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

Percentage Accurate: 90.1% → 96.1%

Time: 12.6s

Alternatives: 13

Speedup: 0.5×

• 46.1% 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: 90.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.1× speedup

Math

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

FPCore

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

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(b * N[(i * N[(c * c), $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 94.9%

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

      1. associate-*l* 99.2%

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

      2. fma-def 99.2%

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

   3. Simplified 99.2%

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

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

   1. Initial program 0.0%

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

      1. associate-*l* 16.7%

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

      2. fma-def 16.7%

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

   3. Simplified 16.7%

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

      1. fma-def 16.7%

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

      2. +-commutative 16.7%

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

   5. Applied egg-rr 16.7%

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

   6. Taylor expanded in b around inf 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unpow2 58.6%

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

      3. distribute-lft-neg-in 58.6%

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

      4. *-commutative 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in i around 0 58.6%

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

       1. associate-*r* 58.6%

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

       2. unpow2 58.6%

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

   11. Simplified 58.6%

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

   12. Taylor expanded in c around 0 58.6%

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

       1. unpow2 58.6%

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

       2. *-commutative 58.6%

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

       3. *-commutative 58.6%

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

       4. associate-*l* 75.3%

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

   14. Simplified 75.3%

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

4. Final simplification 98.1%

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

Alternative 2: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ t_3 := c \cdot \left(t_1 \cdot i\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_3\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+276}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - t_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)) (t_3 (* c (* t_1 i))))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (* z t) t_3))
     (if (<= t_2 2e+276) (* (- (+ (* z t) (* x y)) t_2) 2.0) (* -2.0 t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double t_3 = c * (t_1 * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((z * t) - t_3);
	} else if (t_2 <= 2e+276) {
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	} else {
		tmp = -2.0 * t_3;
	}
	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 = (c * t_1) * i;
	double t_3 = c * (t_1 * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((z * t) - t_3);
	} else if (t_2 <= 2e+276) {
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	} else {
		tmp = -2.0 * t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	t_3 = c * (t_1 * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((z * t) - t_3)
	elif t_2 <= 2e+276:
		tmp = (((z * t) + (x * y)) - t_2) * 2.0
	else:
		tmp = -2.0 * t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	t_3 = Float64(c * Float64(t_1 * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_3));
	elseif (t_2 <= 2e+276)
		tmp = Float64(Float64(Float64(Float64(z * t) + Float64(x * y)) - t_2) * 2.0);
	else
		tmp = Float64(-2.0 * t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	t_3 = c * (t_1 * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((z * t) - t_3);
	elseif (t_2 <= 2e+276)
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	else
		tmp = -2.0 * t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+276], N[(N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision], N[(-2.0 * t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.4%

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

   2. Taylor expanded in x around 0 84.8%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2.0000000000000001e276

   1. Initial program 99.3%

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

   if 2.0000000000000001e276 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 82.3%

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

   2. Taylor expanded in i around inf 95.6%

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

   3. Taylor expanded in i around 0 95.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+276}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 3: 96.1% accurate, 0.5× speedup

Math

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

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 (* (* c t_1) i)) INFINITY)
     (* 2.0 (- t_2 (* t_1 (* c i))))
     (* -2.0 (* b (* i (* c c)))))))

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 - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = -2.0 * (b * (i * (c * c)));
	}
	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 - ((c * t_1) * i)) <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	} else {
		tmp = -2.0 * (b * (i * (c * c)));
	}
	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 - ((c * t_1) * i)) <= math.inf:
		tmp = 2.0 * (t_2 - (t_1 * (c * i)))
	else:
		tmp = -2.0 * (b * (i * (c * c)))
	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(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(t_2 - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))));
	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 - ((c * t_1) * i)) <= Inf)
		tmp = 2.0 * (t_2 - (t_1 * (c * i)));
	else
		tmp = -2.0 * (b * (i * (c * c)));
	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[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(b * N[(i * N[(c * c), $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 94.9%

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

      1. associate-*l* 99.2%

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

      2. fma-def 99.2%

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

   3. Simplified 99.2%

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

      1. fma-def 99.2%

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

      2. +-commutative 99.2%

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

   5. Applied egg-rr 99.2%

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

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

   1. Initial program 0.0%

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

      1. associate-*l* 16.7%

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

      2. fma-def 16.7%

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

   3. Simplified 16.7%

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

      1. fma-def 16.7%

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

      2. +-commutative 16.7%

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

   5. Applied egg-rr 16.7%

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

   6. Taylor expanded in b around inf 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unpow2 58.6%

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

      3. distribute-lft-neg-in 58.6%

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

      4. *-commutative 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in i around 0 58.6%

