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

Percentage Accurate: 89.3% → 97.2%

Time: 17.4s

Alternatives: 17

Speedup: 1.1×

• 47.6% 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: 89.3% 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: 97.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0 - c \cdot i\\ \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), t\_1, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \mathsf{fma}\left(t\_1, \frac{\mathsf{fma}\left(c, b, a\right)}{x}, y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- 0.0 (* c i))))
   (if (<= (- (+ (* x y) (* z t)) (* (* c (+ a (* b c))) i)) INFINITY)
     (* 2.0 (fma (fma b c a) t_1 (fma x y (* z t))))
     (* 2.0 (* x (fma t_1 (/ (fma c b a) x) y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 0.0 - (c * i);
	double tmp;
	if ((((x * y) + (z * t)) - ((c * (a + (b * c))) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * fma(fma(b, c, a), t_1, fma(x, y, (z * t)));
	} else {
		tmp = 2.0 * (x * fma(t_1, (fma(c, b, a) / x), y));
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(b * c + a), $MachinePrecision] * t$95$1 + N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * N[(t$95$1 * N[(N[(c * b + a), $MachinePrecision] / x), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $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 94.6%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-*l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. neg-sub0 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 99.2

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

   4. Applied egg-rr 99.2%

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

   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. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-*l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. neg-sub0 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 40.0

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

   4. Applied egg-rr 40.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), 0 - c \cdot i, \color{blue}{x \cdot y}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 70.0

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

   7. Simplified 70.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \left(y + -1 \cdot \frac{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}{x}\right)\right)} \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. associate-*r* N/A

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

      5. associate-/l* N/A

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

      6. distribute-lft-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. accelerator-lowering-fma.f64 N/A

         \[\leadsto 2 \cdot \left(x \cdot \color{blue}{\mathsf{fma}\left(-1 \cdot \left(c \cdot i\right), \frac{a + b \cdot c}{x}, y\right)}\right) \]

      9. mul-1-neg N/A

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

      10. neg-sub0 N/A

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

      11. --lowering--.f64 N/A

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

      12. *-lowering-*.f64 N/A

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

      13. /-lowering-/.f64 N/A

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

      16. accelerator-lowering-fma.f64 90.0

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

   10. Simplified 90.0%

       \[\leadsto 2 \cdot \color{blue}{\left(x \cdot \mathsf{fma}\left(0 - c \cdot i, \frac{\mathsf{fma}\left(c, b, a\right)}{x}, y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq \infty:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), 0 - c \cdot i, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot \mathsf{fma}\left(0 - c \cdot i, \frac{\mathsf{fma}\left(c, b, a\right)}{x}, y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ t_2 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+123}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma b c a) (* c (* i -2.0)))) (t_2 (* (* c (+ a (* b c))) i)))
   (if (<= t_2 -5e+100)
     t_1
     (if (<= t_2 5e-95)
       (* 2.0 (* z t))
       (if (<= t_2 1e+123) (* x (* y 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, c, a) * (c * (i * -2.0));
	double t_2 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_2 <= -5e+100) {
		tmp = t_1;
	} else if (t_2 <= 5e-95) {
		tmp = 2.0 * (z * t);
	} else if (t_2 <= 1e+123) {
		tmp = x * (y * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(b, c, a) * Float64(c * Float64(i * -2.0)))
	t_2 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_2 <= -5e+100)
		tmp = t_1;
	elseif (t_2 <= 5e-95)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (t_2 <= 1e+123)
		tmp = Float64(x * Float64(y * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b * c + a), $MachinePrecision] * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+100], t$95$1, If[LessEqual[t$95$2, 5e-95], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+123], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 9.99999999999999978e122 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 82.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 83.1

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

   5. Simplified 83.1%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 84.7

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

   7. Applied egg-rr 84.7%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999998e-95

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.8

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

   5. Simplified 56.8%

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

   if 4.9999999999999998e-95 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.99999999999999978e122

