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

Percentage Accurate: 90.0% → 95.7%

Time: 13.4s

Alternatives: 16

Speedup: 0.5×

• 46.5% 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: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(i * N[(c * t$95$1), $MachinePrecision]), $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[(c * N[(c * N[(b * (-i)), $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 90.6%

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

      1. associate-*l* 98.7%

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

      2. fma-def 98.7%

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

   3. Simplified 98.7%

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

      1. fma-def 98.7%

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

      2. +-commutative 98.7%

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

   5. Applied egg-rr 98.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in b around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-in 50.1%

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

      4. unpow2 50.1%

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

      5. distribute-rgt-neg-in 50.1%

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

   4. Simplified 50.1%

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

      1. expm1-log1p-u 33.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right)\right)\right)} \]

      2. expm1-udef 33.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right)\right)} - 1} \]

      3. *-commutative 33.5%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2}\right)} - 1 \]

   6. Applied egg-rr 33.5%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 33.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)\right)} \]

      2. expm1-log1p 50.1%

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

      3. *-commutative 50.1%

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

      4. associate-*r* 50.2%

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

      5. *-commutative 50.2%

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

      6. *-commutative 50.2%

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

      7. distribute-lft-neg-in 50.2%

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

      8. distribute-rgt-neg-in 50.2%

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

      9. distribute-rgt-neg-in 50.2%

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

      10. distribute-rgt-neg-in 50.2%

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

   8. Simplified 50.2%

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

4. Final simplification 96.5%

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

Alternative 2: 94.5% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (fma 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 * (fma(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(fma(x, y, Float64(z * t)) - Float64(Float64(a + Float64(b * c)) * Float64(c * i))))
end

Wolfram

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

Derivation

1. Initial program 86.4%

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

   1. associate-*l* 94.5%

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

   2. fma-def 95.3%

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

3. Simplified 95.3%

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

4. Final simplification 95.3%

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

Alternative 3: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := i \cdot \left(c \cdot t_1\right)\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+300}\right):\\ \;\;\;\;2 \cdot \left(\left(t_1 \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* i (* c t_1))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+300)))
     (* 2.0 (* (* t_1 i) (- c)))
     (* 2.0 (- (+ (* z t) (* x y)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+300)) {
		tmp = 2.0 * ((t_1 * i) * -c);
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - t_2);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = i * (c * t_1);
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+300)) {
		tmp = 2.0 * ((t_1 * i) * -c);
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = i * (c * t_1)
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+300):
		tmp = 2.0 * ((t_1 * i) * -c)
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(i * Float64(c * t_1))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+300))
		tmp = Float64(2.0 * Float64(Float64(t_1 * i) * Float64(-c)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = i * (c * t_1);
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+300)))
		tmp = 2.0 * ((t_1 * i) * -c);
	else
		tmp = 2.0 * (((z * t) + (x * y)) - t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(c * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+300]], $MachinePrecision]], N[(2.0 * N[(N[(t$95$1 * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 5.00000000000000026e300 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 65.4%

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

   2. Taylor expanded in i around inf 90.4%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.00000000000000026e300

   1. Initial program 98.5%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq -\infty \lor \neg \left(i \cdot \left(c \cdot \left(a + b \cdot c\right)\right) \leq 5 \cdot 10^{+300}\right):\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 4: 70.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t + x \cdot y\right)\\ t_3 := 2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -5.3 \cdot 10^{+95}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* i (* a c)))))
        (t_2 (* 2.0 (+ (* z t) (* x y))))
        (t_3 (* 2.0 (* (* (+ a (* b c)) i) (- c)))))
   (if (<= c -5.3e+95)
     t_3
     (if (<= c 1.26e-301)
       t_2
       (if (<= c 7e-143)
         t_1
         (if (<= c 3.4e+45) t_2 (if (<= c 1.65e+59) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * ((z * t) + (x * y));
	double t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -5.3e+95) {
		tmp = t_3;
	} else if (c <= 1.26e-301) {
		tmp = t_2;
	} else if (c <= 7e-143) {
		tmp = t_1;
	} else if (c <= 3.4e+45) {
		tmp = t_2;
	} else if (c <= 1.65e+59) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (i * (a * c)))
    t_2 = 2.0d0 * ((z * t) + (x * y))
    t_3 = 2.0d0 * (((a + (b * c)) * i) * -c)
    if (c <= (-5.3d+95)) then
        tmp = t_3
    else if (c <= 1.26d-301) then
        tmp = t_2
    else if (c <= 7d-143) then
        tmp = t_1
    else if (c <= 3.4d+45) then
        tmp = t_2
    else if (c <= 1.65d+59) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * ((z * t) + (x * y));
	double t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	double tmp;
	if (c <= -5.3e+95) {
		tmp = t_3;
	} else if (c <= 1.26e-301) {
		tmp = t_2;
	} else if (c <= 7e-143) {
		tmp = t_1;
	} else if (c <= 3.4e+45) {
		tmp = t_2;
	} else if (c <= 1.65e+59) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (i * (a * c)))
	t_2 = 2.0 * ((z * t) + (x * y))
	t_3 = 2.0 * (((a + (b * c)) * i) * -c)
	tmp = 0
	if c <= -5.3e+95:
		tmp = t_3
	elif c <= 1.26e-301:
		tmp = t_2
	elif c <= 7e-143:
		tmp = t_1
	elif c <= 3.4e+45:
		tmp = t_2
	elif c <= 1.65e+59:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(a * c))))
	t_2 = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)))
	t_3 = Float64(2.0 * Float64(Float64(Float64(a + Float64(b * c)) * i) * Float64(-c)))
	tmp = 0.0
	if (c <= -5.3e+95)
		tmp = t_3;
	elseif (c <= 1.26e-301)
		tmp = t_2;
	elseif (c <= 7e-143)
		tmp = t_1;
	elseif (c <= 3.4e+45)
		tmp = t_2;
	elseif (c <= 1.65e+59)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (i * (a * c)));
	t_2 = 2.0 * ((z * t) + (x * y));
	t_3 = 2.0 * (((a + (b * c)) * i) * -c);
	tmp = 0.0;
	if (c <= -5.3e+95)
		tmp = t_3;
	elseif (c <= 1.26e-301)
		tmp = t_2;
	elseif (c <= 7e-143)
		tmp = t_1;
	elseif (c <= 3.4e+45)
		tmp = t_2;
	elseif (c <= 1.65e+59)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.3e+95], t$95$3, If[LessEqual[c, 1.26e-301], t$95$2, If[LessEqual[c, 7e-143], t$95$1, If[LessEqual[c, 3.4e+45], t$95$2, If[LessEqual[c, 1.65e+59], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.3000000000000002e95 or 1.65e59 < c

