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

Percentage Accurate: 90.3% → 97.0%

Time: 15.0s

Alternatives: 14

Speedup: 0.6×

• 47.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(y * N[(x - N[(c * N[(N[(i * N[(b * c + a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $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 94.6%

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

      1. fma-define 94.6%

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

      2. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

      1. fma-define 98.4%

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

      2. +-commutative 98.4%

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

   6. Applied egg-rr 98.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf 44.4%

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

   4. Taylor expanded in y around inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. unsub-neg 88.9%

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

      3. associate-/l* 88.9%

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

      4. +-commutative 88.9%

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

      5. fma-undefine 88.9%

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

   6. Simplified 88.9%

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

4. Final simplification 98.0%

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

Alternative 2: 87.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t\_1\right) \cdot i\\ t_3 := c \cdot \left(t\_1 \cdot i\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_3\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot t\_3\\ \end{array} \end{array} \]

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 (- (* x y) t_3))
     (if (<= t_2 2e+55)
       (* 2.0 (- (+ (* x y) (* z t)) (* i (* c (* b c)))))
       (if (<= t_2 2e+305) (* 2.0 (- (* x y) t_2)) (* -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 * ((x * y) - t_3);
	} else if (t_2 <= 2e+55) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * (b * c))));
	} else if (t_2 <= 2e+305) {
		tmp = 2.0 * ((x * y) - t_2);
	} 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 * ((x * y) - t_3);
	} else if (t_2 <= 2e+55) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * (b * c))));
	} else if (t_2 <= 2e+305) {
		tmp = 2.0 * ((x * y) - t_2);
	} 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 * ((x * y) - t_3)
	elif t_2 <= 2e+55:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * (b * c))))
	elif t_2 <= 2e+305:
		tmp = 2.0 * ((x * y) - t_2)
	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(x * y) - t_3));
	elseif (t_2 <= 2e+55)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(c * Float64(b * c)))));
	elseif (t_2 <= 2e+305)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_2));
	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 * ((x * y) - t_3);
	elseif (t_2 <= 2e+55)
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (c * (b * c))));
	elseif (t_2 <= 2e+305)
		tmp = 2.0 * ((x * y) - t_2);
	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[(x * y), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+55], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(c * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+305], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(-2.0 * t$95$3), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 86.7%

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

      1. fma-define 86.7%

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

      2. *-commutative 86.7%

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

      3. associate-*l* 94.2%

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

      4. +-commutative 94.2%

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

      5. fma-define 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 92.8%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 2.00000000000000002e55

   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. Add Preprocessing

   3. Taylor expanded in a around 0 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   if 2.00000000000000002e55 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.9999999999999999e305

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 90.3%

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

   if 1.9999999999999999e305 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.6%