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 63.2

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

   5. Simplified 63.2%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+123}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot -2\right)\right) \cdot \left(b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (+ a (* b c))) i)))
   (if (<= t_1 -5e+100)
     (* b (* -2.0 (* c (* c i))))
     (if (<= t_1 5e-95)
       (* 2.0 (* z t))
       (if (<= t_1 5e+258) (* x (* y 2.0)) (* (* c (* i -2.0)) (* b c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_1 <= -5e+100) {
		tmp = b * (-2.0 * (c * (c * i)));
	} else if (t_1 <= 5e-95) {
		tmp = 2.0 * (z * t);
	} else if (t_1 <= 5e+258) {
		tmp = x * (y * 2.0);
	} else {
		tmp = (c * (i * -2.0)) * (b * 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) :: tmp
    t_1 = (c * (a + (b * c))) * i
    if (t_1 <= (-5d+100)) then
        tmp = b * ((-2.0d0) * (c * (c * i)))
    else if (t_1 <= 5d-95) then
        tmp = 2.0d0 * (z * t)
    else if (t_1 <= 5d+258) then
        tmp = x * (y * 2.0d0)
    else
        tmp = (c * (i * (-2.0d0))) * (b * 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 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_1 <= -5e+100) {
		tmp = b * (-2.0 * (c * (c * i)));
	} else if (t_1 <= 5e-95) {
		tmp = 2.0 * (z * t);
	} else if (t_1 <= 5e+258) {
		tmp = x * (y * 2.0);
	} else {
		tmp = (c * (i * -2.0)) * (b * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * (a + (b * c))) * i
	tmp = 0
	if t_1 <= -5e+100:
		tmp = b * (-2.0 * (c * (c * i)))
	elif t_1 <= 5e-95:
		tmp = 2.0 * (z * t)
	elif t_1 <= 5e+258:
		tmp = x * (y * 2.0)
	else:
		tmp = (c * (i * -2.0)) * (b * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_1 <= -5e+100)
		tmp = Float64(b * Float64(-2.0 * Float64(c * Float64(c * i))));
	elseif (t_1 <= 5e-95)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (t_1 <= 5e+258)
		tmp = Float64(x * Float64(y * 2.0));
	else
		tmp = Float64(Float64(c * Float64(i * -2.0)) * Float64(b * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * (a + (b * c))) * i;
	tmp = 0.0;
	if (t_1 <= -5e+100)
		tmp = b * (-2.0 * (c * (c * i)));
	elseif (t_1 <= 5e-95)
		tmp = 2.0 * (z * t);
	elseif (t_1 <= 5e+258)
		tmp = x * (y * 2.0);
	else
		tmp = (c * (i * -2.0)) * (b * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+100], N[(b * N[(-2.0 * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-95], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+258], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision] * N[(b * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100

   1. Initial program 83.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 87.4

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

   5. Simplified 87.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 70.4

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

   8. Simplified 70.4%

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

   9. Taylor expanded in c around 0

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 N/A

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

       7. unpow2 N/A

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

       8. associate-*l* N/A

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

       9. *-lowering-*.f64 N/A

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

       10. *-lowering-*.f64 75.5

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

   11. Simplified 75.5%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999998e-95

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.8

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

   5. Simplified 56.8%

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

   if 4.9999999999999998e-95 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e258

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 50.4

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

   5. Simplified 50.4%

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

   if 5e258 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 74.6%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 92.3