   1. Initial program 70.8%

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

   2. Taylor expanded in i around inf 87.2%

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

   if -5.3000000000000002e95 < c < 1.2599999999999999e-301 or 7.00000000000000011e-143 < c < 3.4e45

   1. Initial program 93.6%

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

   2. Taylor expanded in c around 0 75.8%

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

   if 1.2599999999999999e-301 < c < 7.00000000000000011e-143 or 3.4e45 < c < 1.65e59

   1. Initial program 99.4%

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

      1. associate-*l* 99.8%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-def 99.8%

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

      2. +-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around inf 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l* 97.1%

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

      3. *-commutative 97.1%

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

   8. Simplified 97.1%

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

   9. Taylor expanded in z around 0 76.2%

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

       1. associate-*r* 88.0%

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

       2. *-commutative 88.0%

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

       3. *-commutative 88.0%

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

       4. *-commutative 88.0%

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

   11. Simplified 88.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.3 \cdot 10^{+95}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{-301}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-143}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+45}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{+59}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 5: 46.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := -2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ t_3 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;c \leq -1.42 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-303}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y)))
        (t_2 (* -2.0 (* (* c c) (* b i))))
        (t_3 (* 2.0 (* z t))))
   (if (<= c -1.42e+110)
     t_2
     (if (<= c -7e-30)
       t_1
       (if (<= c -6.5e-161)
         t_3
         (if (<= c -2e-267)
           t_1
           (if (<= c 8.8e-303) t_3 (if (<= c 9.8e+58) 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 = 2.0 * (x * y);
	double t_2 = -2.0 * ((c * c) * (b * i));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -1.42e+110) {
		tmp = t_2;
	} else if (c <= -7e-30) {
		tmp = t_1;
	} else if (c <= -6.5e-161) {
		tmp = t_3;
	} else if (c <= -2e-267) {
		tmp = t_1;
	} else if (c <= 8.8e-303) {
		tmp = t_3;
	} else if (c <= 9.8e+58) {
		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) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = (-2.0d0) * ((c * c) * (b * i))
    t_3 = 2.0d0 * (z * t)
    if (c <= (-1.42d+110)) then
        tmp = t_2
    else if (c <= (-7d-30)) then
        tmp = t_1
    else if (c <= (-6.5d-161)) then
        tmp = t_3
    else if (c <= (-2d-267)) then
        tmp = t_1
    else if (c <= 8.8d-303) then
        tmp = t_3
    else if (c <= 9.8d+58) 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 = 2.0 * (x * y);
	double t_2 = -2.0 * ((c * c) * (b * i));
	double t_3 = 2.0 * (z * t);
	double tmp;
	if (c <= -1.42e+110) {
		tmp = t_2;
	} else if (c <= -7e-30) {
		tmp = t_1;
	} else if (c <= -6.5e-161) {
		tmp = t_3;
	} else if (c <= -2e-267) {
		tmp = t_1;
	} else if (c <= 8.8e-303) {
		tmp = t_3;
	} else if (c <= 9.8e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = -2.0 * ((c * c) * (b * i))
	t_3 = 2.0 * (z * t)
	tmp = 0
	if c <= -1.42e+110:
		tmp = t_2
	elif c <= -7e-30:
		tmp = t_1
	elif c <= -6.5e-161:
		tmp = t_3
	elif c <= -2e-267:
		tmp = t_1
	elif c <= 8.8e-303:
		tmp = t_3
	elif c <= 9.8e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(-2.0 * Float64(Float64(c * c) * Float64(b * i)))
	t_3 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (c <= -1.42e+110)
		tmp = t_2;
	elseif (c <= -7e-30)
		tmp = t_1;
	elseif (c <= -6.5e-161)
		tmp = t_3;
	elseif (c <= -2e-267)
		tmp = t_1;
	elseif (c <= 8.8e-303)
		tmp = t_3;
	elseif (c <= 9.8e+58)
		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 = 2.0 * (x * y);
	t_2 = -2.0 * ((c * c) * (b * i));
	t_3 = 2.0 * (z * t);
	tmp = 0.0;
	if (c <= -1.42e+110)
		tmp = t_2;
	elseif (c <= -7e-30)
		tmp = t_1;
	elseif (c <= -6.5e-161)
		tmp = t_3;
	elseif (c <= -2e-267)
		tmp = t_1;
	elseif (c <= 8.8e-303)
		tmp = t_3;
	elseif (c <= 9.8e+58)
		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[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.42e+110], t$95$2, If[LessEqual[c, -7e-30], t$95$1, If[LessEqual[c, -6.5e-161], t$95$3, If[LessEqual[c, -2e-267], t$95$1, If[LessEqual[c, 8.8e-303], t$95$3, If[LessEqual[c, 9.8e+58], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.4200000000000001e110 or 9.80000000000000037e58 < c

