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

Percentage Accurate: 90.4% → 96.1%

Time: 13.2s

Alternatives: 13

Speedup: 0.5×

• Unsound rule application detected in e-graph. Results may not be sound.

• 46.9% 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: 90.4% 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: 96.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t + N[(c * N[(b * (-N[(c * i), $MachinePrecision])), $MachinePrecision] + N[(x * y), $MachinePrecision]), $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 97.3%

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

      1. associate-*l* 98.6%

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

      2. fma-def 98.6%

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

   3. Simplified 98.6%

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

      1. fma-def 98.6%

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

      2. +-commutative 98.6%

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

   5. Applied egg-rr 98.6%

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

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

   1. Initial program 0.0%

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

      1. associate--l+ 0.0%

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

      2. +-commutative 0.0%

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

      3. associate-+l- 0.0%

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

      4. fma-neg 50.0%

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

      5. neg-sub0 50.0%

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

      6. associate-+l- 50.0%

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

      7. neg-sub0 50.0%

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

      8. distribute-rgt-neg-in 50.0%

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

      9. *-commutative 50.0%

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

      10. associate-*l* 57.1%

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

      11. fma-def 71.4%

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

      12. +-commutative 71.4%

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

      13. fma-def 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in b around inf 71.4%

      \[\leadsto 2 \cdot \mathsf{fma}\left(z, t, \mathsf{fma}\left(c, \color{blue}{-1 \cdot \left(c \cdot \left(i \cdot b\right)\right)}, x \cdot y\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 71.4%

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

      2. associate-*r* 71.4%

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

      3. *-commutative 71.4%

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

      4. distribute-rgt-neg-in 71.4%

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

      5. distribute-rgt-neg-in 71.4%

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

   6. Simplified 71.4%

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

4. Final simplification 97.1%

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

Alternative 2: 93.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 * 2.0), $MachinePrecision], N[(2.0 * N[(i * N[(N[(c * c), $MachinePrecision] * (-b)), $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 97.3%

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

   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. Step-by-step derivation

      1. associate-*l* 7.1%

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

      2. fma-def 14.3%

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

   3. Simplified 14.3%

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

      1. fma-def 7.1%

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

      2. +-commutative 7.1%

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

   5. Applied egg-rr 7.1%

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

   6. Taylor expanded in b around inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unpow2 57.2%

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

      3. *-commutative 57.2%

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

      4. associate-*r* 57.3%

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

      5. distribute-rgt-neg-in 57.3%

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

      6. distribute-rgt-neg-in 57.3%

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

   8. Simplified 57.3%

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

4. Final simplification 95.1%

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

Alternative 3: 96.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(i * N[(N[(c * c), $MachinePrecision] * (-b)), $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 97.3%