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

   5. Simplified 92.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 79.8

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

   8. Simplified 79.8%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 82.1

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

   10. Applied egg-rr 82.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot \left(i \cdot -2\right)\right) \cdot \left(b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (+ a (* b c))) i)))
   (if (<= t_1 -5e+100)
     (* b (* -2.0 (* c (* c i))))
     (if (<= t_1 5e-95)
       (* 2.0 (* z t))
       (if (<= t_1 5e+258) (* x (* y 2.0)) (* c (* -2.0 (* i (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_1 <= -5e+100) {
		tmp = b * (-2.0 * (c * (c * i)));
	} else if (t_1 <= 5e-95) {
		tmp = 2.0 * (z * t);
	} else if (t_1 <= 5e+258) {
		tmp = x * (y * 2.0);
	} else {
		tmp = c * (-2.0 * (i * (b * 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) :: tmp
    t_1 = (c * (a + (b * c))) * i
    if (t_1 <= (-5d+100)) then
        tmp = b * ((-2.0d0) * (c * (c * i)))
    else if (t_1 <= 5d-95) then
        tmp = 2.0d0 * (z * t)
    else if (t_1 <= 5d+258) then
        tmp = x * (y * 2.0d0)
    else
        tmp = c * ((-2.0d0) * (i * (b * 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 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_1 <= -5e+100) {
		tmp = b * (-2.0 * (c * (c * i)));
	} else if (t_1 <= 5e-95) {
		tmp = 2.0 * (z * t);
	} else if (t_1 <= 5e+258) {
		tmp = x * (y * 2.0);
	} else {
		tmp = c * (-2.0 * (i * (b * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * (a + (b * c))) * i
	tmp = 0
	if t_1 <= -5e+100:
		tmp = b * (-2.0 * (c * (c * i)))
	elif t_1 <= 5e-95:
		tmp = 2.0 * (z * t)
	elif t_1 <= 5e+258:
		tmp = x * (y * 2.0)
	else:
		tmp = c * (-2.0 * (i * (b * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_1 <= -5e+100)
		tmp = Float64(b * Float64(-2.0 * Float64(c * Float64(c * i))));
	elseif (t_1 <= 5e-95)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (t_1 <= 5e+258)
		tmp = Float64(x * Float64(y * 2.0));
	else
		tmp = Float64(c * Float64(-2.0 * Float64(i * Float64(b * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * (a + (b * c))) * i;
	tmp = 0.0;
	if (t_1 <= -5e+100)
		tmp = b * (-2.0 * (c * (c * i)));
	elseif (t_1 <= 5e-95)
		tmp = 2.0 * (z * t);
	elseif (t_1 <= 5e+258)
		tmp = x * (y * 2.0);
	else
		tmp = c * (-2.0 * (i * (b * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+100], N[(b * N[(-2.0 * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-95], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+258], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(c * N[(-2.0 * N[(i * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100

   1. Initial program 83.0%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 87.4

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

   5. Simplified 87.4%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 70.4

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

   8. Simplified 70.4%

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

   9. Taylor expanded in c around 0

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 N/A

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

       7. unpow2 N/A

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

       8. associate-*l* N/A

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

       9. *-lowering-*.f64 N/A

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

       10. *-lowering-*.f64 75.5

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

   11. Simplified 75.5%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999998e-95

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.8

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

   5. Simplified 56.8%

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

   if 4.9999999999999998e-95 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e258

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 50.4

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

   5. Simplified 50.4%

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

   if 5e258 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 74.6%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 92.3

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

   5. Simplified 92.3%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 79.8

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

   8. Simplified 79.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ t_2 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (* -2.0 (* c (* c i))))) (t_2 (* (* c (+ a (* b c))) i)))
   (if (<= t_2 -5e+100)
     t_1
     (if (<= t_2 5e-95)
       (* 2.0 (* z t))
       (if (<= t_2 5e+258) (* x (* y 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * (-2.0 * (c * (c * i)));
	double t_2 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_2 <= -5e+100) {
		tmp = t_1;
	} else if (t_2 <= 5e-95) {
		tmp = 2.0 * (z * t);
	} else if (t_2 <= 5e+258) {
		tmp = x * (y * 2.0);
	} 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) :: t_2
    real(8) :: tmp
    t_1 = b * ((-2.0d0) * (c * (c * i)))
    t_2 = (c * (a + (b * c))) * i
    if (t_2 <= (-5d+100)) then
        tmp = t_1
    else if (t_2 <= 5d-95) then
        tmp = 2.0d0 * (z * t)
    else if (t_2 <= 5d+258) then
        tmp = x * (y * 2.0d0)
    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 = b * (-2.0 * (c * (c * i)));
	double t_2 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_2 <= -5e+100) {
		tmp = t_1;
	} else if (t_2 <= 5e-95) {
		tmp = 2.0 * (z * t);
	} else if (t_2 <= 5e+258) {
		tmp = x * (y * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * (-2.0 * (c * (c * i)))
	t_2 = (c * (a + (b * c))) * i
	tmp = 0
	if t_2 <= -5e+100:
		tmp = t_1
	elif t_2 <= 5e-95:
		tmp = 2.0 * (z * t)
	elif t_2 <= 5e+258:
		tmp = x * (y * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * Float64(-2.0 * Float64(c * Float64(c * i))))
	t_2 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_2 <= -5e+100)
		tmp = t_1;
	elseif (t_2 <= 5e-95)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (t_2 <= 5e+258)
		tmp = Float64(x * Float64(y * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * (-2.0 * (c * (c * i)));
	t_2 = (c * (a + (b * c))) * i;
	tmp = 0.0;
	if (t_2 <= -5e+100)
		tmp = t_1;
	elseif (t_2 <= 5e-95)
		tmp = 2.0 * (z * t);
	elseif (t_2 <= 5e+258)
		tmp = x * (y * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[(-2.0 * N[(c * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+100], t$95$1, If[LessEqual[t$95$2, 5e-95], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+258], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 5e258 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 89.0