   1. Initial program 71.2%

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

   2. Taylor expanded in b around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. *-commutative 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

      4. unpow2 61.5%

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

      5. distribute-rgt-neg-in 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in i around 0 61.5%

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

      1. unpow2 61.5%

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

   7. Simplified 61.5%

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

   if -1.4200000000000001e110 < c < -7.0000000000000006e-30 or -6.50000000000000008e-161 < c < -2e-267 or 8.80000000000000055e-303 < c < 9.80000000000000037e58

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf 49.6%

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

   if -7.0000000000000006e-30 < c < -6.50000000000000008e-161 or -2e-267 < c < 8.80000000000000055e-303

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 61.5%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.42 \cdot 10^{+110}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-30}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -6.5 \cdot 10^{-161}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \]

Alternative 6: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ t_2 := 2 \cdot \left(z \cdot t + x \cdot y\right)\\ t_3 := 2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+121}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* x y) (* i (* a c)))))
        (t_2 (* 2.0 (+ (* z t) (* x y))))
        (t_3 (* 2.0 (* c (* c (* b (- i)))))))
   (if (<= c -8.5e+121)
     t_3
     (if (<= c 1.26e-301)
       t_2
       (if (<= c 2.6e-143)
         t_1
         (if (<= c 7e+44) t_2 (if (<= c 9.5e+85) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * ((z * t) + (x * y));
	double t_3 = 2.0 * (c * (c * (b * -i)));
	double tmp;
	if (c <= -8.5e+121) {
		tmp = t_3;
	} else if (c <= 1.26e-301) {
		tmp = t_2;
	} else if (c <= 2.6e-143) {
		tmp = t_1;
	} else if (c <= 7e+44) {
		tmp = t_2;
	} else if (c <= 9.5e+85) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 2.0d0 * ((x * y) - (i * (a * c)))
    t_2 = 2.0d0 * ((z * t) + (x * y))
    t_3 = 2.0d0 * (c * (c * (b * -i)))
    if (c <= (-8.5d+121)) then
        tmp = t_3
    else if (c <= 1.26d-301) then
        tmp = t_2
    else if (c <= 2.6d-143) then
        tmp = t_1
    else if (c <= 7d+44) then
        tmp = t_2
    else if (c <= 9.5d+85) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((x * y) - (i * (a * c)));
	double t_2 = 2.0 * ((z * t) + (x * y));
	double t_3 = 2.0 * (c * (c * (b * -i)));
	double tmp;
	if (c <= -8.5e+121) {
		tmp = t_3;
	} else if (c <= 1.26e-301) {
		tmp = t_2;
	} else if (c <= 2.6e-143) {
		tmp = t_1;
	} else if (c <= 7e+44) {
		tmp = t_2;
	} else if (c <= 9.5e+85) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((x * y) - (i * (a * c)))
	t_2 = 2.0 * ((z * t) + (x * y))
	t_3 = 2.0 * (c * (c * (b * -i)))
	tmp = 0
	if c <= -8.5e+121:
		tmp = t_3
	elif c <= 1.26e-301:
		tmp = t_2
	elif c <= 2.6e-143:
		tmp = t_1
	elif c <= 7e+44:
		tmp = t_2
	elif c <= 9.5e+85:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(x * y) - Float64(i * Float64(a * c))))
	t_2 = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)))
	t_3 = Float64(2.0 * Float64(c * Float64(c * Float64(b * Float64(-i)))))
	tmp = 0.0
	if (c <= -8.5e+121)
		tmp = t_3;
	elseif (c <= 1.26e-301)
		tmp = t_2;
	elseif (c <= 2.6e-143)
		tmp = t_1;
	elseif (c <= 7e+44)
		tmp = t_2;
	elseif (c <= 9.5e+85)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((x * y) - (i * (a * c)));
	t_2 = 2.0 * ((z * t) + (x * y));
	t_3 = 2.0 * (c * (c * (b * -i)));
	tmp = 0.0;
	if (c <= -8.5e+121)
		tmp = t_3;
	elseif (c <= 1.26e-301)
		tmp = t_2;
	elseif (c <= 2.6e-143)
		tmp = t_1;
	elseif (c <= 7e+44)
		tmp = t_2;
	elseif (c <= 9.5e+85)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(c * N[(c * N[(b * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e+121], t$95$3, If[LessEqual[c, 1.26e-301], t$95$2, If[LessEqual[c, 2.6e-143], t$95$1, If[LessEqual[c, 7e+44], t$95$2, If[LessEqual[c, 9.5e+85], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.5e121 or 9.49999999999999945e85 < c

   1. Initial program 72.2%

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

   2. Taylor expanded in b around inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. *-commutative 64.1%

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

      3. distribute-rgt-neg-in 64.1%

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

      4. unpow2 64.1%

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

      5. distribute-rgt-neg-in 64.1%

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

   4. Simplified 64.1%

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

      1. expm1-log1p-u 31.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right)\right)\right)} \]

      2. expm1-udef 31.8%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right)\right)} - 1} \]

      3. *-commutative 31.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2}\right)} - 1 \]

   6. Applied egg-rr 31.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 31.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)\right)} \]