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

      1. fma-define 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*l* 84.0%

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

      4. +-commutative 84.0%

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

      5. fma-define 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in i around inf 90.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(b \cdot c\right)\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+305}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot \left(t\_1 \cdot i\right)\\ t_3 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_2\right)\\ \mathbf{elif}\;t\_3 \leq 10^{-17}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c (* t_1 i))) (t_3 (* (* c t_1) i)))
   (if (<= t_3 -2e+52)
     (* 2.0 (- (* z t) t_2))
     (if (<= t_3 1e-17)
       (* (+ (* x y) (* z t)) 2.0)
       (if (<= t_3 2e+305) (* 2.0 (- (* x y) t_3)) (* -2.0 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -2e+52) {
		tmp = 2.0 * ((z * t) - t_2);
	} else if (t_3 <= 1e-17) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (t_3 <= 2e+305) {
		tmp = 2.0 * ((x * y) - t_3);
	} else {
		tmp = -2.0 * 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 = a + (b * c)
    t_2 = c * (t_1 * i)
    t_3 = (c * t_1) * i
    if (t_3 <= (-2d+52)) then
        tmp = 2.0d0 * ((z * t) - t_2)
    else if (t_3 <= 1d-17) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else if (t_3 <= 2d+305) then
        tmp = 2.0d0 * ((x * y) - t_3)
    else
        tmp = (-2.0d0) * 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 = a + (b * c);
	double t_2 = c * (t_1 * i);
	double t_3 = (c * t_1) * i;
	double tmp;
	if (t_3 <= -2e+52) {
		tmp = 2.0 * ((z * t) - t_2);
	} else if (t_3 <= 1e-17) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else if (t_3 <= 2e+305) {
		tmp = 2.0 * ((x * y) - t_3);
	} else {
		tmp = -2.0 * t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = c * (t_1 * i)
	t_3 = (c * t_1) * i
	tmp = 0
	if t_3 <= -2e+52:
		tmp = 2.0 * ((z * t) - t_2)
	elif t_3 <= 1e-17:
		tmp = ((x * y) + (z * t)) * 2.0
	elif t_3 <= 2e+305:
		tmp = 2.0 * ((x * y) - t_3)
	else:
		tmp = -2.0 * t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(c * Float64(t_1 * i))
	t_3 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_3 <= -2e+52)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_2));
	elseif (t_3 <= 1e-17)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	elseif (t_3 <= 2e+305)
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_3));
	else
		tmp = Float64(-2.0 * t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = c * (t_1 * i);
	t_3 = (c * t_1) * i;
	tmp = 0.0;
	if (t_3 <= -2e+52)
		tmp = 2.0 * ((z * t) - t_2);
	elseif (t_3 <= 1e-17)
		tmp = ((x * y) + (z * t)) * 2.0;
	elseif (t_3 <= 2e+305)
		tmp = 2.0 * ((x * y) - t_3);
	else
		tmp = -2.0 * t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+52], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e-17], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t$95$3, 2e+305], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision], N[(-2.0 * t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -2e52

   1. Initial program 90.9%

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

      1. fma-define 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-*l* 91.0%

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

      4. +-commutative 91.0%

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

      5. fma-define 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 85.7%

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

   if -2e52 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.00000000000000007e-17

   1. Initial program 98.9%

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

      1. fma-define 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-*l* 100.0%

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

      4. +-commutative 100.0%

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

      5. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in c around 0 94.9%

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

   if 1.00000000000000007e-17 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.9999999999999999e305

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 85.6%

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

   if 1.9999999999999999e305 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.6%

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

      1. fma-define 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*l* 84.0%

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

      4. +-commutative 84.0%

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

      5. fma-define 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in i around inf 90.8%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -2 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 10^{-17}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+305}:\\ \;\;\;\;2 \cdot \left(x \cdot y - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 94.6%

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

      1. fma-define 94.6%

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

      2. associate-*l* 98.4%

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

   3. Simplified 98.4%

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

      1. fma-define 98.4%

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

      2. +-commutative 98.4%

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

   6. Applied egg-rr 98.4%

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

   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. fma-define 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*l* 0.0%

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

      4. +-commutative 0.0%

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

      5. fma-define 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in i around inf 88.9%

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

4. Final simplification 98.0%

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

Alternative 5: 92.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t\_1\right) \cdot i\\ \mathbf{if}\;t\_2 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t\_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(t\_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 2e+305)
     (* (- (+ (* x y) (* z t)) t_2) 2.0)
     (* -2.0 (* c (* t_1 i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= 2e+305) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = -2.0 * (c * (t_1 * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = (c * t_1) * i
    if (t_2 <= 2d+305) then
        tmp = (((x * y) + (z * t)) - t_2) * 2.0d0
    else
        tmp = (-2.0d0) * (c * (t_1 * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= 2e+305) {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	} else {
		tmp = -2.0 * (c * (t_1 * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= 2e+305:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	else:
		tmp = -2.0 * (c * (t_1 * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= 2e+305)
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	else
		tmp = Float64(-2.0 * Float64(c * Float64(t_1 * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if (t_2 <= 2e+305)
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	else
		tmp = -2.0 * (c * (t_1 * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, 2e+305], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision], N[(-2.0 * N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 1.9999999999999999e305

   1. Initial program 95.9%

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

   if 1.9999999999999999e305 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 76.6%

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

      1. fma-define 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*l* 84.0%

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

      4. +-commutative 84.0%

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

      5. fma-define 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in i around inf 90.8%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -1.95 \cdot 10^{-140}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-69}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -1.95e-140)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 7e-69) (* (+ (* x y) (* z t)) 2.0) (* 2.0 (- (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.95e-140) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 7e-69) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-1.95d-140)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 7d-69) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -1.95e-140) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 7e-69) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -1.95e-140:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 7e-69:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -1.95e-140)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 7e-69)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -1.95e-140)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 7e-69)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.95e-140], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e-69], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.9500000000000001e-140