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

   5. Simplified 89.0%

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

   6. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 73.6

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

   8. Simplified 73.6%

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

   9. Taylor expanded in c around 0

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 N/A

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 N/A

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

       7. unpow2 N/A

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

       8. associate-*l* N/A

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

       9. *-lowering-*.f64 N/A

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

       10. *-lowering-*.f64 76.9

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

   11. Simplified 76.9%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999998e-95

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.8

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

   5. Simplified 56.8%

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

   if 4.9999999999999998e-95 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e258

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 50.4

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

   5. Simplified 50.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{-95}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+258}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-2 \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(i \cdot \mathsf{fma}\left(b, c, a\right)\right) \cdot -2\right)\\ t_2 := c \cdot \left(a + b \cdot c\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+36}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (* i (fma b c a)) -2.0))) (t_2 (* c (+ a (* b c)))))
   (if (<= t_2 -2e+149)
     t_1
     (if (<= t_2 -4e-24)
       (* x (* y 2.0))
       (if (<= t_2 5e+36) (* 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((i * fma(b, c, a)) * -2.0);
	double t_2 = c * (a + (b * c));
	double tmp;
	if (t_2 <= -2e+149) {
		tmp = t_1;
	} else if (t_2 <= -4e-24) {
		tmp = x * (y * 2.0);
	} else if (t_2 <= 5e+36) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(i * fma(b, c, a)) * -2.0))
	t_2 = Float64(c * Float64(a + Float64(b * c)))
	tmp = 0.0
	if (t_2 <= -2e+149)
		tmp = t_1;
	elseif (t_2 <= -4e-24)
		tmp = Float64(x * Float64(y * 2.0));
	elseif (t_2 <= 5e+36)
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(i * N[(b * c + a), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+149], t$95$1, If[LessEqual[t$95$2, -4e-24], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+36], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -2.0000000000000001e149 or 4.99999999999999977e36 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 83.2%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 78.8

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

   5. Simplified 78.8%

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

   if -2.0000000000000001e149 < (*.f64 (+.f64 a (*.f64 b c)) c) < -3.99999999999999969e-24

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 63.5

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

   5. Simplified 63.5%

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

   if -3.99999999999999969e-24 < (*.f64 (+.f64 a (*.f64 b c)) c) < 4.99999999999999977e36