      2. expm1-log1p 64.1%

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

      3. *-commutative 64.1%

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

      4. associate-*r* 68.8%

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

      5. *-commutative 68.8%

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

      6. *-commutative 68.8%

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

      7. distribute-lft-neg-in 68.8%

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

      8. distribute-rgt-neg-in 68.8%

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

      9. distribute-rgt-neg-in 68.8%

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

      10. distribute-rgt-neg-in 68.8%

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

   8. Simplified 68.8%

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

   if -8.5e121 < c < 1.2599999999999999e-301 or 2.59999999999999987e-143 < c < 6.9999999999999998e44

   1. Initial program 93.0%

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

   2. Taylor expanded in c around 0 75.1%

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

   if 1.2599999999999999e-301 < c < 2.59999999999999987e-143 or 6.9999999999999998e44 < c < 9.49999999999999945e85

   1. Initial program 93.1%

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

      1. associate-*l* 97.6%

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

      2. fma-def 97.6%

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

   3. Simplified 97.6%

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

      1. fma-def 97.6%

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

      2. +-commutative 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in a around inf 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-*l* 93.0%

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

      3. *-commutative 93.0%

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

   8. Simplified 93.0%

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

   9. Taylor expanded in z around 0 74.4%

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

       1. associate-*r* 82.9%

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

       2. *-commutative 82.9%

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

       3. *-commutative 82.9%

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

       4. *-commutative 82.9%

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

   11. Simplified 82.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+121}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.26 \cdot 10^{-301}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-143}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+44}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(x \cdot y - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \end{array} \]

Alternative 7: 84.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+121} \lor \neg \left(c \leq 6.2 \cdot 10^{+62}\right):\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -5.2e+121) (not (<= c 6.2e+62)))
   (* 2.0 (* (* (+ a (* b c)) i) (- c)))
   (* 2.0 (- (+ (* z t) (* x y)) (* 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 <= -5.2e+121) || !(c <= 6.2e+62)) {
		tmp = 2.0 * (((a + (b * c)) * i) * -c);
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (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 <= (-5.2d+121)) .or. (.not. (c <= 6.2d+62))) then
        tmp = 2.0d0 * (((a + (b * c)) * i) * -c)
    else
        tmp = 2.0d0 * (((z * t) + (x * y)) - (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 <= -5.2e+121) || !(c <= 6.2e+62)) {
		tmp = 2.0 * (((a + (b * c)) * i) * -c);
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -5.2e+121) or not (c <= 6.2e+62):
		tmp = 2.0 * (((a + (b * c)) * i) * -c)
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -5.2e+121) || !(c <= 6.2e+62))
		tmp = Float64(2.0 * Float64(Float64(Float64(a + Float64(b * c)) * i) * Float64(-c)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - 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 <= -5.2e+121) || ~((c <= 6.2e+62)))
		tmp = 2.0 * (((a + (b * c)) * i) * -c);
	else
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -5.2e+121], N[Not[LessEqual[c, 6.2e+62]], $MachinePrecision]], N[(2.0 * N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -5.1999999999999998e121 or 6.20000000000000029e62 < c

   1. Initial program 70.5%

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

   2. Taylor expanded in i around inf 88.7%

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

   if -5.1999999999999998e121 < c < 6.20000000000000029e62

   1. Initial program 94.5%

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

   2. Taylor expanded in a around inf 91.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+121} \lor \neg \left(c \leq 6.2 \cdot 10^{+62}\right):\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 8: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+122} \lor \neg \left(c \leq 6.2 \cdot 10^{+62}\right):\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.1e+122) (not (<= c 6.2e+62)))
   (* 2.0 (* (* (+ a (* b c)) i) (- c)))
   (* 2.0 (- (+ (* z t) (* x y)) (* a (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.1e+122) || !(c <= 6.2e+62)) {
		tmp = 2.0 * (((a + (b * c)) * i) * -c);
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.1d+122)) .or. (.not. (c <= 6.2d+62))) then
        tmp = 2.0d0 * (((a + (b * c)) * i) * -c)
    else
        tmp = 2.0d0 * (((z * t) + (x * y)) - (a * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.1e+122) || !(c <= 6.2e+62)) {
		tmp = 2.0 * (((a + (b * c)) * i) * -c);
	} else {
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.1e+122) or not (c <= 6.2e+62):
		tmp = 2.0 * (((a + (b * c)) * i) * -c)
	else:
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.1e+122) || !(c <= 6.2e+62))
		tmp = Float64(2.0 * Float64(Float64(Float64(a + Float64(b * c)) * i) * Float64(-c)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.1e+122) || ~((c <= 6.2e+62)))
		tmp = 2.0 * (((a + (b * c)) * i) * -c);
	else
		tmp = 2.0 * (((z * t) + (x * y)) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.1e+122], N[Not[LessEqual[c, 6.2e+62]], $MachinePrecision]], N[(2.0 * N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision] * (-c)), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.10000000000000016e122 or 6.20000000000000029e62 < c

