(c \cdot \left(c \cdot -2\right)\right)} \cdot \left(i \cdot b\right) \]

       5. *-commutative 70.6%

          \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(c \cdot \left(c \cdot -2\right)\right)} \]

       6. associate-*l* 70.6%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(c \cdot \left(c \cdot -2\right)\right)\right)} \]

       7. associate-*r* 74.7%

          \[\leadsto i \cdot \color{blue}{\left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)} \]

       8. *-commutative 74.7%

          \[\leadsto i \cdot \left(\color{blue}{\left(c \cdot b\right)} \cdot \left(c \cdot -2\right)\right) \]

   13. Simplified 74.7%

       \[\leadsto \color{blue}{i \cdot \left(\left(c \cdot b\right) \cdot \left(c \cdot -2\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.35 \cdot 10^{+158}:\\ \;\;\;\;\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq -5.7 \cdot 10^{+125}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{+99}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -2.95 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1300000:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+76}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]

Alternative 7: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(t_2 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-90} \lor \neg \left(c \leq 2.5 \cdot 10^{+19}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_2 - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i)))))
        (t_2 (+ (* x y) (* z t))))
   (if (<= c -1.55e+182)
     t_1
     (if (<= c -5.8e+127)
       (* 2.0 (- t_2 (* c (* c (* b i)))))
       (if (or (<= c -4.5e-90) (not (<= c 2.5e+19)))
         t_1
         (* 2.0 (- t_2 (* i (* a c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (c <= -1.55e+182) {
		tmp = t_1;
	} else if (c <= -5.8e+127) {
		tmp = 2.0 * (t_2 - (c * (c * (b * i))));
	} else if ((c <= -4.5e-90) || !(c <= 2.5e+19)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (t_2 - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    t_2 = (x * y) + (z * t)
    if (c <= (-1.55d+182)) then
        tmp = t_1
    else if (c <= (-5.8d+127)) then
        tmp = 2.0d0 * (t_2 - (c * (c * (b * i))))
    else if ((c <= (-4.5d-90)) .or. (.not. (c <= 2.5d+19))) then
        tmp = t_1
    else
        tmp = 2.0d0 * (t_2 - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	double t_2 = (x * y) + (z * t);
	double tmp;
	if (c <= -1.55e+182) {
		tmp = t_1;
	} else if (c <= -5.8e+127) {
		tmp = 2.0 * (t_2 - (c * (c * (b * i))));
	} else if ((c <= -4.5e-90) || !(c <= 2.5e+19)) {
		tmp = t_1;
	} else {
		tmp = 2.0 * (t_2 - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	t_2 = (x * y) + (z * t)
	tmp = 0
	if c <= -1.55e+182:
		tmp = t_1
	elif c <= -5.8e+127:
		tmp = 2.0 * (t_2 - (c * (c * (b * i))))
	elif (c <= -4.5e-90) or not (c <= 2.5e+19):
		tmp = t_1
	else:
		tmp = 2.0 * (t_2 - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -1.55e+182)
		tmp = t_1;
	elseif (c <= -5.8e+127)
		tmp = Float64(2.0 * Float64(t_2 - Float64(c * Float64(c * Float64(b * i)))));
	elseif ((c <= -4.5e-90) || !(c <= 2.5e+19))
		tmp = t_1;
	else
		tmp = Float64(2.0 * Float64(t_2 - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -1.55e+182)
		tmp = t_1;
	elseif (c <= -5.8e+127)
		tmp = 2.0 * (t_2 - (c * (c * (b * i))));
	elseif ((c <= -4.5e-90) || ~((c <= 2.5e+19)))
		tmp = t_1;
	else
		tmp = 2.0 * (t_2 - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+182], t$95$1, If[LessEqual[c, -5.8e+127], N[(2.0 * N[(t$95$2 - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, -4.5e-90], N[Not[LessEqual[c, 2.5e+19]], $MachinePrecision]], t$95$1, N[(2.0 * N[(t$95$2 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.54999999999999998e182 or -5.8000000000000004e127 < c < -4.50000000000000009e-90 or 2.5e19 < c

   1. Initial program 80.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 87.3%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   if -1.54999999999999998e182 < c < -5.8000000000000004e127

   1. Initial program 90.9%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around 0 81.8%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{c}^{2} \cdot \left(i \cdot b\right)}\right) \]
   3. Step-by-step derivation

      1. unpow2 81.8%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. associate-*r* 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   4. Simplified 100.0%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   if -4.50000000000000009e-90 < c < 2.5e19

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf 91.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+182}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+127}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-90} \lor \neg \left(c \leq 2.5 \cdot 10^{+19}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 8: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-90} \lor \neg \left(c \leq 70\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.5e-90) (not (<= c 70.0)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.5e-90) || !(c <= 70.0)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.5d-90)) .or. (.not. (c <= 70.0d0))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.5e-90) || !(c <= 70.0)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.5e-90) or not (c <= 70.0):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.5e-90) || !(c <= 70.0))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.5e-90) || ~((c <= 70.0)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.5e-90], N[Not[LessEqual[c, 70.0]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.4999999999999999e-90 or 70 < c

   1. Initial program 82.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 83.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   if -3.4999999999999999e-90 < c < 70

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 78.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-90} \lor \neg \left(c \leq 70\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 9: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-90} \lor \neg \left(c \leq 2.9 \cdot 10^{+19}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4.5e-90) (not (<= c 2.9e+19)))
   (* 2.0 (- (* x y) (* c (* (+ a (* b c)) i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.5e-90) || !(c <= 2.9e+19)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-4.5d-90)) .or. (.not. (c <= 2.9d+19))) then
        tmp = 2.0d0 * ((x * y) - (c * ((a + (b * c)) * i)))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.5e-90) || !(c <= 2.9e+19)) {
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -4.5e-90) or not (c <= 2.9e+19):
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -4.5e-90) || !(c <= 2.9e+19))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -4.5e-90) || ~((c <= 2.9e+19)))
		tmp = 2.0 * ((x * y) - (c * ((a + (b * c)) * i)));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -4.5e-90], N[Not[LessEqual[c, 2.9e+19]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.50000000000000009e-90 or 2.9e19 < c