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 60.5

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

   5. Simplified 60.5%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -2 \cdot 10^{+149}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \mathsf{fma}\left(b, c, a\right)\right) \cdot -2\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq -4 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 5 \cdot 10^{+36}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(i \cdot \mathsf{fma}\left(b, c, a\right)\right) \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), 0 - c \cdot i, x \cdot y\right)\\ t_2 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+224}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (fma (fma b c a) (- 0.0 (* c i)) (* x y))))
        (t_2 (* (* c (+ a (* b c))) i)))
   (if (<= t_2 -5e+100)
     t_1
     (if (<= t_2 1e+224) (* 2.0 (fma z t (- (* x y) (* i (* a c))))) 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 * fma(fma(b, c, a), (0.0 - (c * i)), (x * y));
	double t_2 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_2 <= -5e+100) {
		tmp = t_1;
	} else if (t_2 <= 1e+224) {
		tmp = 2.0 * fma(z, t, ((x * y) - (i * (a * c))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * fma(fma(b, c, a), Float64(0.0 - Float64(c * i)), Float64(x * y)))
	t_2 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_2 <= -5e+100)
		tmp = t_1;
	elseif (t_2 <= 1e+224)
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(x * y) - Float64(i * Float64(a * c)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(b * c + a), $MachinePrecision] * N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+100], t$95$1, If[LessEqual[t$95$2, 1e+224], N[(2.0 * N[(z * t + N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 9.9999999999999997e223 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.5%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-*l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. neg-sub0 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. accelerator-lowering-fma.f64 N/A

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

      12. *-lowering-*.f64 93.8

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

   4. Applied egg-rr 93.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto 2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), 0 - c \cdot i, \color{blue}{x \cdot y}\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 92.8

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

   7. Simplified 92.8%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.9999999999999997e223

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 95.6

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

   5. Simplified 95.6%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 96.3

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

   7. Applied egg-rr 96.3%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), 0 - c \cdot i, x \cdot y\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+224}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), 0 - c \cdot i, x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \mathsf{fma}\left(b, c, a\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (* c (+ a (* b c))) i)))
   (if (<= t_1 -5e+100)
     (* 2.0 (- (* z t) (* c (* i (fma b c a)))))
     (if (<= t_1 5e+258)
       (* 2.0 (fma z t (- (* x y) (* i (* a c)))))
       (* (fma b c a) (* c (* i -2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_1 <= -5e+100) {
		tmp = 2.0 * ((z * t) - (c * (i * fma(b, c, a))));
	} else if (t_1 <= 5e+258) {
		tmp = 2.0 * fma(z, t, ((x * y) - (i * (a * c))));
	} else {
		tmp = fma(b, c, a) * (c * (i * -2.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_1 <= -5e+100)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(i * fma(b, c, a)))));
	elseif (t_1 <= 5e+258)
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(x * y) - Float64(i * Float64(a * c)))));
	else
		tmp = Float64(fma(b, c, a) * Float64(c * Float64(i * -2.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+100], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(i * N[(b * c + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+258], N[(2.0 * N[(z * t + N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c + a), $MachinePrecision] * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100

   1. Initial program 83.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. +-commutative N/A

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

      9. accelerator-lowering-fma.f64 90.3

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

   5. Simplified 90.3%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e258

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 95.7

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

   5. Simplified 95.7%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 96.4

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

   7. Applied egg-rr 96.4%

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

   if 5e258 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 74.6%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 92.3

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

   5. Simplified 92.3%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 94.6

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

   7. Applied egg-rr 94.6%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(i \cdot \mathsf{fma}\left(b, c, a\right)\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+258}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ t_2 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma b c a) (* c (* i -2.0)))) (t_2 (* (* c (+ a (* b c))) i)))
   (if (<= t_2 -5e+100)
     t_1
     (if (<= t_2 5e+258) (* 2.0 (fma z t (- (* x y) (* i (* a c))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, c, a) * (c * (i * -2.0));
	double t_2 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_2 <= -5e+100) {
		tmp = t_1;
	} else if (t_2 <= 5e+258) {
		tmp = 2.0 * fma(z, t, ((x * y) - (i * (a * c))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(b, c, a) * Float64(c * Float64(i * -2.0)))
	t_2 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_2 <= -5e+100)
		tmp = t_1;
	elseif (t_2 <= 5e+258)
		tmp = Float64(2.0 * fma(z, t, Float64(Float64(x * y) - Float64(i * Float64(a * c)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b * c + a), $MachinePrecision] * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+100], t$95$1, If[LessEqual[t$95$2, 5e+258], N[(2.0 * N[(z * t + N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 5e258 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.1%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 89.0