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

      1. associate-*l* 98.6%

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

      2. fma-def 98.6%

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

   3. Simplified 98.6%

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

      1. fma-def 98.6%

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

      2. +-commutative 98.6%

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

   5. Applied egg-rr 98.6%

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

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

   1. Initial program 0.0%

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

      1. associate-*l* 7.1%

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

      2. fma-def 14.3%

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

   3. Simplified 14.3%

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

      1. fma-def 7.1%

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

      2. +-commutative 7.1%

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

   5. Applied egg-rr 7.1%

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

   6. Taylor expanded in b around inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. unpow2 57.2%

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

      3. *-commutative 57.2%

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

      4. associate-*r* 57.3%

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

      5. distribute-rgt-neg-in 57.3%

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

      6. distribute-rgt-neg-in 57.3%

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

   8. Simplified 57.3%

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

4. Final simplification 96.3%

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

Alternative 4: 81.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{-36} \lor \neg \left(b \leq 0.00029\right):\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(b \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= b -2.05e-36) (not (<= b 0.00029)))
     (* 2.0 (- t_1 (* i (* b (* c c)))))
     (* 2.0 (- t_1 (* i (* a c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((b <= -2.05e-36) || !(b <= 0.00029)) {
		tmp = 2.0 * (t_1 - (i * (b * (c * c))));
	} else {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if ((b <= (-2.05d-36)) .or. (.not. (b <= 0.00029d0))) then
        tmp = 2.0d0 * (t_1 - (i * (b * (c * c))))
    else
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if ((b <= -2.05e-36) || !(b <= 0.00029)) {
		tmp = 2.0 * (t_1 - (i * (b * (c * c))));
	} else {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if (b <= -2.05e-36) or not (b <= 0.00029):
		tmp = 2.0 * (t_1 - (i * (b * (c * c))))
	else:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((b <= -2.05e-36) || !(b <= 0.00029))
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(b * Float64(c * c)))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if ((b <= -2.05e-36) || ~((b <= 0.00029)))
		tmp = 2.0 * (t_1 - (i * (b * (c * c))));
	else
		tmp = 2.0 * (t_1 - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -2.05e-36], N[Not[LessEqual[b, 0.00029]], $MachinePrecision]], N[(2.0 * N[(t$95$1 - N[(i * N[(b * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.05000000000000006e-36 or 2.9e-4 < b

   1. Initial program 87.5%

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

   2. Taylor expanded in a around 0 83.1%

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

      1. unpow2 83.1%

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

   4. Simplified 83.1%

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

   if -2.05000000000000006e-36 < b < 2.9e-4

   1. Initial program 96.9%

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

   2. Taylor expanded in a around inf 90.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{-36} \lor \neg \left(b \leq 0.00029\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(b \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 5: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+55} \lor \neg \left(c \leq 7.1 \cdot 10^{+106}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.9e+55) (not (<= c 7.1e+106)))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.9e+55) || !(c <= 7.1e+106)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.9d+55)) .or. (.not. (c <= 7.1d+106))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.9e+55) || !(c <= 7.1e+106)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.9e+55) or not (c <= 7.1e+106):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.9e+55) || !(c <= 7.1e+106))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.9e+55) || ~((c <= 7.1e+106)))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.9e+55], N[Not[LessEqual[c, 7.1e+106]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.9e55 or 7.1000000000000003e106 < c

   1. Initial program 81.0%

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

   2. Taylor expanded in i around inf 78.1%

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

   if -1.9e55 < c < 7.1000000000000003e106

   1. Initial program 97.8%

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

   2. Taylor expanded in a around inf 90.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+55} \lor \neg \left(c \leq 7.1 \cdot 10^{+106}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 6: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := 2 \cdot \left(\left(-c\right) \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{if}\;c \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 18000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+54}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* 2.0 (* (- c) (* i (* b c))))))
   (if (<= c -1.45e+56)
     t_2
     (if (<= c 18000.0)
       t_1
       (if (<= c 2.7e+54)
         (* (* a c) (* i -2.0))
         (if (<= c 2.9e+91) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (-c * (i * (b * c)));
	double tmp;
	if (c <= -1.45e+56) {
		tmp = t_2;
	} else if (c <= 18000.0) {
		tmp = t_1;
	} else if (c <= 2.7e+54) {
		tmp = (a * c) * (i * -2.0);
	} else if (c <= 2.9e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = 2.0d0 * (-c * (i * (b * c)))
    if (c <= (-1.45d+56)) then
        tmp = t_2
    else if (c <= 18000.0d0) then
        tmp = t_1
    else if (c <= 2.7d+54) then
        tmp = (a * c) * (i * (-2.0d0))
    else if (c <= 2.9d+91) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (-c * (i * (b * c)));
	double tmp;
	if (c <= -1.45e+56) {
		tmp = t_2;
	} else if (c <= 18000.0) {
		tmp = t_1;
	} else if (c <= 2.7e+54) {
		tmp = (a * c) * (i * -2.0);
	} else if (c <= 2.9e+91) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = 2.0 * (-c * (i * (b * c)))
	tmp = 0
	if c <= -1.45e+56:
		tmp = t_2
	elif c <= 18000.0:
		tmp = t_1
	elif c <= 2.7e+54:
		tmp = (a * c) * (i * -2.0)
	elif c <= 2.9e+91:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(2.0 * Float64(Float64(-c) * Float64(i * Float64(b * c))))
	tmp = 0.0
	if (c <= -1.45e+56)
		tmp = t_2;
	elseif (c <= 18000.0)
		tmp = t_1;
	elseif (c <= 2.7e+54)
		tmp = Float64(Float64(a * c) * Float64(i * -2.0));
	elseif (c <= 2.9e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = 2.0 * (-c * (i * (b * c)));
	tmp = 0.0;
	if (c <= -1.45e+56)
		tmp = t_2;
	elseif (c <= 18000.0)
		tmp = t_1;
	elseif (c <= 2.7e+54)
		tmp = (a * c) * (i * -2.0);
	elseif (c <= 2.9e+91)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[((-c) * N[(i * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.45e+56], t$95$2, If[LessEqual[c, 18000.0], t$95$1, If[LessEqual[c, 2.7e+54], N[(N[(a * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.9e+91], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.45000000000000004e56 or 2.90000000000000014e91 < c