   1. Initial program 89.4%

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

      1. fma-define 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*l* 92.7%

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

      4. +-commutative 92.7%

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

      5. fma-define 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around 0 84.0%

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

   if -1.9500000000000001e-140 < c < 7.0000000000000003e-69

   1. Initial program 98.8%

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

      1. fma-define 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-*l* 90.1%

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

      4. +-commutative 90.1%

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

      5. fma-define 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in c around 0 85.6%

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

   if 7.0000000000000003e-69 < c

   1. Initial program 85.2%

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

      1. fma-define 85.2%

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

      2. *-commutative 85.2%

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

      3. associate-*l* 87.5%

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

      4. +-commutative 87.5%

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

      5. fma-define 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around 0 86.9%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{-140}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-69}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* c (* b (* c i))))))
   (if (<= c -5.2e-60)
     t_1
     (if (<= c 9e-177)
       (* x (* y 2.0))
       (if (<= c 1.1e+39) (* t (* z 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -5.2e-60) {
		tmp = t_1;
	} else if (c <= 9e-177) {
		tmp = x * (y * 2.0);
	} else if (c <= 1.1e+39) {
		tmp = t * (z * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) * (c * (b * (c * i)))
    if (c <= (-5.2d-60)) then
        tmp = t_1
    else if (c <= 9d-177) then
        tmp = x * (y * 2.0d0)
    else if (c <= 1.1d+39) then
        tmp = t * (z * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (c * (b * (c * i)));
	double tmp;
	if (c <= -5.2e-60) {
		tmp = t_1;
	} else if (c <= 9e-177) {
		tmp = x * (y * 2.0);
	} else if (c <= 1.1e+39) {
		tmp = t * (z * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (c * (b * (c * i)))
	tmp = 0
	if c <= -5.2e-60:
		tmp = t_1
	elif c <= 9e-177:
		tmp = x * (y * 2.0)
	elif c <= 1.1e+39:
		tmp = t * (z * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))))
	tmp = 0.0
	if (c <= -5.2e-60)
		tmp = t_1;
	elseif (c <= 9e-177)
		tmp = Float64(x * Float64(y * 2.0));
	elseif (c <= 1.1e+39)
		tmp = Float64(t * Float64(z * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (c * (b * (c * i)));
	tmp = 0.0;
	if (c <= -5.2e-60)
		tmp = t_1;
	elseif (c <= 9e-177)
		tmp = x * (y * 2.0);
	elseif (c <= 1.1e+39)
		tmp = t * (z * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e-60], t$95$1, If[LessEqual[c, 9e-177], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e+39], N[(t * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.1999999999999995e-60 or 1.1000000000000001e39 < c

   1. Initial program 84.9%

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

      1. fma-define 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*l* 90.8%

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

      4. +-commutative 90.8%

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

      5. fma-define 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in i around inf 79.6%

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

   6. Taylor expanded in a around 0 67.5%

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

   if -5.1999999999999995e-60 < c < 9.0000000000000007e-177

   1. Initial program 98.5%

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

      1. fma-define 98.5%

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

      2. *-commutative 98.5%

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

      3. associate-*l* 90.3%

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

      4. +-commutative 90.3%

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

      5. fma-define 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in x around inf 54.8%

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

      1. *-commutative 54.8%

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

      2. associate-*l* 54.8%

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

   7. Simplified 54.8%

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

   if 9.0000000000000007e-177 < c < 1.1000000000000001e39

   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. Step-by-step derivation

      1. fma-define 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l* 88.3%

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

      4. +-commutative 88.3%

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

      5. fma-define 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in z around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. *-commutative 49.2%