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

       1. associate-*r* 58.6%

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

       2. unpow2 58.6%

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

   11. Simplified 58.6%

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

   12. Taylor expanded in c around 0 58.6%

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

       1. unpow2 58.6%

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

       2. *-commutative 58.6%

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

       3. *-commutative 58.6%

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

       4. associate-*l* 75.3%

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

   14. Simplified 75.3%

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

4. Final simplification 98.0%

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

Alternative 4: 46.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := -2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ t_3 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -2.3 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-247}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 31000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+122}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* z t)))
        (t_2 (* -2.0 (* b (* i (* c c)))))
        (t_3 (* 2.0 (* x y))))
   (if (<= c -2.3e-67)
     t_2
     (if (<= c -3.1e-168)
       t_1
       (if (<= c 9.2e-247)
         t_3
         (if (<= c 4.2e-146)
           t_1
           (if (<= c 5.5e-35)
             t_3
             (if (<= c 31000.0)
               t_1
               (if (<= c 4.2e+122) (* (* c -2.0) (* a i)) 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 * (b * (i * (c * c)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -2.3e-67) {
		tmp = t_2;
	} else if (c <= -3.1e-168) {
		tmp = t_1;
	} else if (c <= 9.2e-247) {
		tmp = t_3;
	} else if (c <= 4.2e-146) {
		tmp = t_1;
	} else if (c <= 5.5e-35) {
		tmp = t_3;
	} else if (c <= 31000.0) {
		tmp = t_1;
	} else if (c <= 4.2e+122) {
		tmp = (c * -2.0) * (a * i);
	} 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 * (z * t)
    t_2 = (-2.0d0) * (b * (i * (c * c)))
    t_3 = 2.0d0 * (x * y)
    if (c <= (-2.3d-67)) then
        tmp = t_2
    else if (c <= (-3.1d-168)) then
        tmp = t_1
    else if (c <= 9.2d-247) then
        tmp = t_3
    else if (c <= 4.2d-146) then
        tmp = t_1
    else if (c <= 5.5d-35) then
        tmp = t_3
    else if (c <= 31000.0d0) then
        tmp = t_1
    else if (c <= 4.2d+122) then
        tmp = (c * (-2.0d0)) * (a * i)
    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 * (b * (i * (c * c)));
	double t_3 = 2.0 * (x * y);
	double tmp;
	if (c <= -2.3e-67) {
		tmp = t_2;
	} else if (c <= -3.1e-168) {
		tmp = t_1;
	} else if (c <= 9.2e-247) {
		tmp = t_3;
	} else if (c <= 4.2e-146) {
		tmp = t_1;
	} else if (c <= 5.5e-35) {
		tmp = t_3;
	} else if (c <= 31000.0) {
		tmp = t_1;
	} else if (c <= 4.2e+122) {
		tmp = (c * -2.0) * (a * i);
	} 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 * (b * (i * (c * c)))
	t_3 = 2.0 * (x * y)
	tmp = 0
	if c <= -2.3e-67:
		tmp = t_2
	elif c <= -3.1e-168:
		tmp = t_1
	elif c <= 9.2e-247:
		tmp = t_3
	elif c <= 4.2e-146:
		tmp = t_1
	elif c <= 5.5e-35:
		tmp = t_3
	elif c <= 31000.0:
		tmp = t_1
	elif c <= 4.2e+122:
		tmp = (c * -2.0) * (a * i)
	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(b * Float64(i * Float64(c * c))))
	t_3 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -2.3e-67)
		tmp = t_2;
	elseif (c <= -3.1e-168)
		tmp = t_1;
	elseif (c <= 9.2e-247)
		tmp = t_3;
	elseif (c <= 4.2e-146)
		tmp = t_1;
	elseif (c <= 5.5e-35)
		tmp = t_3;
	elseif (c <= 31000.0)
		tmp = t_1;
	elseif (c <= 4.2e+122)
		tmp = Float64(Float64(c * -2.0) * Float64(a * i));
	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 * (b * (i * (c * c)));
	t_3 = 2.0 * (x * y);
	tmp = 0.0;
	if (c <= -2.3e-67)
		tmp = t_2;
	elseif (c <= -3.1e-168)
		tmp = t_1;
	elseif (c <= 9.2e-247)
		tmp = t_3;
	elseif (c <= 4.2e-146)
		tmp = t_1;
	elseif (c <= 5.5e-35)
		tmp = t_3;
	elseif (c <= 31000.0)
		tmp = t_1;
	elseif (c <= 4.2e+122)
		tmp = (c * -2.0) * (a * i);
	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[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.3e-67], t$95$2, If[LessEqual[c, -3.1e-168], t$95$1, If[LessEqual[c, 9.2e-247], t$95$3, If[LessEqual[c, 4.2e-146], t$95$1, If[LessEqual[c, 5.5e-35], t$95$3, If[LessEqual[c, 31000.0], t$95$1, If[LessEqual[c, 4.2e+122], N[(N[(c * -2.0), $MachinePrecision] * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.3e-67 or 4.20000000000000032e122 < c