   1. Initial program 81.4%

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

      1. *-commutative 81.4%

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

      2. +-commutative 81.4%

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

      3. distribute-rgt-in 72.5%

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

   3. Applied egg-rr 72.5%

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

   4. Taylor expanded in b around inf 62.1%

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

      1. mul-1-neg 62.1%

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

      2. associate-*r* 66.5%

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

      3. distribute-rgt-neg-in 66.5%

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

      4. unpow2 66.5%

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

      5. associate-*l* 69.8%

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

   6. Simplified 69.8%

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

   7. Taylor expanded in c around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. unpow2 62.1%

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

      3. *-commutative 62.1%

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

      4. associate-*r* 62.4%

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

      5. distribute-rgt-neg-in 62.4%

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

      6. associate-*r* 66.7%

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

      7. distribute-rgt-neg-in 66.7%

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

   9. Simplified 66.7%

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

   if -1.45000000000000004e56 < c < 18000 or 2.70000000000000011e54 < c < 2.90000000000000014e91

   1. Initial program 98.3%

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

   2. Taylor expanded in c around 0 80.0%

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

   if 18000 < c < 2.70000000000000011e54

   1. Initial program 90.0%

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

   2. Taylor expanded in a around inf 61.5%

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

      1. associate-*r* 61.5%

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

      2. neg-mul-1 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in c around 0 61.5%

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

      1. *-commutative 61.5%

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

      2. *-commutative 61.5%

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

      3. associate-*r* 70.8%

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

      4. associate-*l* 70.8%

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

   7. Simplified 70.8%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \left(\left(-c\right) \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq 18000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+54}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(-c\right) \cdot \left(i \cdot \left(b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 7: 67.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := 2 \cdot \left(b \cdot \left(c \cdot \left(-c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -2.4 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+53}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* 2.0 (* b (* c (- (* c i)))))))
   (if (<= c -2.4e+103)
     t_2
     (if (<= c 5000.0)
       t_1
       (if (<= c 8.6e+53)
         (* (* a c) (* i -2.0))
         (if (<= c 2.7e+119) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (b * (c * -(c * i)));
	double tmp;
	if (c <= -2.4e+103) {
		tmp = t_2;
	} else if (c <= 5000.0) {
		tmp = t_1;
	} else if (c <= 8.6e+53) {
		tmp = (a * c) * (i * -2.0);
	} else if (c <= 2.7e+119) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = 2.0d0 * (b * (c * -(c * i)))
    if (c <= (-2.4d+103)) then
        tmp = t_2
    else if (c <= 5000.0d0) then
        tmp = t_1
    else if (c <= 8.6d+53) then
        tmp = (a * c) * (i * (-2.0d0))
    else if (c <= 2.7d+119) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (b * (c * -(c * i)));
	double tmp;
	if (c <= -2.4e+103) {
		tmp = t_2;
	} else if (c <= 5000.0) {
		tmp = t_1;
	} else if (c <= 8.6e+53) {
		tmp = (a * c) * (i * -2.0);
	} else if (c <= 2.7e+119) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = 2.0 * (b * (c * -(c * i)))
	tmp = 0
	if c <= -2.4e+103:
		tmp = t_2
	elif c <= 5000.0:
		tmp = t_1
	elif c <= 8.6e+53:
		tmp = (a * c) * (i * -2.0)
	elif c <= 2.7e+119:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(2.0 * Float64(b * Float64(c * Float64(-Float64(c * i)))))
	tmp = 0.0
	if (c <= -2.4e+103)
		tmp = t_2;
	elseif (c <= 5000.0)
		tmp = t_1;
	elseif (c <= 8.6e+53)
		tmp = Float64(Float64(a * c) * Float64(i * -2.0));
	elseif (c <= 2.7e+119)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = 2.0 * (b * (c * -(c * i)));
	tmp = 0.0;
	if (c <= -2.4e+103)
		tmp = t_2;
	elseif (c <= 5000.0)
		tmp = t_1;
	elseif (c <= 8.6e+53)
		tmp = (a * c) * (i * -2.0);
	elseif (c <= 2.7e+119)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(b * N[(c * (-N[(c * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.4e+103], t$95$2, If[LessEqual[c, 5000.0], t$95$1, If[LessEqual[c, 8.6e+53], N[(N[(a * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.7e+119], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.3999999999999998e103 or 2.6999999999999998e119 < c