   1. Initial program 81.7%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around 0 84.2%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)} \]

   if -4.50000000000000009e-90 < c < 2.9e19

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf 91.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-90} \lor \neg \left(c \leq 2.9 \cdot 10^{+19}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 10: 36.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(\left(a \cdot i\right) \cdot \left(-c\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -5800000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* 2.0 (* (* a i) (- c))))
        (t_3 (* 2.0 (* x y))))
   (if (<= y -5800000000.0)
     t_3
     (if (<= y -3.15e-263)
       t_1
       (if (<= y 5e-222)
         t_2
         (if (<= y 1.4e-48) t_1 (if (<= y 3.9e+123) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * ((a * i) * -c);
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (y <= -5800000000.0) {
		tmp = t_3;
	} else if (y <= -3.15e-263) {
		tmp = t_1;
	} else if (y <= 5e-222) {
		tmp = t_2;
	} else if (y <= 1.4e-48) {
		tmp = t_1;
	} else if (y <= 3.9e+123) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * ((a * i) * -c)
    t_3 = 2.0d0 * (x * y)
    if (y <= (-5800000000.0d0)) then
        tmp = t_3
    else if (y <= (-3.15d-263)) then
        tmp = t_1
    else if (y <= 5d-222) then
        tmp = t_2
    else if (y <= 1.4d-48) then
        tmp = t_1
    else if (y <= 3.9d+123) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * ((a * i) * -c);
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (y <= -5800000000.0) {
		tmp = t_3;
	} else if (y <= -3.15e-263) {
		tmp = t_1;
	} else if (y <= 5e-222) {
		tmp = t_2;
	} else if (y <= 1.4e-48) {
		tmp = t_1;
	} else if (y <= 3.9e+123) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * ((a * i) * -c)
	t_3 = 2.0 * (x * y)
	tmp = 0
	if y <= -5800000000.0:
		tmp = t_3
	elif y <= -3.15e-263:
		tmp = t_1
	elif y <= 5e-222:
		tmp = t_2
	elif y <= 1.4e-48:
		tmp = t_1
	elif y <= 3.9e+123:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(Float64(a * i) * Float64(-c)))
	t_3 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -5800000000.0)
		tmp = t_3;
	elseif (y <= -3.15e-263)
		tmp = t_1;
	elseif (y <= 5e-222)
		tmp = t_2;
	elseif (y <= 1.4e-48)
		tmp = t_1;
	elseif (y <= 3.9e+123)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * ((a * i) * -c);
	t_3 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -5800000000.0)
		tmp = t_3;
	elseif (y <= -3.15e-263)
		tmp = t_1;
	elseif (y <= 5e-222)
		tmp = t_2;
	elseif (y <= 1.4e-48)
		tmp = t_1;
	elseif (y <= 3.9e+123)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(a * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5800000000.0], t$95$3, If[LessEqual[y, -3.15e-263], t$95$1, If[LessEqual[y, 5e-222], t$95$2, If[LessEqual[y, 1.4e-48], t$95$1, If[LessEqual[y, 3.9e+123], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8e9 or 3.89999999999999993e123 < y

   1. Initial program 86.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf 57.5%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -5.8e9 < y < -3.14999999999999986e-263 or 5.00000000000000008e-222 < y < 1.40000000000000002e-48

   1. Initial program 93.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf 32.6%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -3.14999999999999986e-263 < y < 5.00000000000000008e-222 or 1.40000000000000002e-48 < y < 3.89999999999999993e123

   1. Initial program 86.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf 27.1%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot a\right)\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 27.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(i \cdot a\right)\right)} \]

      2. neg-mul-1 27.1%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(i \cdot a\right)\right) \]

   4. Simplified 27.1%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5800000000:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{-263}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-222}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-48}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 11: 37.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -12000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-221}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= y -12000000.0)
     t_2
     (if (<= y -3.8e-261)
       t_1
       (if (<= y 4.4e-221)
         (* 2.0 (* (* a i) (- c)))
         (if (<= y 1.22e-49)
           t_1
           (if (<= y 3.8e+123) (* 2.0 (* i (* a (- c)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -12000000.0) {
		tmp = t_2;
	} else if (y <= -3.8e-261) {
		tmp = t_1;
	} else if (y <= 4.4e-221) {
		tmp = 2.0 * ((a * i) * -c);
	} else if (y <= 1.22e-49) {
		tmp = t_1;
	} else if (y <= 3.8e+123) {
		tmp = 2.0 * (i * (a * -c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (y <= (-12000000.0d0)) then
        tmp = t_2
    else if (y <= (-3.8d-261)) then
        tmp = t_1
    else if (y <= 4.4d-221) then
        tmp = 2.0d0 * ((a * i) * -c)
    else if (y <= 1.22d-49) then
        tmp = t_1
    else if (y <= 3.8d+123) then
        tmp = 2.0d0 * (i * (a * -c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -12000000.0) {
		tmp = t_2;
	} else if (y <= -3.8e-261) {
		tmp = t_1;
	} else if (y <= 4.4e-221) {
		tmp = 2.0 * ((a * i) * -c);
	} else if (y <= 1.22e-49) {
		tmp = t_1;
	} else if (y <= 3.8e+123) {
		tmp = 2.0 * (i * (a * -c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if y <= -12000000.0:
		tmp = t_2
	elif y <= -3.8e-261:
		tmp = t_1
	elif y <= 4.4e-221:
		tmp = 2.0 * ((a * i) * -c)
	elif y <= 1.22e-49:
		tmp = t_1
	elif y <= 3.8e+123:
		tmp = 2.0 * (i * (a * -c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -12000000.0)
		tmp = t_2;
	elseif (y <= -3.8e-261)
		tmp = t_1;
	elseif (y <= 4.4e-221)
		tmp = Float64(2.0 * Float64(Float64(a * i) * Float64(-c)));
	elseif (y <= 1.22e-49)
		tmp = t_1;
	elseif (y <= 3.8e+123)
		tmp = Float64(2.0 * Float64(i * Float64(a * Float64(-c))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -12000000.0)
		tmp = t_2;
	elseif (y <= -3.8e-261)
		tmp = t_1;
	elseif (y <= 4.4e-221)
		tmp = 2.0 * ((a * i) * -c);
	elseif (y <= 1.22e-49)
		tmp = t_1;
	elseif (y <= 3.8e+123)
		tmp = 2.0 * (i * (a * -c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -12000000.0], t$95$2, If[LessEqual[y, -3.8e-261], t$95$1, If[LessEqual[y, 4.4e-221], N[(2.0 * N[(N[(a * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e-49], t$95$1, If[LessEqual[y, 3.8e+123], N[(2.0 * N[(i * N[(a * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2e7 or 3.79999999999999994e123 < y