   1. Initial program 82.9%

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

      1. associate-*l* 90.3%

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

      2. fma-def 90.3%

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

   3. Simplified 90.3%

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

      1. fma-def 90.3%

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

      2. +-commutative 90.3%

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

   5. Applied egg-rr 90.3%

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

   6. Taylor expanded in b around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unpow2 56.4%

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

      3. distribute-lft-neg-in 56.4%

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

      4. *-commutative 56.4%

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

   8. Simplified 56.4%

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

   9. Taylor expanded in i around 0 56.4%

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

       1. associate-*r* 56.4%

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

       2. unpow2 56.4%

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

   11. Simplified 56.4%

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

   12. Taylor expanded in c around 0 56.4%

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

       1. unpow2 56.4%

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

       2. *-commutative 56.4%

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

       3. *-commutative 56.4%

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

       4. associate-*l* 61.1%

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

   14. Simplified 61.1%

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

   if -2.3e-67 < c < -3.1e-168 or 9.2000000000000001e-247 < c < 4.1999999999999998e-146 or 5.4999999999999997e-35 < c < 31000

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 59.0%

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

   if -3.1e-168 < c < 9.2000000000000001e-247 or 4.1999999999999998e-146 < c < 5.4999999999999997e-35

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 58.9%

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

   if 31000 < c < 4.20000000000000032e122

   1. Initial program 78.7%

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

   2. Taylor expanded in i around inf 60.3%

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

   3. Taylor expanded in c around 0 39.8%

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

      1. associate-*r* 39.8%

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

      2. *-commutative 39.8%

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

   5. Simplified 39.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.3 \cdot 10^{-67}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{-168}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-247}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-146}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{-35}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 31000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+122}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \end{array} \]

Alternative 5: 46.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -2.45 \cdot 10^{-67}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-247}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1050000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+122}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= c -2.45e-67)
     (* -2.0 (* b (* i (* c c))))
     (if (<= c -1.12e-167)
       t_1
       (if (<= c 1.85e-247)
         t_2
         (if (<= c 1.3e-145)
           t_1
           (if (<= c 4.8e-35)
             t_2
             (if (<= c 1050000000000.0)
               t_1
               (if (<= c 3.8e+122)
                 (* (* c -2.0) (* a 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 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -2.45e-67) {
		tmp = -2.0 * (b * (i * (c * c)));
	} else if (c <= -1.12e-167) {
		tmp = t_1;
	} else if (c <= 1.85e-247) {
		tmp = t_2;
	} else if (c <= 1.3e-145) {
		tmp = t_1;
	} else if (c <= 4.8e-35) {
		tmp = t_2;
	} else if (c <= 1050000000000.0) {
		tmp = t_1;
	} else if (c <= 3.8e+122) {
		tmp = (c * -2.0) * (a * i);
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (z * t)
    t_2 = 2.0d0 * (x * y)
    if (c <= (-2.45d-67)) then
        tmp = (-2.0d0) * (b * (i * (c * c)))
    else if (c <= (-1.12d-167)) then
        tmp = t_1
    else if (c <= 1.85d-247) then
        tmp = t_2
    else if (c <= 1.3d-145) then
        tmp = t_1
    else if (c <= 4.8d-35) then
        tmp = t_2
    else if (c <= 1050000000000.0d0) then
        tmp = t_1
    else if (c <= 3.8d+122) then
        tmp = (c * (-2.0d0)) * (a * i)
    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 t_1 = 2.0 * (z * t);
	double t_2 = 2.0 * (x * y);
	double tmp;
	if (c <= -2.45e-67) {
		tmp = -2.0 * (b * (i * (c * c)));
	} else if (c <= -1.12e-167) {
		tmp = t_1;
	} else if (c <= 1.85e-247) {
		tmp = t_2;
	} else if (c <= 1.3e-145) {
		tmp = t_1;
	} else if (c <= 4.8e-35) {
		tmp = t_2;
	} else if (c <= 1050000000000.0) {
		tmp = t_1;
	} else if (c <= 3.8e+122) {
		tmp = (c * -2.0) * (a * i);
	} else {
		tmp = -2.0 * (c * (c * (b * i)));
	}
	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 c <= -2.45e-67:
		tmp = -2.0 * (b * (i * (c * c)))
	elif c <= -1.12e-167:
		tmp = t_1
	elif c <= 1.85e-247:
		tmp = t_2
	elif c <= 1.3e-145:
		tmp = t_1
	elif c <= 4.8e-35:
		tmp = t_2
	elif c <= 1050000000000.0:
		tmp = t_1
	elif c <= 3.8e+122:
		tmp = (c * -2.0) * (a * 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(2.0 * Float64(z * t))
	t_2 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (c <= -2.45e-67)
		tmp = Float64(-2.0 * Float64(b * Float64(i * Float64(c * c))));
	elseif (c <= -1.12e-167)
		tmp = t_1;
	elseif (c <= 1.85e-247)
		tmp = t_2;
	elseif (c <= 1.3e-145)
		tmp = t_1;
	elseif (c <= 4.8e-35)
		tmp = t_2;
	elseif (c <= 1050000000000.0)
		tmp = t_1;
	elseif (c <= 3.8e+122)
		tmp = Float64(Float64(c * -2.0) * Float64(a * i));
	else
		tmp = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))));
	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 (c <= -2.45e-67)
		tmp = -2.0 * (b * (i * (c * c)));
	elseif (c <= -1.12e-167)
		tmp = t_1;
	elseif (c <= 1.85e-247)
		tmp = t_2;
	elseif (c <= 1.3e-145)
		tmp = t_1;
	elseif (c <= 4.8e-35)
		tmp = t_2;
	elseif (c <= 1050000000000.0)
		tmp = t_1;
	elseif (c <= 3.8e+122)
		tmp = (c * -2.0) * (a * 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[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.45e-67], N[(-2.0 * N[(b * N[(i * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.12e-167], t$95$1, If[LessEqual[c, 1.85e-247], t$95$2, If[LessEqual[c, 1.3e-145], t$95$1, If[LessEqual[c, 4.8e-35], t$95$2, If[LessEqual[c, 1050000000000.0], t$95$1, If[LessEqual[c, 3.8e+122], N[(N[(c * -2.0), $MachinePrecision] * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.44999999999999997e-67