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. +-commutative 80.8%

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

      3. distribute-rgt-in 70.4%

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

   3. Applied egg-rr 70.4%

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

   4. Taylor expanded in b around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. associate-*r* 72.2%

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

      3. distribute-rgt-neg-in 72.2%

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

      4. unpow2 72.2%

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

      5. associate-*l* 76.1%

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

   6. Simplified 76.1%

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

   if -2.3999999999999998e103 < c < 5e3 or 8.5999999999999995e53 < c < 2.6999999999999998e119

   1. Initial program 97.2%

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

   2. Taylor expanded in c around 0 76.9%

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

   if 5e3 < c < 8.5999999999999995e53

   1. Initial program 90.0%

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

   2. Taylor expanded in a around inf 61.5%

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

      1. associate-*r* 61.5%

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

      2. neg-mul-1 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in c around 0 61.5%

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

      1. *-commutative 61.5%

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

      2. *-commutative 61.5%

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

      3. associate-*r* 70.8%

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

      4. associate-*l* 70.8%

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

   7. Simplified 70.8%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+103}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(-c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 5000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 8.6 \cdot 10^{+53}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+119}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(-c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 8: 68.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(b \cdot \left(c \cdot \left(-c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -6.5 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-36}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+119}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* b (* c (- (* c i)))))))
   (if (<= c -6.5e+102)
     t_1
     (if (<= c 1.5e-36)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= c 3.5e+119) (* 2.0 (- (* x y) (* 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 = 2.0 * (b * (c * -(c * i)));
	double tmp;
	if (c <= -6.5e+102) {
		tmp = t_1;
	} else if (c <= 1.5e-36) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 3.5e+119) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (b * (c * -(c * i)))
    if (c <= (-6.5d+102)) then
        tmp = t_1
    else if (c <= 1.5d-36) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (c <= 3.5d+119) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (b * (c * -(c * i)));
	double tmp;
	if (c <= -6.5e+102) {
		tmp = t_1;
	} else if (c <= 1.5e-36) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (c <= 3.5e+119) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (b * (c * -(c * i)))
	tmp = 0
	if c <= -6.5e+102:
		tmp = t_1
	elif c <= 1.5e-36:
		tmp = ((x * y) + (z * t)) * 2.0
	elif c <= 3.5e+119:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(b * Float64(c * Float64(-Float64(c * i)))))
	tmp = 0.0
	if (c <= -6.5e+102)
		tmp = t_1;
	elseif (c <= 1.5e-36)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (c <= 3.5e+119)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (b * (c * -(c * i)));
	tmp = 0.0;
	if (c <= -6.5e+102)
		tmp = t_1;
	elseif (c <= 1.5e-36)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (c <= 3.5e+119)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	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[(b * N[(c * (-N[(c * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.5e+102], t$95$1, If[LessEqual[c, 1.5e-36], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[c, 3.5e+119], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.5000000000000004e102 or 3.5000000000000001e119 < c

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. +-commutative 80.8%

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

      3. distribute-rgt-in 70.4%

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

   3. Applied egg-rr 70.4%

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

   4. Taylor expanded in b around inf 65.8%

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

      1. mul-1-neg 65.8%

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

      2. associate-*r* 72.2%

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

      3. distribute-rgt-neg-in 72.2%

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

      4. unpow2 72.2%

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

      5. associate-*l* 76.1%

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

   6. Simplified 76.1%

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

   if -6.5000000000000004e102 < c < 1.5000000000000001e-36

   1. Initial program 97.4%

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

   2. Taylor expanded in c around 0 80.0%

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

   if 1.5000000000000001e-36 < c < 3.5000000000000001e119

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 73.5%

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

   3. Taylor expanded in z around 0 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-*l* 70.4%

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

      3. *-commutative 70.4%

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

   5. Simplified 70.4%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(-c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-36}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+119}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(c \cdot \left(-c \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 9: 74.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+45} \lor \neg \left(c \leq 1250\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.05e+45) (not (<= c 1250.0)))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.05e+45) || !(c <= 1250.0)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.05d+45)) .or. (.not. (c <= 1250.0d0))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.05e+45) || !(c <= 1250.0)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.05e+45) or not (c <= 1250.0):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.05e+45) || !(c <= 1250.0))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.05e+45) || ~((c <= 1250.0)))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.05e+45], N[Not[LessEqual[c, 1250.0]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.04999999999999997e45 or 1250 < c