   1. Initial program 86.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf 57.5%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -1.2e7 < y < -3.8e-261 or 4.40000000000000003e-221 < y < 1.2199999999999999e-49

   1. Initial program 93.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf 32.6%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if -3.8e-261 < y < 4.40000000000000003e-221

   1. Initial program 90.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around inf 25.5%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot a\right)\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 25.5%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(-1 \cdot c\right) \cdot \left(i \cdot a\right)\right)} \]

      2. neg-mul-1 25.5%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(-c\right)} \cdot \left(i \cdot a\right)\right) \]

   4. Simplified 25.5%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(-c\right) \cdot \left(i \cdot a\right)\right)} \]

   if 1.2199999999999999e-49 < y < 3.79999999999999994e123

   1. Initial program 81.8%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*l* 92.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. fma-def 92.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 92.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(x \cdot y + z \cdot t\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

      2. +-commutative 92.4%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   5. Applied egg-rr 92.4%

      \[\leadsto 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

   6. Taylor expanded in a around inf 29.0%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot a\right)\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 29.0%

         \[\leadsto 2 \cdot \color{blue}{\left(-c \cdot \left(i \cdot a\right)\right)} \]

      2. *-commutative 29.0%

         \[\leadsto 2 \cdot \left(-c \cdot \color{blue}{\left(a \cdot i\right)}\right) \]

      3. associate-*r* 39.2%

         \[\leadsto 2 \cdot \left(-\color{blue}{\left(c \cdot a\right) \cdot i}\right) \]

      4. distribute-rgt-neg-in 39.2%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot a\right) \cdot \left(-i\right)\right)} \]

   8. Simplified 39.2%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot a\right) \cdot \left(-i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12000000:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-221}:\\ \;\;\;\;2 \cdot \left(\left(a \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-49}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(a \cdot \left(-c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 66.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+157}:\\ \;\;\;\;\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{+43}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -9.5e+157)
   (* (* b (* c i)) (* c -2.0))
   (if (<= c -1.5e+70)
     (* 2.0 (- (* z t) (* c (* a i))))
     (if (<= c -4.5e+43)
       (* -2.0 (* (* b i) (* c c)))
       (if (<= c 3.25e+186)
         (* 2.0 (+ (* x y) (* z t)))
         (* i (* (* b c) (* c -2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -9.5e+157) {
		tmp = (b * (c * i)) * (c * -2.0);
	} else if (c <= -1.5e+70) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (c <= -4.5e+43) {
		tmp = -2.0 * ((b * i) * (c * c));
	} else if (c <= 3.25e+186) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = i * ((b * c) * (c * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-9.5d+157)) then
        tmp = (b * (c * i)) * (c * (-2.0d0))
    else if (c <= (-1.5d+70)) then
        tmp = 2.0d0 * ((z * t) - (c * (a * i)))
    else if (c <= (-4.5d+43)) then
        tmp = (-2.0d0) * ((b * i) * (c * c))
    else if (c <= 3.25d+186) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = i * ((b * c) * (c * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -9.5e+157) {
		tmp = (b * (c * i)) * (c * -2.0);
	} else if (c <= -1.5e+70) {
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	} else if (c <= -4.5e+43) {
		tmp = -2.0 * ((b * i) * (c * c));
	} else if (c <= 3.25e+186) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = i * ((b * c) * (c * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -9.5e+157:
		tmp = (b * (c * i)) * (c * -2.0)
	elif c <= -1.5e+70:
		tmp = 2.0 * ((z * t) - (c * (a * i)))
	elif c <= -4.5e+43:
		tmp = -2.0 * ((b * i) * (c * c))
	elif c <= 3.25e+186:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = i * ((b * c) * (c * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -9.5e+157)
		tmp = Float64(Float64(b * Float64(c * i)) * Float64(c * -2.0));
	elseif (c <= -1.5e+70)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(a * i))));
	elseif (c <= -4.5e+43)
		tmp = Float64(-2.0 * Float64(Float64(b * i) * Float64(c * c)));
	elseif (c <= 3.25e+186)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(i * Float64(Float64(b * c) * Float64(c * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -9.5e+157)
		tmp = (b * (c * i)) * (c * -2.0);
	elseif (c <= -1.5e+70)
		tmp = 2.0 * ((z * t) - (c * (a * i)));
	elseif (c <= -4.5e+43)
		tmp = -2.0 * ((b * i) * (c * c));
	elseif (c <= 3.25e+186)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = i * ((b * c) * (c * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -9.5e+157], N[(N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.5e+70], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.5e+43], N[(-2.0 * N[(N[(b * i), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.25e+186], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(b * c), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -9.4999999999999996e157