   1. Initial program 70.5%

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

   2. Taylor expanded in i around inf 88.7%

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

   if -2.10000000000000016e122 < c < 6.20000000000000029e62

   1. Initial program 94.5%

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

      1. associate-*l* 95.3%

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

      2. fma-def 96.4%

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

   3. Simplified 96.4%

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

      1. fma-def 95.3%

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

      2. +-commutative 95.3%

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

   5. Applied egg-rr 95.3%

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

   6. Taylor expanded in a around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-*l* 91.1%

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

      3. *-commutative 91.1%

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

   8. Simplified 91.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{+122} \lor \neg \left(c \leq 6.2 \cdot 10^{+62}\right):\\ \;\;\;\;2 \cdot \left(\left(\left(a + b \cdot c\right) \cdot i\right) \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 9: 35.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-272}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= a -5.8e+127)
     (* c (* -2.0 (* a i)))
     (if (<= a -1.95e+56)
       t_1
       (if (<= a -3.4e-272)
         t_2
         (if (<= a 2.6e-106)
           t_1
           (if (<= a 5e+137) t_2 (* (* c i) (* a -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 t_2 = 2.0 * (x * y);
	double tmp;
	if (a <= -5.8e+127) {
		tmp = c * (-2.0 * (a * i));
	} else if (a <= -1.95e+56) {
		tmp = t_1;
	} else if (a <= -3.4e-272) {
		tmp = t_2;
	} else if (a <= 2.6e-106) {
		tmp = t_1;
	} else if (a <= 5e+137) {
		tmp = t_2;
	} else {
		tmp = (c * i) * (a * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (a <= (-5.8d+127)) then
        tmp = c * ((-2.0d0) * (a * i))
    else if (a <= (-1.95d+56)) then
        tmp = t_1
    else if (a <= (-3.4d-272)) then
        tmp = t_2
    else if (a <= 2.6d-106) then
        tmp = t_1
    else if (a <= 5d+137) then
        tmp = t_2
    else
        tmp = (c * i) * (a * (-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 t_2 = 2.0 * (x * y);
	double tmp;
	if (a <= -5.8e+127) {
		tmp = c * (-2.0 * (a * i));
	} else if (a <= -1.95e+56) {
		tmp = t_1;
	} else if (a <= -3.4e-272) {
		tmp = t_2;
	} else if (a <= 2.6e-106) {
		tmp = t_1;
	} else if (a <= 5e+137) {
		tmp = t_2;
	} else {
		tmp = (c * i) * (a * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if a <= -5.8e+127:
		tmp = c * (-2.0 * (a * i))
	elif a <= -1.95e+56:
		tmp = t_1
	elif a <= -3.4e-272:
		tmp = t_2
	elif a <= 2.6e-106:
		tmp = t_1
	elif a <= 5e+137:
		tmp = t_2
	else:
		tmp = (c * i) * (a * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (a <= -5.8e+127)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	elseif (a <= -1.95e+56)
		tmp = t_1;
	elseif (a <= -3.4e-272)
		tmp = t_2;
	elseif (a <= 2.6e-106)
		tmp = t_1;
	elseif (a <= 5e+137)
		tmp = t_2;
	else
		tmp = Float64(Float64(c * i) * Float64(a * -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);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (a <= -5.8e+127)
		tmp = c * (-2.0 * (a * i));
	elseif (a <= -1.95e+56)
		tmp = t_1;
	elseif (a <= -3.4e-272)
		tmp = t_2;
	elseif (a <= 2.6e-106)
		tmp = t_1;
	elseif (a <= 5e+137)
		tmp = t_2;
	else
		tmp = (c * i) * (a * -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]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.8e+127], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e+56], t$95$1, If[LessEqual[a, -3.4e-272], t$95$2, If[LessEqual[a, 2.6e-106], t$95$1, If[LessEqual[a, 5e+137], t$95$2, N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.8000000000000004e127

   1. Initial program 79.3%

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

      1. associate-*l* 94.4%

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

      2. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-def 94.4%

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

      2. +-commutative 94.4%

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

   5. Applied egg-rr 94.4%

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

   6. Taylor expanded in a around inf 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*l* 89.2%

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

      3. *-commutative 89.2%

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

   8. Simplified 89.2%

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

   9. Taylor expanded in a around inf 63.9%

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

       1. associate-*r* 63.9%

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

       2. *-commutative 63.9%

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

       3. *-commutative 63.9%

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

       4. associate-*l* 63.9%

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

       5. *-commutative 63.9%

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

       6. associate-*l* 63.9%

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

   11. Simplified 63.9%

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

   if -5.8000000000000004e127 < a < -1.94999999999999997e56 or -3.4000000000000003e-272 < a < 2.6000000000000001e-106

   1. Initial program 91.0%

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

   2. Taylor expanded in z around inf 42.5%

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

   if -1.94999999999999997e56 < a < -3.4000000000000003e-272 or 2.6000000000000001e-106 < a < 5.0000000000000002e137

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf 44.3%

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

   if 5.0000000000000002e137 < a

   1. Initial program 87.6%

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

      1. associate-*l* 95.6%

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

      2. fma-def 95.6%

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

   3. Simplified 95.6%

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

      1. fma-def 95.6%

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

      2. +-commutative 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in a around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-*l* 87.4%

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

      3. *-commutative 87.4%

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

   8. Simplified 87.4%

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

   9. Taylor expanded in a around inf 49.0%

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

       1. associate-*r* 49.0%

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

       2. *-commutative 49.0%

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

       3. *-commutative 49.0%

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

       4. associate-*l* 49.0%

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

       5. *-commutative 49.0%

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

       6. associate-*l* 49.0%

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

   11. Simplified 49.0%

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

       1. expm1-log1p-u 17.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(\left(i \cdot a\right) \cdot -2\right)\right)\right)} \]

       2. expm1-udef 17.2%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(c \cdot \left(\left(i \cdot a\right) \cdot -2\right)\right)} - 1} \]

       3. associate-*l* 17.2%

          \[\leadsto e^{\mathsf{log1p}\left(c \cdot \color{blue}{\left(i \cdot \left(a \cdot -2\right)\right)}\right)} - 1 \]