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

   5. Simplified 89.0%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 90.7

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

   7. Applied egg-rr 90.7%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5e258

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 95.7

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

   5. Simplified 95.7%

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. *-lowering-*.f64 96.4

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

   7. Applied egg-rr 96.4%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+258}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ t_2 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+224}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, a \cdot \left(0 - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma b c a) (* c (* i -2.0)))) (t_2 (* (* c (+ a (* b c))) i)))
   (if (<= t_2 -5e+100)
     t_1
     (if (<= t_2 1e+224) (* 2.0 (fma z t (* a (- 0.0 (* c i))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, c, a) * (c * (i * -2.0));
	double t_2 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_2 <= -5e+100) {
		tmp = t_1;
	} else if (t_2 <= 1e+224) {
		tmp = 2.0 * fma(z, t, (a * (0.0 - (c * i))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(b, c, a) * Float64(c * Float64(i * -2.0)))
	t_2 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_2 <= -5e+100)
		tmp = t_1;
	elseif (t_2 <= 1e+224)
		tmp = Float64(2.0 * fma(z, t, Float64(a * Float64(0.0 - Float64(c * i)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b * c + a), $MachinePrecision] * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+100], t$95$1, If[LessEqual[t$95$2, 1e+224], N[(2.0 * N[(z * t + N[(a * N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 9.9999999999999997e223 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.5%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 87.5

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

   5. Simplified 87.5%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 89.2

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

   7. Applied egg-rr 89.2%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.9999999999999997e223

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 95.6

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

   5. Simplified 95.6%

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

   6. Taylor expanded in x around 0

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

      1. --lowering--.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 59.0

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

   8. Simplified 59.0%

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

      1. sub-neg N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. *-lowering-*.f64 N/A

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

      6. neg-sub0 N/A

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

      7. --lowering--.f64 N/A

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

      8. *-lowering-*.f64 59.0

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

   10. Applied egg-rr 59.0%

       \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(z, t, a \cdot \left(0 - c \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+224}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(z, t, a \cdot \left(0 - c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ t_2 := \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+224}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (fma b c a) (* c (* i -2.0)))) (t_2 (* (* c (+ a (* b c))) i)))
   (if (<= t_2 -5e+100)
     t_1
     (if (<= t_2 1e+224) (* 2.0 (- (* z t) (* a (* c i)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(b, c, a) * (c * (i * -2.0));
	double t_2 = (c * (a + (b * c))) * i;
	double tmp;
	if (t_2 <= -5e+100) {
		tmp = t_1;
	} else if (t_2 <= 1e+224) {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(b, c, a) * Float64(c * Float64(i * -2.0)))
	t_2 = Float64(Float64(c * Float64(a + Float64(b * c))) * i)
	tmp = 0.0
	if (t_2 <= -5e+100)
		tmp = t_1;
	elseif (t_2 <= 1e+224)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b * c + a), $MachinePrecision] * N[(c * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+100], t$95$1, If[LessEqual[t$95$2, 1e+224], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.9999999999999999e100 or 9.9999999999999997e223 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 80.5%

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

   3. Taylor expanded in i around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-*r* N/A

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

      5. distribute-lft-out N/A

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 N/A

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

      8. distribute-lft-out N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. *-lowering-*.f64 N/A

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

      13. *-commutative N/A

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

      14. *-lowering-*.f64 N/A

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

      15. +-commutative N/A

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

      16. accelerator-lowering-fma.f64 87.5

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

   5. Simplified 87.5%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

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

      5. accelerator-lowering-fma.f64 N/A

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

      6. *-lowering-*.f64 N/A

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

      7. *-lowering-*.f64 89.2

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

   7. Applied egg-rr 89.2%

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

   if -4.9999999999999999e100 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 9.9999999999999997e223