   1. Initial program 65.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf 64.7%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 64.7%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 64.7%

         \[\leadsto 2 \cdot \color{blue}{\left({c}^{2} \cdot \left(-i \cdot b\right)\right)} \]

      3. unpow2 64.7%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(-i \cdot b\right)\right) \]

   4. Simplified 64.7%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot c\right) \cdot \left(-i \cdot b\right)\right)} \]

   5. Taylor expanded in c around 0 64.7%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 64.7%

         \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

      2. unpow2 64.7%

         \[\leadsto \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \cdot -2 \]

      3. *-commutative 64.7%

         \[\leadsto \left(\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \cdot -2 \]

      4. associate-*r* 72.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)} \cdot -2 \]

      5. *-commutative 72.5%

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(b \cdot i\right)\right) \cdot c\right)} \cdot -2 \]

      6. associate-*l* 72.5%

         \[\leadsto \color{blue}{\left(c \cdot \left(b \cdot i\right)\right) \cdot \left(c \cdot -2\right)} \]

      7. associate-*r* 72.9%

         \[\leadsto \color{blue}{\left(\left(c \cdot b\right) \cdot i\right)} \cdot \left(c \cdot -2\right) \]

      8. *-commutative 72.9%

         \[\leadsto \left(\color{blue}{\left(b \cdot c\right)} \cdot i\right) \cdot \left(c \cdot -2\right) \]

      9. associate-*l* 76.5%

         \[\leadsto \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)} \cdot \left(c \cdot -2\right) \]

   7. Simplified 76.5%

      \[\leadsto \color{blue}{\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)} \]

   if -9.4999999999999996e157 < c < -1.49999999999999988e70

   1. Initial program 91.6%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \]

      2. *-commutative 100.0%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot i\right) \cdot \left(a + b \cdot c\right)}\right) \]

      3. flip-+ 73.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot i\right) \cdot \color{blue}{\frac{a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)}{a - b \cdot c}}\right) \]

      4. associate-*r/ 69.1%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{\left(c \cdot i\right) \cdot \left(a \cdot a - \left(b \cdot c\right) \cdot \left(b \cdot c\right)\right)}{a - b \cdot c}}\right) \]

      5. pow2 69.1%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{\left(c \cdot i\right) \cdot \left(a \cdot a - \color{blue}{{\left(b \cdot c\right)}^{2}}\right)}{a - b \cdot c}\right) \]

   3. Applied egg-rr 69.1%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{\left(c \cdot i\right) \cdot \left(a \cdot a - {\left(b \cdot c\right)}^{2}\right)}{a - b \cdot c}}\right) \]
   4. Step-by-step derivation

      1. associate-/l* 73.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot i}{\frac{a - b \cdot c}{a \cdot a - {\left(b \cdot c\right)}^{2}}}}\right) \]

      2. *-commutative 73.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{a - \color{blue}{c \cdot b}}{a \cdot a - {\left(b \cdot c\right)}^{2}}}\right) \]

      3. *-commutative 73.4%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\frac{a - c \cdot b}{a \cdot a - {\color{blue}{\left(c \cdot b\right)}}^{2}}}\right) \]

   5. Simplified 73.4%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\frac{c \cdot i}{\frac{a - c \cdot b}{a \cdot a - {\left(c \cdot b\right)}^{2}}}}\right) \]

   6. Taylor expanded in a around inf 73.3%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \frac{c \cdot i}{\color{blue}{\frac{1}{a}}}\right) \]

   7. Taylor expanded in x around 0 64.4%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z - c \cdot \left(i \cdot a\right)\right)} \]

   if -1.49999999999999988e70 < c < -4.5e43

   1. Initial program 36.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf 100.0%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 100.0%

         \[\leadsto 2 \cdot \color{blue}{\left({c}^{2} \cdot \left(-i \cdot b\right)\right)} \]

      3. unpow2 100.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(-i \cdot b\right)\right) \]

   4. Simplified 100.0%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot c\right) \cdot \left(-i \cdot b\right)\right)} \]

   5. Taylor expanded in c around 0 100.0%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 100.0%

         \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{-2 \cdot \left(\left(c \cdot c\right) \cdot \left(i \cdot b\right)\right)} \]

   if -4.5e43 < c < 3.2499999999999998e186

   1. Initial program 94.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 65.0%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 3.2499999999999998e186 < c

   1. Initial program 79.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around 0 66.2%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{c}^{2} \cdot \left(i \cdot b\right)}\right) \]
   3. Step-by-step derivation

      1. unpow2 66.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. associate-*r* 78.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   4. Simplified 78.9%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   5. Taylor expanded in z around 0 70.6%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - {c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 70.6%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. *-commutative 70.6%

         \[\leadsto 2 \cdot \left(y \cdot x - \left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      3. associate-*r* 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c \cdot \left(c \cdot \left(b \cdot i\right)\right)}\right) \]

      4. associate-*r* 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(\left(c \cdot b\right) \cdot i\right)}\right) \]

      5. *-commutative 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \left(\color{blue}{\left(b \cdot c\right)} \cdot i\right)\right) \]

      6. associate-*l* 78.9%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]