   13. Applied egg-rr 17.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\right)} - 1} \]
   14. Step-by-step derivation

       1. expm1-def 17.2%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\right)\right)} \]

       2. expm1-log1p 49.0%

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

       3. associate-*r* 58.9%

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

       4. *-commutative 58.9%

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

       5. *-commutative 58.9%

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

   15. Simplified 58.9%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+127}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+56}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-272}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-106}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+137}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \end{array} \]

Alternative 10: 69.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+123} \lor \neg \left(c \leq 3.9 \cdot 10^{+62}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -8e+123) (not (<= c 3.9e+62)))
   (* 2.0 (* c (* c (* b (- i)))))
   (* 2.0 (+ (* z t) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -8e+123) || !(c <= 3.9e+62)) {
		tmp = 2.0 * (c * (c * (b * -i)));
	} else {
		tmp = 2.0 * ((z * t) + (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 ((c <= (-8d+123)) .or. (.not. (c <= 3.9d+62))) then
        tmp = 2.0d0 * (c * (c * (b * -i)))
    else
        tmp = 2.0d0 * ((z * t) + (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 ((c <= -8e+123) || !(c <= 3.9e+62)) {
		tmp = 2.0 * (c * (c * (b * -i)));
	} else {
		tmp = 2.0 * ((z * t) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -8e+123) or not (c <= 3.9e+62):
		tmp = 2.0 * (c * (c * (b * -i)))
	else:
		tmp = 2.0 * ((z * t) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -8e+123) || !(c <= 3.9e+62))
		tmp = Float64(2.0 * Float64(c * Float64(c * Float64(b * Float64(-i)))));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -8e+123) || ~((c <= 3.9e+62)))
		tmp = 2.0 * (c * (c * (b * -i)));
	else
		tmp = 2.0 * ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -8e+123], N[Not[LessEqual[c, 3.9e+62]], $MachinePrecision]], N[(2.0 * N[(c * N[(c * N[(b * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.99999999999999982e123 or 3.9e62 < c

   1. Initial program 70.5%

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

   2. Taylor expanded in b around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. *-commutative 62.8%

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

      3. distribute-rgt-neg-in 62.8%

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

      4. unpow2 62.8%

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

      5. distribute-rgt-neg-in 62.8%

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

   4. Simplified 62.8%

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

      1. expm1-log1p-u 32.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right)\right)\right)} \]

      2. expm1-udef 32.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right)\right)} - 1} \]

      3. *-commutative 32.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2}\right)} - 1 \]

   6. Applied egg-rr 32.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 32.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)\right)} \]

      2. expm1-log1p 62.8%

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

      3. *-commutative 62.8%

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

      4. associate-*r* 67.2%

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

      5. *-commutative 67.2%

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

      6. *-commutative 67.2%

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

      7. distribute-lft-neg-in 67.2%

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

      8. distribute-rgt-neg-in 67.2%

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

      9. distribute-rgt-neg-in 67.2%

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

      10. distribute-rgt-neg-in 67.2%

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

   8. Simplified 67.2%

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

   if -7.99999999999999982e123 < c < 3.9e62

   1. Initial program 94.5%

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

   2. Taylor expanded in c around 0 72.0%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+123} \lor \neg \left(c \leq 3.9 \cdot 10^{+62}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot \left(-i\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 11: 38.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= y -3.4e-53)
     t_2
     (if (<= y -6.2e-261)
       t_1
       (if (<= y 2.7e-247)
         (* c (* -2.0 (* a i)))
         (if (<= y 4.2e+68) 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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -3.4e-53) {
		tmp = t_2;
	} else if (y <= -6.2e-261) {
		tmp = t_1;
	} else if (y <= 2.7e-247) {
		tmp = c * (-2.0 * (a * i));
	} else if (y <= 4.2e+68) {
		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 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (y <= (-3.4d-53)) then
        tmp = t_2
    else if (y <= (-6.2d-261)) then
        tmp = t_1
    else if (y <= 2.7d-247) then
        tmp = c * ((-2.0d0) * (a * i))
    else if (y <= 4.2d+68) 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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -3.4e-53) {
		tmp = t_2;
	} else if (y <= -6.2e-261) {
		tmp = t_1;
	} else if (y <= 2.7e-247) {
		tmp = c * (-2.0 * (a * i));
	} else if (y <= 4.2e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if y <= -3.4e-53:
		tmp = t_2
	elif y <= -6.2e-261:
		tmp = t_1
	elif y <= 2.7e-247:
		tmp = c * (-2.0 * (a * i))
	elif y <= 4.2e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -3.4e-53)
		tmp = t_2;
	elseif (y <= -6.2e-261)
		tmp = t_1;
	elseif (y <= 2.7e-247)
		tmp = Float64(c * Float64(-2.0 * Float64(a * i)));
	elseif (y <= 4.2e+68)
		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 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -3.4e-53)
		tmp = t_2;
	elseif (y <= -6.2e-261)
		tmp = t_1;
	elseif (y <= 2.7e-247)
		tmp = c * (-2.0 * (a * i));
	elseif (y <= 4.2e+68)
		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[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e-53], t$95$2, If[LessEqual[y, -6.2e-261], t$95$1, If[LessEqual[y, 2.7e-247], N[(c * N[(-2.0 * N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e-53 or 4.20000000000000002e68 < y

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf 46.7%

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

   if -3.4e-53 < y < -6.1999999999999997e-261 or 2.70000000000000008e-247 < y < 4.20000000000000002e68