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

      3. *-commutative 49.2%

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

      4. associate-*r* 49.2%

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

   7. Simplified 49.2%

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

Alternative 8: 36.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 \cdot \left(a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;c \leq -8 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -2.0 (* a (* c i)))))
   (if (<= c -8e+32)
     t_1
     (if (<= c 5.4e-179)
       (* x (* y 2.0))
       (if (<= c 1.9e+59) (* t (* z 2.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double tmp;
	if (c <= -8e+32) {
		tmp = t_1;
	} else if (c <= 5.4e-179) {
		tmp = x * (y * 2.0);
	} else if (c <= 1.9e+59) {
		tmp = t * (z * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) * (a * (c * i))
    if (c <= (-8d+32)) then
        tmp = t_1
    else if (c <= 5.4d-179) then
        tmp = x * (y * 2.0d0)
    else if (c <= 1.9d+59) then
        tmp = t * (z * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -2.0 * (a * (c * i));
	double tmp;
	if (c <= -8e+32) {
		tmp = t_1;
	} else if (c <= 5.4e-179) {
		tmp = x * (y * 2.0);
	} else if (c <= 1.9e+59) {
		tmp = t * (z * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -2.0 * (a * (c * i))
	tmp = 0
	if c <= -8e+32:
		tmp = t_1
	elif c <= 5.4e-179:
		tmp = x * (y * 2.0)
	elif c <= 1.9e+59:
		tmp = t * (z * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-2.0 * Float64(a * Float64(c * i)))
	tmp = 0.0
	if (c <= -8e+32)
		tmp = t_1;
	elseif (c <= 5.4e-179)
		tmp = Float64(x * Float64(y * 2.0));
	elseif (c <= 1.9e+59)
		tmp = Float64(t * Float64(z * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -2.0 * (a * (c * i));
	tmp = 0.0;
	if (c <= -8e+32)
		tmp = t_1;
	elseif (c <= 5.4e-179)
		tmp = x * (y * 2.0);
	elseif (c <= 1.9e+59)
		tmp = t * (z * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-2.0 * N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8e+32], t$95$1, If[LessEqual[c, 5.4e-179], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.9e+59], N[(t * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.00000000000000043e32 or 1.9e59 < c

   1. Initial program 84.3%

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

      1. fma-define 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*l* 91.1%

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

      4. +-commutative 91.1%

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

      5. fma-define 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in a around inf 40.4%

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

   if -8.00000000000000043e32 < c < 5.39999999999999977e-179

   1. Initial program 98.7%

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

      1. fma-define 98.7%

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

      2. *-commutative 98.7%

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

      3. associate-*l* 91.9%

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

      4. +-commutative 91.9%

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

      5. fma-define 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-*l* 51.2%

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

   7. Simplified 51.2%

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

   if 5.39999999999999977e-179 < c < 1.9e59

   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. Step-by-step derivation

      1. fma-define 96.1%

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

      2. *-commutative 96.1%

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

      3. associate-*l* 85.7%

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

      4. +-commutative 85.7%

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

      5. fma-define 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in z around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. *-commutative 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-*r* 48.4%

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

   7. Simplified 48.4%

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

Alternative 9: 75.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{+34} \lor \neg \left(c \leq 1.15 \cdot 10^{+35}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4.1e+34) (not (<= c 1.15e+35)))
   (* -2.0 (* c (* (+ a (* b c)) i)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.1e+34) || !(c <= 1.15e+35)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-4.1d+34)) .or. (.not. (c <= 1.15d+35))) then
        tmp = (-2.0d0) * (c * ((a + (b * c)) * i))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.1e+34) || !(c <= 1.15e+35)) {
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -4.1e+34) or not (c <= 1.15e+35):
		tmp = -2.0 * (c * ((a + (b * c)) * i))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -4.1e+34) || !(c <= 1.15e+35))
		tmp = Float64(-2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * i)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -4.1e+34) || ~((c <= 1.15e+35)))
		tmp = -2.0 * (c * ((a + (b * c)) * i));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -4.1e+34], N[Not[LessEqual[c, 1.15e+35]], $MachinePrecision]], N[(-2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.0999999999999998e34 or 1.1499999999999999e35 < c

   1. Initial program 83.4%

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

      1. fma-define 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*l* 89.9%

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

      4. +-commutative 89.9%

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

      5. fma-define 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in i around inf 83.5%