   1. Initial program 84.2%

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

   2. Taylor expanded in i around inf 75.8%

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

   if -1.04999999999999997e45 < c < 1250

   1. Initial program 98.1%

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

   2. Taylor expanded in c around 0 81.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+45} \lor \neg \left(c \leq 1250\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 10: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 60200000 \lor \neg \left(t \leq 1.8 \cdot 10^{+96}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))))
   (if (<= t -1.35e-32)
     t_1
     (if (<= t 3.5e-58)
       (* 2.0 (* x y))
       (if (or (<= t 60200000.0) (not (<= t 1.8e+96)))
         t_1
         (* (* 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 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.35e-32) {
		tmp = t_1;
	} else if (t <= 3.5e-58) {
		tmp = 2.0 * (x * y);
	} else if ((t <= 60200000.0) || !(t <= 1.8e+96)) {
		tmp = t_1;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    if (t <= (-1.35d-32)) then
        tmp = t_1
    else if (t <= 3.5d-58) then
        tmp = 2.0d0 * (x * y)
    else if ((t <= 60200000.0d0) .or. (.not. (t <= 1.8d+96))) then
        tmp = t_1
    else
        tmp = (a * (c * i)) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (z * t);
	double tmp;
	if (t <= -1.35e-32) {
		tmp = t_1;
	} else if (t <= 3.5e-58) {
		tmp = 2.0 * (x * y);
	} else if ((t <= 60200000.0) || !(t <= 1.8e+96)) {
		tmp = t_1;
	} else {
		tmp = (a * (c * i)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	tmp = 0
	if t <= -1.35e-32:
		tmp = t_1
	elif t <= 3.5e-58:
		tmp = 2.0 * (x * y)
	elif (t <= 60200000.0) or not (t <= 1.8e+96):
		tmp = t_1
	else:
		tmp = (a * (c * i)) * -2.0
	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 (t <= -1.35e-32)
		tmp = t_1;
	elseif (t <= 3.5e-58)
		tmp = Float64(2.0 * Float64(x * y));
	elseif ((t <= 60200000.0) || !(t <= 1.8e+96))
		tmp = t_1;
	else
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	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 (t <= -1.35e-32)
		tmp = t_1;
	elseif (t <= 3.5e-58)
		tmp = 2.0 * (x * y);
	elseif ((t <= 60200000.0) || ~((t <= 1.8e+96)))
		tmp = t_1;
	else
		tmp = (a * (c * i)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-32], t$95$1, If[LessEqual[t, 3.5e-58], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 60200000.0], N[Not[LessEqual[t, 1.8e+96]], $MachinePrecision]], t$95$1, N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3499999999999999e-32 or 3.4999999999999999e-58 < t < 6.02e7 or 1.80000000000000007e96 < t

   1. Initial program 87.1%

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

   2. Taylor expanded in z around inf 44.6%

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

   if -1.3499999999999999e-32 < t < 3.4999999999999999e-58

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf 50.5%

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

   if 6.02e7 < t < 1.80000000000000007e96

   1. Initial program 91.2%

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

   2. Taylor expanded in a around inf 29.6%

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

      1. associate-*r* 29.6%

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

      2. neg-mul-1 29.6%

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

   4. Simplified 29.6%

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

   5. Taylor expanded in c around 0 29.6%

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

      1. associate-*r* 29.6%

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

      2. *-commutative 29.6%

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

   7. Simplified 29.6%

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

   8. Taylor expanded in c around 0 29.6%

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

      1. associate-*r* 50.7%

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

   10. Simplified 50.7%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-32}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 60200000 \lor \neg \left(t \leq 1.8 \cdot 10^{+96}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]