   7. Simplified 78.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)} \]

   8. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

      2. *-commutative 70.6%

         \[\leadsto \color{blue}{\left(\left(i \cdot b\right) \cdot {c}^{2}\right)} \cdot -2 \]

      3. associate-*l* 70.6%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left({c}^{2} \cdot -2\right)} \]

      4. unpow2 70.6%

         \[\leadsto \left(i \cdot b\right) \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot -2\right) \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(\left(c \cdot c\right) \cdot -2\right)} \]

   11. Taylor expanded in i around 0 70.6%

       \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   12. Step-by-step derivation

       1. unpow2 70.6%

          \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

       2. associate-*r* 70.6%

          \[\leadsto \color{blue}{\left(-2 \cdot \left(c \cdot c\right)\right) \cdot \left(i \cdot b\right)} \]

       3. *-commutative 70.6%

          \[\leadsto \color{blue}{\left(\left(c \cdot c\right) \cdot -2\right)} \cdot \left(i \cdot b\right) \]

       4. associate-*r* 70.6%

          \[\leadsto \color{blue}{\left(c \cdot \left(c \cdot -2\right)\right)} \cdot \left(i \cdot b\right) \]

       5. *-commutative 70.6%

          \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(c \cdot \left(c \cdot -2\right)\right)} \]

       6. associate-*l* 70.6%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(c \cdot \left(c \cdot -2\right)\right)\right)} \]

       7. associate-*r* 74.7%

          \[\leadsto i \cdot \color{blue}{\left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)} \]

       8. *-commutative 74.7%

          \[\leadsto i \cdot \left(\color{blue}{\left(c \cdot b\right)} \cdot \left(c \cdot -2\right)\right) \]

   13. Simplified 74.7%

       \[\leadsto \color{blue}{i \cdot \left(\left(c \cdot b\right) \cdot \left(c \cdot -2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+157}:\\ \;\;\;\;\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{+70}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{+43}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]

Alternative 13: 71.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -4.5e-90)
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (if (<= c 2.5e+19)
     (* 2.0 (+ (* x y) (* z t)))
     (* 2.0 (- (* x y) (* c (* b (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -4.5e-90) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else if (c <= 2.5e+19) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-4.5d-90)) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else if (c <= 2.5d+19) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = 2.0d0 * ((x * y) - (c * (b * (c * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -4.5e-90) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else if (c <= 2.5e+19) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -4.5e-90:
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	elif c <= 2.5e+19:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -4.5e-90)
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	elseif (c <= 2.5e+19)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(c * Float64(b * Float64(c * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -4.5e-90)
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	elseif (c <= 2.5e+19)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = 2.0 * ((x * y) - (c * (b * (c * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -4.5e-90], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+19], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.50000000000000009e-90

   1. Initial program 81.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf 67.3%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)\right)} \]

   if -4.50000000000000009e-90 < c < 2.5e19

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 76.3%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 2.5e19 < c

   1. Initial program 82.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around 0 69.3%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{c}^{2} \cdot \left(i \cdot b\right)}\right) \]
   3. Step-by-step derivation

      1. unpow2 69.3%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. associate-*r* 77.5%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   4. Simplified 77.5%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   5. Taylor expanded in z around 0 67.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - {c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 67.9%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. *-commutative 67.9%

         \[\leadsto 2 \cdot \left(y \cdot x - \left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      3. associate-*r* 74.3%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c \cdot \left(c \cdot \left(b \cdot i\right)\right)}\right) \]

      4. associate-*r* 74.2%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(\left(c \cdot b\right) \cdot i\right)}\right) \]

      5. *-commutative 74.2%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \left(\color{blue}{\left(b \cdot c\right)} \cdot i\right)\right) \]

      6. associate-*l* 75.8%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]

   7. Simplified 75.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-90}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+19}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 14: 73.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.65 \cdot 10^{-90} \lor \neg \left(c \leq 205\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3.65e-90) (not (<= c 205.0)))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.65e-90) || !(c <= 205.0)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-3.65d-90)) .or. (.not. (c <= 205.0d0))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -3.65e-90) || !(c <= 205.0)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -3.65e-90) or not (c <= 205.0):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -3.65e-90) || !(c <= 205.0))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -3.65e-90) || ~((c <= 205.0)))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -3.65e-90], N[Not[LessEqual[c, 205.0]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.64999999999999999e-90 or 205 < c

   1. Initial program 82.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in i around inf 68.3%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)\right)} \]

   if -3.64999999999999999e-90 < c < 205

   1. Initial program 99.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 78.1%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.65 \cdot 10^{-90} \lor \neg \left(c \leq 205\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 15: 46.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-170}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* (* b i) (* c c)))))
   (if (<= c -4e-73)
     t_1
     (if (<= c 5.1e-170)
       (* 2.0 (* z t))
       (if (<= c 2.5e+83) (* 2.0 (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * ((b * i) * (c * c));
	double tmp;
	if (c <= -4e-73) {
		tmp = t_1;
	} else if (c <= 5.1e-170) {
		tmp = 2.0 * (z * t);
	} else if (c <= 2.5e+83) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) * ((b * i) * (c * c))
    if (c <= (-4d-73)) then
        tmp = t_1
    else if (c <= 5.1d-170) then
        tmp = 2.0d0 * (z * t)
    else if (c <= 2.5d+83) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * ((b * i) * (c * c));
	double tmp;
	if (c <= -4e-73) {
		tmp = t_1;
	} else if (c <= 5.1e-170) {
		tmp = 2.0 * (z * t);
	} else if (c <= 2.5e+83) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * ((b * i) * (c * c))
	tmp = 0
	if c <= -4e-73:
		tmp = t_1
	elif c <= 5.1e-170:
		tmp = 2.0 * (z * t)
	elif c <= 2.5e+83:
		tmp = 2.0 * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(Float64(b * i) * Float64(c * c)))
	tmp = 0.0
	if (c <= -4e-73)
		tmp = t_1;
	elseif (c <= 5.1e-170)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (c <= 2.5e+83)
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * ((b * i) * (c * c));
	tmp = 0.0;
	if (c <= -4e-73)
		tmp = t_1;
	elseif (c <= 5.1e-170)
		tmp = 2.0 * (z * t);
	elseif (c <= 2.5e+83)
		tmp = 2.0 * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(N[(b * i), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4e-73], t$95$1, If[LessEqual[c, 5.1e-170], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+83], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.99999999999999999e-73 or 2.50000000000000014e83 < c