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 95.6

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

   5. Simplified 95.6%

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

   6. Taylor expanded in x around 0

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

      1. --lowering--.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 59.0

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

   8. Simplified 59.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{+224}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -200000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(a \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;z \cdot t \leq 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -200000.0)
   (* 2.0 (* z t))
   (if (<= (* z t) -1e-55)
     (* c (* a (* i -2.0)))
     (if (<= (* z t) 1e-39) (* x (* y 2.0)) (* t (* z 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -200000.0) {
		tmp = 2.0 * (z * t);
	} else if ((z * t) <= -1e-55) {
		tmp = c * (a * (i * -2.0));
	} else if ((z * t) <= 1e-39) {
		tmp = x * (y * 2.0);
	} else {
		tmp = t * (z * 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 ((z * t) <= (-200000.0d0)) then
        tmp = 2.0d0 * (z * t)
    else if ((z * t) <= (-1d-55)) then
        tmp = c * (a * (i * (-2.0d0)))
    else if ((z * t) <= 1d-39) then
        tmp = x * (y * 2.0d0)
    else
        tmp = t * (z * 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 ((z * t) <= -200000.0) {
		tmp = 2.0 * (z * t);
	} else if ((z * t) <= -1e-55) {
		tmp = c * (a * (i * -2.0));
	} else if ((z * t) <= 1e-39) {
		tmp = x * (y * 2.0);
	} else {
		tmp = t * (z * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -200000.0:
		tmp = 2.0 * (z * t)
	elif (z * t) <= -1e-55:
		tmp = c * (a * (i * -2.0))
	elif (z * t) <= 1e-39:
		tmp = x * (y * 2.0)
	else:
		tmp = t * (z * 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -200000.0)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(z * t) <= -1e-55)
		tmp = Float64(c * Float64(a * Float64(i * -2.0)));
	elseif (Float64(z * t) <= 1e-39)
		tmp = Float64(x * Float64(y * 2.0));
	else
		tmp = Float64(t * Float64(z * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -200000.0)
		tmp = 2.0 * (z * t);
	elseif ((z * t) <= -1e-55)
		tmp = c * (a * (i * -2.0));
	elseif ((z * t) <= 1e-39)
		tmp = x * (y * 2.0);
	else
		tmp = t * (z * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -200000.0], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -1e-55], N[(c * N[(a * N[(i * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-39], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -2e5

   1. Initial program 91.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.5

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

   5. Simplified 61.5%

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

   if -2e5 < (*.f64 z t) < -9.99999999999999995e-56

   1. Initial program 76.1%

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

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-lowering-*.f64 N/A

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

      9. *-lowering-*.f64 52.2

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

   5. Simplified 52.2%

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

   if -9.99999999999999995e-56 < (*.f64 z t) < 9.99999999999999929e-40

   1. Initial program 90.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 42.7

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

   5. Simplified 42.7%

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

   if 9.99999999999999929e-40 < (*.f64 z t)

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 58.7

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

   5. Simplified 58.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 58.7

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

   7. Applied egg-rr 58.7%

      \[\leadsto \color{blue}{\left(2 \cdot z\right) \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -200000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-55}:\\ \;\;\;\;c \cdot \left(a \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;z \cdot t \leq 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 94.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \mathsf{fma}\left(\mathsf{fma}\left(b, c, a\right), 0 - c \cdot i, \mathsf{fma}\left(x, y, z \cdot t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (fma (fma b c a) (- 0.0 (* c i)) (fma x y (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * fma(fma(b, c, a), (0.0 - (c * i)), fma(x, y, (z * t)));
}

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * fma(fma(b, c, a), Float64(0.0 - Float64(c * i)), fma(x, y, Float64(z * t))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(b * c + a), $MachinePrecision] * N[(0.0 - N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. associate-*l* N/A

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

   4. distribute-rgt-neg-in N/A

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

   5. accelerator-lowering-fma.f64 N/A

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

   6. +-commutative N/A

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

   7. accelerator-lowering-fma.f64 N/A

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

   8. neg-sub0 N/A

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

   9. --lowering--.f64 N/A

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

   10. *-lowering-*.f64 N/A

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

   11. accelerator-lowering-fma.f64 N/A

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

   12. *-lowering-*.f64 96.9

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

4. Applied egg-rr 96.9%

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

Alternative 14: 91.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative N/A