Alternative 11: 39.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-34} \lor \neg \left(t \leq 4 \cdot 10^{-60}\right) \land \left(t \leq 2 \cdot 10^{+54} \lor \neg \left(t \leq 1.8 \cdot 10^{+96}\right)\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -3.3e-34)
         (and (not (<= t 4e-60)) (or (<= t 2e+54) (not (<= t 1.8e+96)))))
   (* 2.0 (* z t))
   (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((t <= -3.3e-34) || (!(t <= 4e-60) && ((t <= 2e+54) || !(t <= 1.8e+96)))) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	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 ((t <= (-3.3d-34)) .or. (.not. (t <= 4d-60)) .and. (t <= 2d+54) .or. (.not. (t <= 1.8d+96))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    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 ((t <= -3.3e-34) || (!(t <= 4e-60) && ((t <= 2e+54) || !(t <= 1.8e+96)))) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (t <= -3.3e-34) or (not (t <= 4e-60) and ((t <= 2e+54) or not (t <= 1.8e+96))):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((t <= -3.3e-34) || (!(t <= 4e-60) && ((t <= 2e+54) || !(t <= 1.8e+96))))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((t <= -3.3e-34) || (~((t <= 4e-60)) && ((t <= 2e+54) || ~((t <= 1.8e+96)))))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[t, -3.3e-34], And[N[Not[LessEqual[t, 4e-60]], $MachinePrecision], Or[LessEqual[t, 2e+54], N[Not[LessEqual[t, 1.8e+96]], $MachinePrecision]]]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.29999999999999983e-34 or 3.9999999999999999e-60 < t < 2.0000000000000002e54 or 1.80000000000000007e96 < t

   1. Initial program 87.5%

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

   2. Taylor expanded in z around inf 43.4%

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

   if -3.29999999999999983e-34 < t < 3.9999999999999999e-60 or 2.0000000000000002e54 < t < 1.80000000000000007e96

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 50.1%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-34} \lor \neg \left(t \leq 4 \cdot 10^{-60}\right) \land \left(t \leq 2 \cdot 10^{+54} \lor \neg \left(t \leq 1.8 \cdot 10^{+96}\right)\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 58.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+109} \lor \neg \left(i \leq 1.18 \cdot 10^{+206}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -2.9e+109) (not (<= i 1.18e+206)))
   (* (* a (* c i)) -2.0)
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -2.9e+109) || !(i <= 1.18e+206)) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = ((x * y) + (z * t)) * 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 ((i <= (-2.9d+109)) .or. (.not. (i <= 1.18d+206))) then
        tmp = (a * (c * i)) * (-2.0d0)
    else
        tmp = ((x * y) + (z * t)) * 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 ((i <= -2.9e+109) || !(i <= 1.18e+206)) {
		tmp = (a * (c * i)) * -2.0;
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -2.9e+109) or not (i <= 1.18e+206):
		tmp = (a * (c * i)) * -2.0
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -2.9e+109) || !(i <= 1.18e+206))
		tmp = Float64(Float64(a * Float64(c * i)) * -2.0);
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -2.9e+109) || ~((i <= 1.18e+206)))
		tmp = (a * (c * i)) * -2.0;
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -2.9e+109], N[Not[LessEqual[i, 1.18e+206]], $MachinePrecision]], N[(N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.9e109 or 1.18e206 < i

   1. Initial program 94.1%

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

   2. Taylor expanded in a around inf 38.6%

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

      1. associate-*r* 38.6%

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

      2. neg-mul-1 38.6%

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

   4. Simplified 38.6%

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

   5. Taylor expanded in c around 0 38.6%

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

      1. associate-*r* 38.6%

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

      2. *-commutative 38.6%

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

   7. Simplified 38.6%

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

   8. Taylor expanded in c around 0 38.6%

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

      1. associate-*r* 52.5%

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

   10. Simplified 52.5%

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

   if -2.9e109 < i < 1.18e206

   1. Initial program 91.2%

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

   2. Taylor expanded in c around 0 68.2%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+109} \lor \neg \left(i \leq 1.18 \cdot 10^{+206}\right):\\ \;\;\;\;\left(a \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 13: 29.4% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.0%

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

2. Taylor expanded in z around inf 30.1%

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

3. Final simplification 30.1%

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

Developer target: 94.0% 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 2023171 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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