   1. Initial program 90.3%

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

      1. associate-*l* 93.4%

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

      2. fma-def 93.4%

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

   3. Simplified 93.4%

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

      1. fma-def 93.4%

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

      2. +-commutative 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in b around inf 49.6%

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

      1. mul-1-neg 49.6%

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

      2. unpow2 49.6%

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

      3. distribute-lft-neg-in 49.6%

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

      4. *-commutative 49.6%

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

   8. Simplified 49.6%

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

   9. Taylor expanded in i around 0 49.6%

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

       1. associate-*r* 49.6%

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

       2. unpow2 49.6%

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

   11. Simplified 49.6%

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

   12. Taylor expanded in c around 0 49.6%

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

       1. unpow2 49.6%

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

       2. *-commutative 49.6%

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

       3. *-commutative 49.6%

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

       4. associate-*l* 54.3%

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

   14. Simplified 54.3%

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

   if -2.44999999999999997e-67 < c < -1.1200000000000001e-167 or 1.85000000000000005e-247 < c < 1.3e-145 or 4.8000000000000003e-35 < c < 1.05e12

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 59.0%

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

   if -1.1200000000000001e-167 < c < 1.85000000000000005e-247 or 1.3e-145 < c < 4.8000000000000003e-35

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 58.9%

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

   if 1.05e12 < c < 3.7999999999999998e122

   1. Initial program 78.7%

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

   2. Taylor expanded in i around inf 60.3%

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

   3. Taylor expanded in c around 0 39.8%

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

      1. associate-*r* 39.8%

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

      2. *-commutative 39.8%

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

   5. Simplified 39.8%

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

   if 3.7999999999999998e122 < c

   1. Initial program 71.6%

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

      1. associate-*l* 85.5%

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

      2. fma-def 85.5%

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

   3. Simplified 85.5%

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

      1. fma-def 85.5%

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

      2. +-commutative 85.5%

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

   5. Applied egg-rr 85.5%

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

   6. Taylor expanded in b around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unpow2 66.7%

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

      3. distribute-lft-neg-in 66.7%

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

      4. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in i around 0 66.7%

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

       1. *-commutative 66.7%

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

       2. *-commutative 66.7%

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

       3. unpow2 66.7%

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

       4. associate-*r* 75.1%

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

       5. *-commutative 75.1%

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

       6. *-commutative 75.1%

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

       7. associate-*r* 75.0%

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