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

   2. associate--l+ N/A

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

   3. accelerator-lowering-fma.f64 N/A

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

   4. --lowering--.f64 N/A

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

   5. *-lowering-*.f64 N/A

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

   6. associate-*l* N/A

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

   7. *-commutative N/A

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

   8. associate-*l* N/A

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

   9. *-lowering-*.f64 N/A

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

   10. *-lowering-*.f64 N/A

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

   11. +-commutative N/A

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

   12. accelerator-lowering-fma.f64 95.8

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

4. Applied egg-rr 95.8%

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

Alternative 15: 42.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -1e-53)
   (* 2.0 (* z t))
   (if (<= (* z t) 1e-39) (* x (* y 2.0)) (* t (* z 2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -1e-53) {
		tmp = 2.0 * (z * t);
	} else if ((z * t) <= 1e-39) {
		tmp = x * (y * 2.0);
	} else {
		tmp = t * (z * 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 ((z * t) <= (-1d-53)) then
        tmp = 2.0d0 * (z * t)
    else if ((z * t) <= 1d-39) then
        tmp = x * (y * 2.0d0)
    else
        tmp = t * (z * 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 ((z * t) <= -1e-53) {
		tmp = 2.0 * (z * t);
	} else if ((z * t) <= 1e-39) {
		tmp = x * (y * 2.0);
	} else {
		tmp = t * (z * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -1e-53:
		tmp = 2.0 * (z * t)
	elif (z * t) <= 1e-39:
		tmp = x * (y * 2.0)
	else:
		tmp = t * (z * 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -1e-53)
		tmp = Float64(2.0 * Float64(z * t));
	elseif (Float64(z * t) <= 1e-39)
		tmp = Float64(x * Float64(y * 2.0));
	else
		tmp = Float64(t * Float64(z * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -1e-53)
		tmp = 2.0 * (z * t);
	elseif ((z * t) <= 1e-39)
		tmp = x * (y * 2.0);
	else
		tmp = t * (z * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e-53], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-39], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(t * N[(z * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.00000000000000003e-53

   1. Initial program 88.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 53.1

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

   5. Simplified 53.1%

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

   if -1.00000000000000003e-53 < (*.f64 z t) < 9.99999999999999929e-40

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 42.3

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

   5. Simplified 42.3%

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

   if 9.99999999999999929e-40 < (*.f64 z t)

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 58.7

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

   5. Simplified 58.7%

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 58.7

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

   7. Applied egg-rr 58.7%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= (* z t) -1e-53) t_1 (if (<= (* z t) 1e-39) (* x (* y 2.0)) 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 * (z * t);
	double tmp;
	if ((z * t) <= -1e-53) {
		tmp = t_1;
	} else if ((z * t) <= 1e-39) {
		tmp = x * (y * 2.0);
	} 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 * (z * t)
    if ((z * t) <= (-1d-53)) then
        tmp = t_1
    else if ((z * t) <= 1d-39) then
        tmp = x * (y * 2.0d0)
    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 * (z * t);
	double tmp;
	if ((z * t) <= -1e-53) {
		tmp = t_1;
	} else if ((z * t) <= 1e-39) {
		tmp = x * (y * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if (z * t) <= -1e-53:
		tmp = t_1
	elif (z * t) <= 1e-39:
		tmp = x * (y * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (Float64(z * t) <= -1e-53)
		tmp = t_1;
	elseif (Float64(z * t) <= 1e-39)
		tmp = Float64(x * Float64(y * 2.0));
	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 * (z * t);
	tmp = 0.0;
	if ((z * t) <= -1e-53)
		tmp = t_1;
	elseif ((z * t) <= 1e-39)
		tmp = x * (y * 2.0);
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e-53], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 1e-39], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.00000000000000003e-53 or 9.99999999999999929e-40 < (*.f64 z t)

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 56.0

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

   5. Simplified 56.0%

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

   if -1.00000000000000003e-53 < (*.f64 z t) < 9.99999999999999929e-40

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 42.3

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

   5. Simplified 42.3%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.7% accurate, 3.6× 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 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. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto 2 \cdot \color{blue}{\left(t \cdot z\right)} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 33.4

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

5. Simplified 33.4%

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

6. Final simplification 33.4%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]
7. Add Preprocessing

Developer Target 1: 93.4% 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 2024195 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

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