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

   if -4.0999999999999998e34 < c < 1.1499999999999999e35

   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. Step-by-step derivation

      1. fma-define 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*l* 90.5%

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

      4. +-commutative 90.5%

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

      5. fma-define 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in c around 0 76.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{+34} \lor \neg \left(c \leq 1.15 \cdot 10^{+35}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{-140}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t\_1\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+35}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -5.2e-140)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 3.8e+35) (* (+ (* x y) (* z t)) 2.0) (* -2.0 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -5.2e-140) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 3.8e+35) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = -2.0 * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-5.2d-140)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 3.8d+35) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = (-2.0d0) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -5.2e-140) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 3.8e+35) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = -2.0 * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -5.2e-140:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 3.8e+35:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = -2.0 * t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -5.2e-140)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 3.8e+35)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(-2.0 * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -5.2e-140)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 3.8e+35)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = -2.0 * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e-140], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e+35], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(-2.0 * t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.1999999999999996e-140

   1. Initial program 89.4%

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

      1. fma-define 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*l* 92.7%

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

      4. +-commutative 92.7%

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

      5. fma-define 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around 0 84.0%

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

   if -5.1999999999999996e-140 < c < 3.8e35

   1. Initial program 99.0%

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

      1. fma-define 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*l* 90.0%

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

      4. +-commutative 90.0%

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

      5. fma-define 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in c around 0 81.4%

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

   if 3.8e35 < c

   1. Initial program 81.2%

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

      1. fma-define 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l* 87.0%

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

      4. +-commutative 87.0%

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

      5. fma-define 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in i around inf 87.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{-140}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+35}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.7 \cdot 10^{+54} \lor \neg \left(c \leq 3.2 \cdot 10^{+41}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -4.7e+54) (not (<= c 3.2e+41)))
   (* -2.0 (* c (* b (* c i))))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.7e+54) || !(c <= 3.2e+41)) {
		tmp = -2.0 * (c * (b * (c * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-4.7d+54)) .or. (.not. (c <= 3.2d+41))) then
        tmp = (-2.0d0) * (c * (b * (c * i)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -4.7e+54) || !(c <= 3.2e+41)) {
		tmp = -2.0 * (c * (b * (c * i)));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -4.7e+54) or not (c <= 3.2e+41):
		tmp = -2.0 * (c * (b * (c * i)))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -4.7e+54) || !(c <= 3.2e+41))
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -4.7e+54) || ~((c <= 3.2e+41)))
		tmp = -2.0 * (c * (b * (c * i)));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -4.7e+54], N[Not[LessEqual[c, 3.2e+41]], $MachinePrecision]], N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.69999999999999993e54 or 3.2000000000000001e41 < c

   1. Initial program 82.8%

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

      1. fma-define 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-*l* 89.6%

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

      4. +-commutative 89.6%

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

      5. fma-define 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in i around inf 84.6%

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

   6. Taylor expanded in a around 0 72.5%

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

   if -4.69999999999999993e54 < c < 3.2000000000000001e41

   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. Step-by-step derivation

      1. fma-define 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*l* 90.8%

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

      4. +-commutative 90.8%

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

      5. fma-define 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in c around 0 76.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.7 \cdot 10^{+54} \lor \neg \left(c \leq 3.2 \cdot 10^{+41}\right):\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.26 \cdot 10^{+55}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+43}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(i \cdot -2\right) \cdot \left(c \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -2.26e+55)
   (* -2.0 (* c (* b (* c i))))
   (if (<= c 3.6e+43)
     (* (+ (* x y) (* z t)) 2.0)
     (* b (* (* i -2.0) (* c c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -2.26e+55) {
		tmp = -2.0 * (c * (b * (c * i)));
	} else if (c <= 3.6e+43) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = b * ((i * -2.0) * (c * 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 <= (-2.26d+55)) then
        tmp = (-2.0d0) * (c * (b * (c * i)))
    else if (c <= 3.6d+43) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = b * ((i * (-2.0d0)) * (c * 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 <= -2.26e+55) {
		tmp = -2.0 * (c * (b * (c * i)));
	} else if (c <= 3.6e+43) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = b * ((i * -2.0) * (c * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -2.26e+55:
		tmp = -2.0 * (c * (b * (c * i)))
	elif c <= 3.6e+43:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = b * ((i * -2.0) * (c * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -2.26e+55)
		tmp = Float64(-2.0 * Float64(c * Float64(b * Float64(c * i))));
	elseif (c <= 3.6e+43)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(b * Float64(Float64(i * -2.0) * Float64(c * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -2.26e+55)
		tmp = -2.0 * (c * (b * (c * i)));
	elseif (c <= 3.6e+43)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = b * ((i * -2.0) * (c * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -2.26e+55], N[(-2.0 * N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.6e+43], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(b * N[(N[(i * -2.0), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.2600000000000001e55