       8. *-commutative 75.0%

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

       9. *-commutative 75.0%

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

       10. *-commutative 75.0%

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

       11. associate-*r* 75.1%

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

   11. Simplified 75.1%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{-67}:\\ \;\;\;\;-2 \cdot \left(b \cdot \left(i \cdot \left(c \cdot c\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-167}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-247}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-145}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-35}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1050000000000:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+122}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 6: 34.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t\right)\\ t_2 := 2 \cdot \left(x \cdot y\right)\\ t_3 := \left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{+43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-170}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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)))
        (t_3 (* (* c -2.0) (* a i))))
   (if (<= x -5e+231)
     t_2
     (if (<= x -1.55e+190)
       t_1
       (if (<= x -6.2e+128)
         t_2
         (if (<= x -3.15e+43)
           t_3
           (if (<= x -1.1e+31)
             t_2
             (if (<= x 2.8e-304) t_1 (if (<= x 6.6e-170) t_3 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 t_3 = (c * -2.0) * (a * i);
	double tmp;
	if (x <= -5e+231) {
		tmp = t_2;
	} else if (x <= -1.55e+190) {
		tmp = t_1;
	} else if (x <= -6.2e+128) {
		tmp = t_2;
	} else if (x <= -3.15e+43) {
		tmp = t_3;
	} else if (x <= -1.1e+31) {
		tmp = t_2;
	} else if (x <= 2.8e-304) {
		tmp = t_1;
	} else if (x <= 6.6e-170) {
		tmp = t_3;
	} 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 * (z * t)
    t_2 = 2.0d0 * (x * y)
    t_3 = (c * (-2.0d0)) * (a * i)
    if (x <= (-5d+231)) then
        tmp = t_2
    else if (x <= (-1.55d+190)) then
        tmp = t_1
    else if (x <= (-6.2d+128)) then
        tmp = t_2
    else if (x <= (-3.15d+43)) then
        tmp = t_3
    else if (x <= (-1.1d+31)) then
        tmp = t_2
    else if (x <= 2.8d-304) then
        tmp = t_1
    else if (x <= 6.6d-170) then
        tmp = t_3
    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 t_3 = (c * -2.0) * (a * i);
	double tmp;
	if (x <= -5e+231) {
		tmp = t_2;
	} else if (x <= -1.55e+190) {
		tmp = t_1;
	} else if (x <= -6.2e+128) {
		tmp = t_2;
	} else if (x <= -3.15e+43) {
		tmp = t_3;
	} else if (x <= -1.1e+31) {
		tmp = t_2;
	} else if (x <= 2.8e-304) {
		tmp = t_1;
	} else if (x <= 6.6e-170) {
		tmp = t_3;
	} 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)
	t_3 = (c * -2.0) * (a * i)
	tmp = 0
	if x <= -5e+231:
		tmp = t_2
	elif x <= -1.55e+190:
		tmp = t_1
	elif x <= -6.2e+128:
		tmp = t_2
	elif x <= -3.15e+43:
		tmp = t_3
	elif x <= -1.1e+31:
		tmp = t_2
	elif x <= 2.8e-304:
		tmp = t_1
	elif x <= 6.6e-170:
		tmp = t_3
	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))
	t_3 = Float64(Float64(c * -2.0) * Float64(a * i))
	tmp = 0.0
	if (x <= -5e+231)
		tmp = t_2;
	elseif (x <= -1.55e+190)
		tmp = t_1;
	elseif (x <= -6.2e+128)
		tmp = t_2;
	elseif (x <= -3.15e+43)
		tmp = t_3;
	elseif (x <= -1.1e+31)
		tmp = t_2;
	elseif (x <= 2.8e-304)
		tmp = t_1;
	elseif (x <= 6.6e-170)
		tmp = t_3;
	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);
	t_3 = (c * -2.0) * (a * i);
	tmp = 0.0;
	if (x <= -5e+231)
		tmp = t_2;
	elseif (x <= -1.55e+190)
		tmp = t_1;
	elseif (x <= -6.2e+128)
		tmp = t_2;
	elseif (x <= -3.15e+43)
		tmp = t_3;
	elseif (x <= -1.1e+31)
		tmp = t_2;
	elseif (x <= 2.8e-304)
		tmp = t_1;
	elseif (x <= 6.6e-170)
		tmp = t_3;
	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]}, Block[{t$95$3 = N[(N[(c * -2.0), $MachinePrecision] * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+231], t$95$2, If[LessEqual[x, -1.55e+190], t$95$1, If[LessEqual[x, -6.2e+128], t$95$2, If[LessEqual[x, -3.15e+43], t$95$3, If[LessEqual[x, -1.1e+31], t$95$2, If[LessEqual[x, 2.8e-304], t$95$1, If[LessEqual[x, 6.6e-170], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.00000000000000028e231 or -1.5500000000000001e190 < x < -6.20000000000000008e128 or -3.1499999999999999e43 < x < -1.10000000000000005e31 or 6.60000000000000007e-170 < x