   1. Initial program 84.0%

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

   2. Taylor expanded in z around inf 33.6%

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

   if -6.1999999999999997e-261 < y < 2.70000000000000008e-247

   1. Initial program 85.7%

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

      1. associate-*l* 94.9%

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

      2. fma-def 94.9%

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

   3. Simplified 94.9%

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

      1. fma-def 94.9%

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

      2. +-commutative 94.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in a around inf 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in a around inf 41.3%

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

       1. associate-*r* 41.3%

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

       2. *-commutative 41.3%

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

       3. *-commutative 41.3%

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

       4. associate-*l* 41.3%

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

       5. *-commutative 41.3%

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

       6. associate-*l* 41.3%

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

   11. Simplified 41.3%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(-2 \cdot \left(a \cdot i\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+68}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 38.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-247}:\\ \;\;\;\;i \cdot \left(\left(a \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t))) (t_2 (* 2.0 (* x y))))
   (if (<= y -1.7e-62)
     t_2
     (if (<= y -6.5e-261)
       t_1
       (if (<= y 1.28e-247)
         (* i (* (* a c) -2.0))
         (if (<= y 7.2e+68) 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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -1.7e-62) {
		tmp = t_2;
	} else if (y <= -6.5e-261) {
		tmp = t_1;
	} else if (y <= 1.28e-247) {
		tmp = i * ((a * c) * -2.0);
	} else if (y <= 7.2e+68) {
		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 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (y <= (-1.7d-62)) then
        tmp = t_2
    else if (y <= (-6.5d-261)) then
        tmp = t_1
    else if (y <= 1.28d-247) then
        tmp = i * ((a * c) * (-2.0d0))
    else if (y <= 7.2d+68) 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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (y <= -1.7e-62) {
		tmp = t_2;
	} else if (y <= -6.5e-261) {
		tmp = t_1;
	} else if (y <= 1.28e-247) {
		tmp = i * ((a * c) * -2.0);
	} else if (y <= 7.2e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (z * t)
	t_2 = 2.0 * (x * y)
	tmp = 0
	if y <= -1.7e-62:
		tmp = t_2
	elif y <= -6.5e-261:
		tmp = t_1
	elif y <= 1.28e-247:
		tmp = i * ((a * c) * -2.0)
	elif y <= 7.2e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -1.7e-62)
		tmp = t_2;
	elseif (y <= -6.5e-261)
		tmp = t_1;
	elseif (y <= 1.28e-247)
		tmp = Float64(i * Float64(Float64(a * c) * -2.0));
	elseif (y <= 7.2e+68)
		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 = 2.0 * (z * t);
	t_2 = 2.0 * (x * y);
	tmp = 0.0;
	if (y <= -1.7e-62)
		tmp = t_2;
	elseif (y <= -6.5e-261)
		tmp = t_1;
	elseif (y <= 1.28e-247)
		tmp = i * ((a * c) * -2.0);
	elseif (y <= 7.2e+68)
		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[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e-62], t$95$2, If[LessEqual[y, -6.5e-261], t$95$1, If[LessEqual[y, 1.28e-247], N[(i * N[(N[(a * c), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999994e-62 or 7.1999999999999998e68 < y

   1. Initial program 87.7%

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

   2. Taylor expanded in x around inf 46.3%

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

   if -1.69999999999999994e-62 < y < -6.49999999999999984e-261 or 1.28000000000000007e-247 < y < 7.1999999999999998e68

   1. Initial program 84.7%

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

   2. Taylor expanded in z around inf 33.9%

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

   if -6.49999999999999984e-261 < y < 1.28000000000000007e-247

   1. Initial program 85.7%

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

      1. associate-*l* 94.9%

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

      2. fma-def 94.9%

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

   3. Simplified 94.9%

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

      1. fma-def 94.9%

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

      2. +-commutative 94.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in a around inf 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in a around inf 41.3%

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

       1. associate-*r* 41.3%

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

       2. *-commutative 41.3%

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

       3. *-commutative 41.3%

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

       4. associate-*l* 41.3%

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

       5. associate-*r* 36.8%

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

       6. associate-*l* 36.8%

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

       7. *-commutative 36.8%

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

   11. Simplified 36.8%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-62}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-261}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-247}:\\ \;\;\;\;i \cdot \left(\left(a \cdot c\right) \cdot -2\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+68}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 13: 68.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+123} \lor \neg \left(c \leq 6 \cdot 10^{+62}\right):\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.65e+123) (not (<= c 6e+62)))
   (* -2.0 (* (* c c) (* b i)))
   (* 2.0 (+ (* z t) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.65e+123) || !(c <= 6e+62)) {
		tmp = -2.0 * ((c * c) * (b * i));
	} else {
		tmp = 2.0 * ((z * t) + (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 ((c <= (-1.65d+123)) .or. (.not. (c <= 6d+62))) then
        tmp = (-2.0d0) * ((c * c) * (b * i))
    else
        tmp = 2.0d0 * ((z * t) + (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 ((c <= -1.65e+123) || !(c <= 6e+62)) {
		tmp = -2.0 * ((c * c) * (b * i));
	} else {
		tmp = 2.0 * ((z * t) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.65e+123) or not (c <= 6e+62):
		tmp = -2.0 * ((c * c) * (b * i))
	else:
		tmp = 2.0 * ((z * t) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.65e+123) || !(c <= 6e+62))
		tmp = Float64(-2.0 * Float64(Float64(c * c) * Float64(b * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.65e+123) || ~((c <= 6e+62)))
		tmp = -2.0 * ((c * c) * (b * i));
	else
		tmp = 2.0 * ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.65e+123], N[Not[LessEqual[c, 6e+62]], $MachinePrecision]], N[(-2.0 * N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.65000000000000001e123 or 6e62 < c