   1. Initial program 81.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf 52.0%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 52.0%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 52.0%

         \[\leadsto 2 \cdot \color{blue}{\left({c}^{2} \cdot \left(-i \cdot b\right)\right)} \]

      3. unpow2 52.0%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(-i \cdot b\right)\right) \]

   4. Simplified 52.0%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot c\right) \cdot \left(-i \cdot b\right)\right)} \]

   5. Taylor expanded in c around 0 52.0%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 52.0%

         \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

   7. Simplified 52.0%

      \[\leadsto \color{blue}{-2 \cdot \left(\left(c \cdot c\right) \cdot \left(i \cdot b\right)\right)} \]

   if -3.99999999999999999e-73 < c < 5.09999999999999982e-170

   1. Initial program 97.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf 46.2%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

   if 5.09999999999999982e-170 < c < 2.50000000000000014e83

   1. Initial program 96.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf 43.7%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-73}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 5.1 \cdot 10^{-170}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \end{array} \]

Alternative 16: 66.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+54} \lor \neg \left(c \leq 3.3 \cdot 10^{+186}\right):\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.5e+54) (not (<= c 3.3e+186)))
   (* -2.0 (* (* b i) (* c c)))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.5e+54) || !(c <= 3.3e+186)) {
		tmp = -2.0 * ((b * i) * (c * c));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.5d+54)) .or. (.not. (c <= 3.3d+186))) then
        tmp = (-2.0d0) * ((b * i) * (c * c))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.5e+54) || !(c <= 3.3e+186)) {
		tmp = -2.0 * ((b * i) * (c * c));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.5e+54) or not (c <= 3.3e+186):
		tmp = -2.0 * ((b * i) * (c * c))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.5e+54) || !(c <= 3.3e+186))
		tmp = Float64(-2.0 * Float64(Float64(b * i) * Float64(c * c)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.5e+54) || ~((c <= 3.3e+186)))
		tmp = -2.0 * ((b * i) * (c * c));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.5e+54], N[Not[LessEqual[c, 3.3e+186]], $MachinePrecision]], N[(-2.0 * N[(N[(b * i), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.50000000000000003e54 or 3.30000000000000023e186 < c

   1. Initial program 76.4%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf 62.5%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 62.5%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 62.5%

         \[\leadsto 2 \cdot \color{blue}{\left({c}^{2} \cdot \left(-i \cdot b\right)\right)} \]

      3. unpow2 62.5%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(-i \cdot b\right)\right) \]

   4. Simplified 62.5%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot c\right) \cdot \left(-i \cdot b\right)\right)} \]

   5. Taylor expanded in c around 0 62.5%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 62.5%

         \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

   7. Simplified 62.5%

      \[\leadsto \color{blue}{-2 \cdot \left(\left(c \cdot c\right) \cdot \left(i \cdot b\right)\right)} \]

   if -2.50000000000000003e54 < c < 3.30000000000000023e186

   1. Initial program 94.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 65.0%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+54} \lor \neg \left(c \leq 3.3 \cdot 10^{+186}\right):\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 17: 66.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.8e+49)
   (* -2.0 (* (* b i) (* c c)))
   (if (<= c 3.25e+186)
     (* 2.0 (+ (* x y) (* z t)))
     (* i (* (* b c) (* c -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.8e+49) {
		tmp = -2.0 * ((b * i) * (c * c));
	} else if (c <= 3.25e+186) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = i * ((b * c) * (c * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-1.8d+49)) then
        tmp = (-2.0d0) * ((b * i) * (c * c))
    else if (c <= 3.25d+186) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = i * ((b * c) * (c * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.8e+49) {
		tmp = -2.0 * ((b * i) * (c * c));
	} else if (c <= 3.25e+186) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = i * ((b * c) * (c * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.8e+49:
		tmp = -2.0 * ((b * i) * (c * c))
	elif c <= 3.25e+186:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = i * ((b * c) * (c * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.8e+49)
		tmp = Float64(-2.0 * Float64(Float64(b * i) * Float64(c * c)));
	elseif (c <= 3.25e+186)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(i * Float64(Float64(b * c) * Float64(c * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1.8e+49)
		tmp = -2.0 * ((b * i) * (c * c));
	elseif (c <= 3.25e+186)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = i * ((b * c) * (c * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.8e+49], N[(-2.0 * N[(N[(b * i), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.25e+186], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(b * c), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.79999999999999998e49

   1. Initial program 75.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf 58.8%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 58.8%

         \[\leadsto 2 \cdot \color{blue}{\left({c}^{2} \cdot \left(-i \cdot b\right)\right)} \]

      3. unpow2 58.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(-i \cdot b\right)\right) \]

   4. Simplified 58.8%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot c\right) \cdot \left(-i \cdot b\right)\right)} \]

   5. Taylor expanded in c around 0 58.8%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 58.8%

         \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

   7. Simplified 58.8%

      \[\leadsto \color{blue}{-2 \cdot \left(\left(c \cdot c\right) \cdot \left(i \cdot b\right)\right)} \]

   if -1.79999999999999998e49 < c < 3.2499999999999998e186

   1. Initial program 94.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 65.0%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 3.2499999999999998e186 < c