   1. Initial program 89.7%

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

   2. Taylor expanded in x around inf 41.6%

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

   if -5.00000000000000028e231 < x < -1.5500000000000001e190 or -1.10000000000000005e31 < x < 2.7999999999999998e-304

   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. Taylor expanded in z around inf 45.9%

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

   if -6.20000000000000008e128 < x < -3.1499999999999999e43 or 2.7999999999999998e-304 < x < 6.60000000000000007e-170

   1. Initial program 86.9%

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

   2. Taylor expanded in i around inf 70.3%

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

   3. Taylor expanded in c around 0 39.7%

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

      1. associate-*r* 39.7%

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

      2. *-commutative 39.7%

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

   5. Simplified 39.7%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+231}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+190}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+128}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{+43}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+31}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-304}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-170}:\\ \;\;\;\;\left(c \cdot -2\right) \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 7: 79.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{-108} \lor \neg \left(c \leq 5.8 \cdot 10^{-56}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.65e-108) (not (<= c 5.8e-56)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.65e-108) || !(c <= 5.8e-56)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.65d-108)) .or. (.not. (c <= 5.8d-56))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.65e-108) || !(c <= 5.8e-56)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.65e-108) or not (c <= 5.8e-56):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.65e-108) || !(c <= 5.8e-56))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.65e-108) || ~((c <= 5.8e-56)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.65e-108], N[Not[LessEqual[c, 5.8e-56]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.6500000000000001e-108 or 5.79999999999999982e-56 < c

   1. Initial program 84.4%

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

   2. Taylor expanded in x around 0 82.7%

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

   if -1.6500000000000001e-108 < c < 5.79999999999999982e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in c around 0 90.1%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{-108} \lor \neg \left(c \leq 5.8 \cdot 10^{-56}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 8: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+65} \lor \neg \left(c \leq 9.5 \cdot 10^{-48}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3e+65) (not (<= c 9.5e-48)))
   (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))
   (* 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 <= -3e+65) || !(c <= 9.5e-48)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} 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 <= (-3d+65)) .or. (.not. (c <= 9.5d-48))) then
        tmp = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    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 <= -3e+65) || !(c <= 9.5e-48)) {
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	} 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 <= -3e+65) or not (c <= 9.5e-48):
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	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 <= -3e+65) || !(c <= 9.5e-48))
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))));
	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 <= -3e+65) || ~((c <= 9.5e-48)))
		tmp = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	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, -3e+65], N[Not[LessEqual[c, 9.5e-48]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $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 < -3.0000000000000002e65 or 9.50000000000000036e-48 < c

   1. Initial program 80.8%

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

   2. Taylor expanded in x around 0 86.4%

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

   if -3.0000000000000002e65 < c < 9.50000000000000036e-48

   1. Initial program 99.2%

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

   2. Taylor expanded in a around inf 93.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+65} \lor \neg \left(c \leq 9.5 \cdot 10^{-48}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 9: 68.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+84} \lor \neg \left(c \leq 2.9 \cdot 10^{+23} \lor \neg \left(c \leq 2.05 \cdot 10^{+38}\right) \land c \leq 2.55 \cdot 10^{+135}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.02e+84)
         (not
          (or (<= c 2.9e+23) (and (not (<= c 2.05e+38)) (<= c 2.55e+135)))))
   (* -2.0 (* c (* c (* b i))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.02e+84) || !((c <= 2.9e+23) || (!(c <= 2.05e+38) && (c <= 2.55e+135)))) {
		tmp = -2.0 * (c * (c * (b * i)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.02d+84)) .or. (.not. (c <= 2.9d+23) .or. (.not. (c <= 2.05d+38)) .and. (c <= 2.55d+135))) then
        tmp = (-2.0d0) * (c * (c * (b * i)))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.02e+84) || !((c <= 2.9e+23) || (!(c <= 2.05e+38) && (c <= 2.55e+135)))) {
		tmp = -2.0 * (c * (c * (b * i)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.02e+84) or not ((c <= 2.9e+23) or (not (c <= 2.05e+38) and (c <= 2.55e+135))):
		tmp = -2.0 * (c * (c * (b * i)))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.02e+84) || !((c <= 2.9e+23) || (!(c <= 2.05e+38) && (c <= 2.55e+135))))
		tmp = Float64(-2.0 * Float64(c * Float64(c * Float64(b * i))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.02e+84) || ~(((c <= 2.9e+23) || (~((c <= 2.05e+38)) && (c <= 2.55e+135)))))
		tmp = -2.0 * (c * (c * (b * i)));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.02e+84], N[Not[Or[LessEqual[c, 2.9e+23], And[N[Not[LessEqual[c, 2.05e+38]], $MachinePrecision], LessEqual[c, 2.55e+135]]]], $MachinePrecision]], N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.0199999999999999e84 or 2.90000000000000013e23 < c < 2.0500000000000002e38 or 2.54999999999999991e135 < c