   1. Initial program 84.5%

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

      1. fma-define 84.5%

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

      2. *-commutative 84.5%

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

      3. associate-*l* 92.1%

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

      4. +-commutative 92.1%

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

      5. fma-define 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in i around inf 81.4%

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

   6. Taylor expanded in a around 0 73.0%

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

   if -2.2600000000000001e55 < c < 3.6000000000000001e43

   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. Step-by-step derivation

      1. fma-define 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*l* 90.8%

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

      4. +-commutative 90.8%

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

      5. fma-define 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in c around 0 76.0%

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

   if 3.6000000000000001e43 < c

   1. Initial program 81.2%

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

      1. fma-define 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l* 87.0%

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

      4. +-commutative 87.0%

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

      5. fma-define 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in c around inf 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-*r* 74.8%

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

      3. *-commutative 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-*r* 74.8%

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

   7. Simplified 74.8%

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

      1. unpow2 74.8%

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

   9. Applied egg-rr 74.8%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.26 \cdot 10^{+55}:\\ \;\;\;\;-2 \cdot \left(c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+43}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(i \cdot -2\right) \cdot \left(c \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13600000 \lor \neg \left(z \leq 3.4 \cdot 10^{-72}\right):\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -13600000.0) (not (<= z 3.4e-72)))
   (* t (* z 2.0))
   (* 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 ((z <= -13600000.0) || !(z <= 3.4e-72)) {
		tmp = t * (z * 2.0);
	} else {
		tmp = 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 ((z <= (-13600000.0d0)) .or. (.not. (z <= 3.4d-72))) then
        tmp = t * (z * 2.0d0)
    else
        tmp = 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 ((z <= -13600000.0) || !(z <= 3.4e-72)) {
		tmp = t * (z * 2.0);
	} else {
		tmp = x * (y * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -13600000.0) or not (z <= 3.4e-72):
		tmp = t * (z * 2.0)
	else:
		tmp = x * (y * 2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -13600000.0) || !(z <= 3.4e-72))
		tmp = Float64(t * Float64(z * 2.0));
	else
		tmp = Float64(x * Float64(y * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -13600000.0) || ~((z <= 3.4e-72)))
		tmp = t * (z * 2.0);
	else
		tmp = x * (y * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -13600000.0], N[Not[LessEqual[z, 3.4e-72]], $MachinePrecision]], N[(t * N[(z * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.36e7 or 3.3999999999999998e-72 < z

   1. Initial program 89.4%

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

      1. fma-define 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*l* 88.8%

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

      4. +-commutative 88.8%

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

      5. fma-define 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around inf 36.6%

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

      1. *-commutative 36.6%

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

      2. *-commutative 36.6%

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

      3. *-commutative 36.6%

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

      4. associate-*r* 36.6%

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

   7. Simplified 36.6%

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

   if -1.36e7 < z < 3.3999999999999998e-72

   1. Initial program 93.7%

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

      1. fma-define 93.7%

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

      2. *-commutative 93.7%

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

      3. associate-*l* 92.2%

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

      4. +-commutative 92.2%

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

      5. fma-define 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf 39.9%

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

      1. *-commutative 39.9%

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

      2. associate-*l* 39.9%

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

   7. Simplified 39.9%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13600000 \lor \neg \left(z \leq 3.4 \cdot 10^{-72}\right):\\ \;\;\;\;t \cdot \left(z \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.7% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

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 = t * (z * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.3%

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

   1. fma-define 91.3%

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

   2. *-commutative 91.3%

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

   3. associate-*l* 90.2%

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

   4. +-commutative 90.2%

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

   5. fma-define 90.2%

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

3. Simplified 90.2%

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

5. Taylor expanded in z around inf 24.5%

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

   1. *-commutative 24.5%

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

   2. *-commutative 24.5%

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

   3. *-commutative 24.5%

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

   4. associate-*r* 24.5%

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

7. Simplified 24.5%

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

Developer Target 1: 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 2024165 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i)))))

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