   1. Initial program 79.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around 0 66.2%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{c}^{2} \cdot \left(i \cdot b\right)}\right) \]
   3. Step-by-step derivation

      1. unpow2 66.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. associate-*r* 78.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   4. Simplified 78.9%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   5. Taylor expanded in z around 0 70.6%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - {c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 70.6%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. *-commutative 70.6%

         \[\leadsto 2 \cdot \left(y \cdot x - \left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      3. associate-*r* 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c \cdot \left(c \cdot \left(b \cdot i\right)\right)}\right) \]

      4. associate-*r* 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(\left(c \cdot b\right) \cdot i\right)}\right) \]

      5. *-commutative 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \left(\color{blue}{\left(b \cdot c\right)} \cdot i\right)\right) \]

      6. associate-*l* 78.9%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]

   7. Simplified 78.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)} \]

   8. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

      2. *-commutative 70.6%

         \[\leadsto \color{blue}{\left(\left(i \cdot b\right) \cdot {c}^{2}\right)} \cdot -2 \]

      3. associate-*l* 70.6%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left({c}^{2} \cdot -2\right)} \]

      4. unpow2 70.6%

         \[\leadsto \left(i \cdot b\right) \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot -2\right) \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(\left(c \cdot c\right) \cdot -2\right)} \]

   11. Taylor expanded in i around 0 70.6%

       \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   12. Step-by-step derivation

       1. unpow2 70.6%

          \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

       2. associate-*r* 70.6%

          \[\leadsto \color{blue}{\left(-2 \cdot \left(c \cdot c\right)\right) \cdot \left(i \cdot b\right)} \]

       3. *-commutative 70.6%

          \[\leadsto \color{blue}{\left(\left(c \cdot c\right) \cdot -2\right)} \cdot \left(i \cdot b\right) \]

       4. associate-*r* 70.6%

          \[\leadsto \color{blue}{\left(c \cdot \left(c \cdot -2\right)\right)} \cdot \left(i \cdot b\right) \]

       5. *-commutative 70.6%

          \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(c \cdot \left(c \cdot -2\right)\right)} \]

       6. associate-*l* 70.6%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(c \cdot \left(c \cdot -2\right)\right)\right)} \]

       7. associate-*r* 74.7%

          \[\leadsto i \cdot \color{blue}{\left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)} \]

       8. *-commutative 74.7%

          \[\leadsto i \cdot \left(\color{blue}{\left(c \cdot b\right)} \cdot \left(c \cdot -2\right)\right) \]

   13. Simplified 74.7%

       \[\leadsto \color{blue}{i \cdot \left(\left(c \cdot b\right) \cdot \left(c \cdot -2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{+49}:\\ \;\;\;\;-2 \cdot \left(\left(b \cdot i\right) \cdot \left(c \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]

Alternative 18: 66.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+51}:\\ \;\;\;\;\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -3.8e+51)
   (* (* b (* c i)) (* c -2.0))
   (if (<= c 3.25e+186)
     (* 2.0 (+ (* x y) (* z t)))
     (* i (* (* b c) (* c -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3.8e+51) {
		tmp = (b * (c * i)) * (c * -2.0);
	} else if (c <= 3.25e+186) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = i * ((b * c) * (c * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-3.8d+51)) then
        tmp = (b * (c * i)) * (c * (-2.0d0))
    else if (c <= 3.25d+186) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = i * ((b * c) * (c * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -3.8e+51) {
		tmp = (b * (c * i)) * (c * -2.0);
	} else if (c <= 3.25e+186) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = i * ((b * c) * (c * -2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -3.8e+51:
		tmp = (b * (c * i)) * (c * -2.0)
	elif c <= 3.25e+186:
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = i * ((b * c) * (c * -2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -3.8e+51)
		tmp = Float64(Float64(b * Float64(c * i)) * Float64(c * -2.0));
	elseif (c <= 3.25e+186)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(i * Float64(Float64(b * c) * Float64(c * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -3.8e+51)
		tmp = (b * (c * i)) * (c * -2.0);
	elseif (c <= 3.25e+186)
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = i * ((b * c) * (c * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -3.8e+51], N[(N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.25e+186], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(b * c), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.7999999999999997e51

   1. Initial program 75.2%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in b around inf 58.8%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto 2 \cdot \color{blue}{\left(-{c}^{2} \cdot \left(i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-in 58.8%

         \[\leadsto 2 \cdot \color{blue}{\left({c}^{2} \cdot \left(-i \cdot b\right)\right)} \]

      3. unpow2 58.8%

         \[\leadsto 2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(-i \cdot b\right)\right) \]

   4. Simplified 58.8%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(c \cdot c\right) \cdot \left(-i \cdot b\right)\right)} \]

   5. Taylor expanded in c around 0 58.8%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 58.8%

         \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

      2. unpow2 58.8%

         \[\leadsto \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \cdot -2 \]

      3. *-commutative 58.8%

         \[\leadsto \left(\left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \cdot -2 \]

      4. associate-*r* 60.8%

         \[\leadsto \color{blue}{\left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)} \cdot -2 \]

      5. *-commutative 60.8%

         \[\leadsto \color{blue}{\left(\left(c \cdot \left(b \cdot i\right)\right) \cdot c\right)} \cdot -2 \]

      6. associate-*l* 60.8%

         \[\leadsto \color{blue}{\left(c \cdot \left(b \cdot i\right)\right) \cdot \left(c \cdot -2\right)} \]

      7. associate-*r* 59.0%

         \[\leadsto \color{blue}{\left(\left(c \cdot b\right) \cdot i\right)} \cdot \left(c \cdot -2\right) \]