   1. Initial program 78.2%

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

      1. associate-*l* 87.7%

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

      2. fma-def 87.7%

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

   3. Simplified 87.7%

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

      1. fma-def 87.7%

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

      2. +-commutative 87.7%

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

   5. Applied egg-rr 87.7%

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

   6. Taylor expanded in b around inf 67.3%

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

      1. mul-1-neg 67.3%

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

      2. unpow2 67.3%

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

      3. distribute-lft-neg-in 67.3%

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

      4. *-commutative 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in i around 0 67.3%

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

       1. *-commutative 67.3%

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

       2. *-commutative 67.3%

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

       3. unpow2 67.3%

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

       4. associate-*r* 72.9%

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

       5. *-commutative 72.9%

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

       6. *-commutative 72.9%

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

       7. associate-*r* 73.0%

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

       8. *-commutative 73.0%

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

       9. *-commutative 73.0%

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

       10. *-commutative 73.0%

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

       11. associate-*r* 72.9%

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

   11. Simplified 72.9%

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

   if -1.0199999999999999e84 < c < 2.90000000000000013e23 or 2.0500000000000002e38 < c < 2.54999999999999991e135

   1. Initial program 96.1%

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

   2. Taylor expanded in c around 0 73.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+84} \lor \neg \left(c \leq 2.9 \cdot 10^{+23} \lor \neg \left(c \leq 2.05 \cdot 10^{+38}\right) \land c \leq 2.55 \cdot 10^{+135}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 10: 68.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+84}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+22} \lor \neg \left(c \leq 4.5 \cdot 10^{+37}\right) \land c \leq 1.95 \cdot 10^{+135}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -5.8e+84)
   (* 2.0 (* c (* i (* b (- c)))))
   (if (or (<= c 2.5e+22) (and (not (<= c 4.5e+37)) (<= c 1.95e+135)))
     (* (+ (* z t) (* x y)) 2.0)
     (* -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 <= -5.8e+84) {
		tmp = 2.0 * (c * (i * (b * -c)));
	} else if ((c <= 2.5e+22) || (!(c <= 4.5e+37) && (c <= 1.95e+135))) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} 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 <= (-5.8d+84)) then
        tmp = 2.0d0 * (c * (i * (b * -c)))
    else if ((c <= 2.5d+22) .or. (.not. (c <= 4.5d+37)) .and. (c <= 1.95d+135)) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    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 <= -5.8e+84) {
		tmp = 2.0 * (c * (i * (b * -c)));
	} else if ((c <= 2.5e+22) || (!(c <= 4.5e+37) && (c <= 1.95e+135))) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} 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 <= -5.8e+84:
		tmp = 2.0 * (c * (i * (b * -c)))
	elif (c <= 2.5e+22) or (not (c <= 4.5e+37) and (c <= 1.95e+135)):
		tmp = ((z * t) + (x * y)) * 2.0
	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 <= -5.8e+84)
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(b * Float64(-c)))));
	elseif ((c <= 2.5e+22) || (!(c <= 4.5e+37) && (c <= 1.95e+135)))
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	else
		tmp = Float64(-2.0 * Float64(c * Float64(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 <= -5.8e+84)
		tmp = 2.0 * (c * (i * (b * -c)));
	elseif ((c <= 2.5e+22) || (~((c <= 4.5e+37)) && (c <= 1.95e+135)))
		tmp = ((z * t) + (x * y)) * 2.0;
	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, -5.8e+84], N[(2.0 * N[(c * N[(i * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 2.5e+22], And[N[Not[LessEqual[c, 4.5e+37]], $MachinePrecision], LessEqual[c, 1.95e+135]]], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(-2.0 * N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.79999999999999977e84

   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. Step-by-step derivation

      1. associate-*l* 91.1%

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

      2. fma-def 91.1%

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

   3. Simplified 91.1%

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

      1. fma-def 91.1%

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

      2. +-commutative 91.1%

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

   5. Applied egg-rr 91.1%

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

   6. Taylor expanded in a around 0 74.5%

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

   7. Taylor expanded in c around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unpow2 68.2%

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

      3. *-commutative 68.2%

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

      4. associate-*r* 71.2%

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

      5. distribute-rgt-neg-in 71.2%

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

      6. associate-*r* 74.2%

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

      7. *-commutative 74.2%

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

      8. associate-*r* 71.6%

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

      9. *-commutative 71.6%

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

      10. associate-*l* 71.5%

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

   9. Simplified 71.5%

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

   if -5.79999999999999977e84 < c < 2.4999999999999998e22 or 4.49999999999999962e37 < c < 1.95000000000000016e135