   1. Initial program 70.5%

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

   2. Taylor expanded in b around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. *-commutative 62.8%

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

      3. distribute-rgt-neg-in 62.8%

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

      4. unpow2 62.8%

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

      5. distribute-rgt-neg-in 62.8%

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

   4. Simplified 62.8%

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

   5. Taylor expanded in i around 0 62.8%

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

      1. unpow2 62.8%

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

   7. Simplified 62.8%

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

   if -1.65000000000000001e123 < c < 6e62

   1. Initial program 94.5%

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

   2. Taylor expanded in c around 0 72.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+123} \lor \neg \left(c \leq 6 \cdot 10^{+62}\right):\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 14: 68.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.25e+123)
   (* 2.0 (* b (* i (* c (- c)))))
   (if (<= c 1.2e+62)
     (* 2.0 (+ (* z t) (* x y)))
     (* -2.0 (* (* c c) (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.25e+123) {
		tmp = 2.0 * (b * (i * (c * -c)));
	} else if (c <= 1.2e+62) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else {
		tmp = -2.0 * ((c * c) * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-1.25d+123)) then
        tmp = 2.0d0 * (b * (i * (c * -c)))
    else if (c <= 1.2d+62) then
        tmp = 2.0d0 * ((z * t) + (x * y))
    else
        tmp = (-2.0d0) * ((c * c) * (b * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.25e+123) {
		tmp = 2.0 * (b * (i * (c * -c)));
	} else if (c <= 1.2e+62) {
		tmp = 2.0 * ((z * t) + (x * y));
	} else {
		tmp = -2.0 * ((c * c) * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.25e+123:
		tmp = 2.0 * (b * (i * (c * -c)))
	elif c <= 1.2e+62:
		tmp = 2.0 * ((z * t) + (x * y))
	else:
		tmp = -2.0 * ((c * c) * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.25e+123)
		tmp = Float64(2.0 * Float64(b * Float64(i * Float64(c * Float64(-c)))));
	elseif (c <= 1.2e+62)
		tmp = Float64(2.0 * Float64(Float64(z * t) + Float64(x * y)));
	else
		tmp = Float64(-2.0 * Float64(Float64(c * c) * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1.25e+123)
		tmp = 2.0 * (b * (i * (c * -c)));
	elseif (c <= 1.2e+62)
		tmp = 2.0 * ((z * t) + (x * y));
	else
		tmp = -2.0 * ((c * c) * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.25e+123], N[(2.0 * N[(b * N[(i * N[(c * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.2e+62], N[(2.0 * N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(c * c), $MachinePrecision] * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.24999999999999994e123

   1. Initial program 78.6%

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

   2. Taylor expanded in b around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. *-commutative 67.8%

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

      3. distribute-rgt-neg-in 67.8%

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

      4. unpow2 67.8%

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

      5. distribute-rgt-neg-in 67.8%

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

   4. Simplified 67.8%

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

      1. expm1-log1p-u 32.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right)\right)\right)} \]

      2. expm1-udef 32.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right)\right)} - 1} \]

      3. *-commutative 32.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2}\right)} - 1 \]

   6. Applied egg-rr 32.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 32.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(i \cdot b\right) \cdot \left(c \cdot \left(-c\right)\right)\right) \cdot 2\right)\right)} \]

      2. expm1-log1p 67.8%

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

      3. *-commutative 67.8%

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

      4. *-commutative 67.8%

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

      5. distribute-rgt-neg-out 67.8%

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

      6. unpow2 67.8%

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

      7. distribute-lft-neg-in 67.8%

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

      8. associate-*r* 70.9%

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

      9. unpow2 70.9%

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

      10. distribute-lft-neg-in 70.9%

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

      11. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   if -1.24999999999999994e123 < c < 1.2e62

   1. Initial program 94.5%

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

   2. Taylor expanded in c around 0 72.0%

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

   if 1.2e62 < c

   1. Initial program 63.6%

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

   2. Taylor expanded in b around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. *-commutative 58.5%

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

      3. distribute-rgt-neg-in 58.5%

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

      4. unpow2 58.5%

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

      5. distribute-rgt-neg-in 58.5%

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

   4. Simplified 58.5%

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

   5. Taylor expanded in i around 0 58.5%

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

      1. unpow2 58.5%

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

   7. Simplified 58.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.25 \cdot 10^{+123}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\left(c \cdot c\right) \cdot \left(b \cdot i\right)\right)\\ \end{array} \]

Alternative 15: 40.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-54} \lor \neg \left(y \leq 5.5 \cdot 10^{+68}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -7e-54) (not (<= y 5.5e+68))) (* 2.0 (* x y)) (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7e-54) || !(y <= 5.5e+68)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-7d-54)) .or. (.not. (y <= 5.5d+68))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -7e-54) || !(y <= 5.5e+68)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -7e-54) or not (y <= 5.5e+68):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -7e-54) || !(y <= 5.5e+68))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -7e-54) || ~((y <= 5.5e+68)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -7e-54], N[Not[LessEqual[y, 5.5e+68]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999964e-54 or 5.5000000000000004e68 < y

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf 46.7%

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

   if -6.99999999999999964e-54 < y < 5.5000000000000004e68

   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 z around inf 34.2%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-54} \lor \neg \left(y \leq 5.5 \cdot 10^{+68}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 16: 29.7% 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 86.4%

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

2. Taylor expanded in z around inf 25.3%

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

3. Final simplification 25.3%

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

Developer target: 94.1% 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 2023238 
(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))))