      8. *-commutative 59.0%

         \[\leadsto \left(\color{blue}{\left(b \cdot c\right)} \cdot i\right) \cdot \left(c \cdot -2\right) \]

      9. associate-*l* 62.7%

         \[\leadsto \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)} \cdot \left(c \cdot -2\right) \]

   7. Simplified 62.7%

      \[\leadsto \color{blue}{\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)} \]

   if -3.7999999999999997e51 < c < 3.2499999999999998e186

   1. Initial program 94.5%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in c around 0 65.0%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x + t \cdot z\right)} \]

   if 3.2499999999999998e186 < c

   1. Initial program 79.1%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in a around 0 66.2%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{{c}^{2} \cdot \left(i \cdot b\right)}\right) \]
   3. Step-by-step derivation

      1. unpow2 66.2%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. associate-*r* 78.9%

         \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   4. Simplified 78.9%

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(c \cdot \left(i \cdot b\right)\right)}\right) \]

   5. Taylor expanded in z around 0 70.6%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - {c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. unpow2 70.6%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

      2. *-commutative 70.6%

         \[\leadsto 2 \cdot \left(y \cdot x - \left(c \cdot c\right) \cdot \color{blue}{\left(b \cdot i\right)}\right) \]

      3. associate-*r* 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - \color{blue}{c \cdot \left(c \cdot \left(b \cdot i\right)\right)}\right) \]

      4. associate-*r* 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(\left(c \cdot b\right) \cdot i\right)}\right) \]

      5. *-commutative 79.0%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \left(\color{blue}{\left(b \cdot c\right)} \cdot i\right)\right) \]

      6. associate-*l* 78.9%

         \[\leadsto 2 \cdot \left(y \cdot x - c \cdot \color{blue}{\left(b \cdot \left(c \cdot i\right)\right)}\right) \]

   7. Simplified 78.9%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)} \]

   8. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   9. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{\left({c}^{2} \cdot \left(i \cdot b\right)\right) \cdot -2} \]

      2. *-commutative 70.6%

         \[\leadsto \color{blue}{\left(\left(i \cdot b\right) \cdot {c}^{2}\right)} \cdot -2 \]

      3. associate-*l* 70.6%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left({c}^{2} \cdot -2\right)} \]

      4. unpow2 70.6%

         \[\leadsto \left(i \cdot b\right) \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot -2\right) \]

   10. Simplified 70.6%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(\left(c \cdot c\right) \cdot -2\right)} \]

   11. Taylor expanded in i around 0 70.6%

       \[\leadsto \color{blue}{-2 \cdot \left({c}^{2} \cdot \left(i \cdot b\right)\right)} \]
   12. Step-by-step derivation

       1. unpow2 70.6%

          \[\leadsto -2 \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot \left(i \cdot b\right)\right) \]

       2. associate-*r* 70.6%

          \[\leadsto \color{blue}{\left(-2 \cdot \left(c \cdot c\right)\right) \cdot \left(i \cdot b\right)} \]

       3. *-commutative 70.6%

          \[\leadsto \color{blue}{\left(\left(c \cdot c\right) \cdot -2\right)} \cdot \left(i \cdot b\right) \]

       4. associate-*r* 70.6%

          \[\leadsto \color{blue}{\left(c \cdot \left(c \cdot -2\right)\right)} \cdot \left(i \cdot b\right) \]

       5. *-commutative 70.6%

          \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot \left(c \cdot \left(c \cdot -2\right)\right)} \]

       6. associate-*l* 70.6%

          \[\leadsto \color{blue}{i \cdot \left(b \cdot \left(c \cdot \left(c \cdot -2\right)\right)\right)} \]

       7. associate-*r* 74.7%

          \[\leadsto i \cdot \color{blue}{\left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)} \]

       8. *-commutative 74.7%

          \[\leadsto i \cdot \left(\color{blue}{\left(c \cdot b\right)} \cdot \left(c \cdot -2\right)\right) \]

   13. Simplified 74.7%

       \[\leadsto \color{blue}{i \cdot \left(\left(c \cdot b\right) \cdot \left(c \cdot -2\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+51}:\\ \;\;\;\;\left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq 3.25 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(\left(b \cdot c\right) \cdot \left(c \cdot -2\right)\right)\\ \end{array} \]

Alternative 19: 39.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -70000000000 \lor \neg \left(y \leq 1.45 \cdot 10^{+69}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -70000000000.0) (not (<= y 1.45e+69)))
   (* 2.0 (* x y))
   (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -70000000000.0) || !(y <= 1.45e+69)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-70000000000.0d0)) .or. (.not. (y <= 1.45d+69))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -70000000000.0) || !(y <= 1.45e+69)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -70000000000.0) or not (y <= 1.45e+69):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -70000000000.0) || !(y <= 1.45e+69))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -70000000000.0) || ~((y <= 1.45e+69)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -70000000000.0], N[Not[LessEqual[y, 1.45e+69]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7e10 or 1.4499999999999999e69 < y

   1. Initial program 85.0%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in x around inf 53.2%

      \[\leadsto 2 \cdot \color{blue}{\left(y \cdot x\right)} \]

   if -7e10 < y < 1.4499999999999999e69

   1. Initial program 92.3%

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Taylor expanded in z around inf 30.4%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -70000000000 \lor \neg \left(y \leq 1.45 \cdot 10^{+69}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 20: 28.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(z \cdot t\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* 2.0 (* z t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (z * t);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (z * t)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (z * t);
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (z * t)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(z * t))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (z * t);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.3%

   \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

2. Taylor expanded in z around inf 25.8%

   \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]

3. Final simplification 25.8%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]

Developer target: 93.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))