   1. Initial program 96.1%

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

   2. Taylor expanded in c around 0 73.4%

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

   if 2.4999999999999998e22 < c < 4.49999999999999962e37 or 1.95000000000000016e135 < c

   1. Initial program 73.0%

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

      1. associate-*l* 85.2%

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

      2. fma-def 85.2%

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

   3. Simplified 85.2%

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

      1. fma-def 85.2%

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

      2. +-commutative 85.2%

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

   5. Applied egg-rr 85.2%

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

   6. Taylor expanded in b around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unpow2 66.7%

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

      3. distribute-lft-neg-in 66.7%

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

      4. *-commutative 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in i around 0 66.7%

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

       1. *-commutative 66.7%

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

       2. *-commutative 66.7%

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

       3. unpow2 66.7%

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

       4. associate-*r* 74.1%

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

       5. *-commutative 74.1%

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

       6. *-commutative 74.1%

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

       7. associate-*r* 74.1%

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

       8. *-commutative 74.1%

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

       9. *-commutative 74.1%

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

       10. *-commutative 74.1%

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

       11. associate-*r* 74.1%

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

   11. Simplified 74.1%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{+84}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+22} \lor \neg \left(c \leq 4.5 \cdot 10^{+37}\right) \land c \leq 1.95 \cdot 10^{+135}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 11: 71.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{-108} \lor \neg \left(c \leq 112\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.65e-108) (not (<= c 112.0)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.65e-108) || !(c <= 112.0)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.65d-108)) .or. (.not. (c <= 112.0d0))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.65e-108) || !(c <= 112.0)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.65e-108) or not (c <= 112.0):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.65e-108) || !(c <= 112.0))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.65e-108) || ~((c <= 112.0)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.65e-108], N[Not[LessEqual[c, 112.0]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.6500000000000001e-108 or 112 < c

   1. Initial program 83.1%

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

   2. Taylor expanded in i around inf 71.8%

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

   3. Taylor expanded in i around 0 71.8%

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

   if -1.6500000000000001e-108 < c < 112

   1. Initial program 99.9%

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

   2. Taylor expanded in c around 0 86.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{-108} \lor \neg \left(c \leq 112\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 12: 36.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+231} \lor \neg \left(x \leq -1.52 \cdot 10^{+190} \lor \neg \left(x \leq -9.5 \cdot 10^{+30}\right) \land x \leq 1.25 \cdot 10^{-242}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5e+231)
         (not
          (or (<= x -1.52e+190) (and (not (<= x -9.5e+30)) (<= x 1.25e-242)))))
   (* 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 ((x <= -5e+231) || !((x <= -1.52e+190) || (!(x <= -9.5e+30) && (x <= 1.25e-242)))) {
		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 ((x <= (-5d+231)) .or. (.not. (x <= (-1.52d+190)) .or. (.not. (x <= (-9.5d+30))) .and. (x <= 1.25d-242))) 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 ((x <= -5e+231) || !((x <= -1.52e+190) || (!(x <= -9.5e+30) && (x <= 1.25e-242)))) {
		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 (x <= -5e+231) or not ((x <= -1.52e+190) or (not (x <= -9.5e+30) and (x <= 1.25e-242))):
		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 ((x <= -5e+231) || !((x <= -1.52e+190) || (!(x <= -9.5e+30) && (x <= 1.25e-242))))
		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 ((x <= -5e+231) || ~(((x <= -1.52e+190) || (~((x <= -9.5e+30)) && (x <= 1.25e-242)))))
		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[x, -5e+231], N[Not[Or[LessEqual[x, -1.52e+190], And[N[Not[LessEqual[x, -9.5e+30]], $MachinePrecision], LessEqual[x, 1.25e-242]]]], $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 x < -5.00000000000000028e231 or -1.5199999999999999e190 < x < -9.5000000000000003e30 or 1.25e-242 < x

   1. Initial program 88.6%

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

   2. Taylor expanded in x around inf 38.5%

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

   if -5.00000000000000028e231 < x < -1.5199999999999999e190 or -9.5000000000000003e30 < x < 1.25e-242

   1. Initial program 93.7%

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

   2. Taylor expanded in z around inf 42.3%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+231} \lor \neg \left(x \leq -1.52 \cdot 10^{+190} \lor \neg \left(x \leq -9.5 \cdot 10^{+30}\right) \land x \leq 1.25 \cdot 10^{-242}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 13: 29.1% 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 90.4%

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

2. Taylor expanded in z around inf 28.0%

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

3. Final simplification 28.0%

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

Developer target: 94.2% 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 2023240 
(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))))