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

Percentage Accurate: 89.8% → 92.2%

Time: 19.1s

Alternatives: 15

Speedup: 0.5×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = 2.501124220877663e-143
  2. y = -1.055955770600042e+170
  3. z = 3.2127050007479974e-268
  4. t = 2.7015227905879875e+91
  5. a = -3.8762921684996564e-16
  6. b = 1.9565449488672878e+262
  7. c = 9.560309355573813e-14
  8. i = -4.634260050724758e-121

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.8% 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: 92.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+266}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(t\_1 \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c t_1)))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (- (fma x y (* z t)) (* c (* b (* c i)))))
     (if (<= t_2 2e+266)
       (* 2.0 (- (+ (* x y) (* z t)) (* i t_2)))
       (* 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;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (c * (b * (c * i))));
	} else if (t_2 <= 2e+266) {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_2));
	} 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(c * t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(c * Float64(b * Float64(c * i)))));
	elseif (t_2 <= 2e+266)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * t_2)));
	else
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	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[(c * t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+266], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 64.1%

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

      1. associate--l+ 64.1%

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

      2. *-commutative 64.1%

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

      3. associate--l+ 64.1%

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

      4. associate--l+ 64.1%

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

      5. *-commutative 64.1%

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

      6. associate--l+ 64.1%

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

      7. fma-define 64.1%

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

      8. *-commutative 64.1%

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

      9. associate-*l* 89.9%

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

      10. +-commutative 89.9%

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

      11. 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 b around inf 86.3%

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 2.0000000000000001e266

   1. Initial program 98.3%

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

   if 2.0000000000000001e266 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 73.0%

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

   3. Taylor expanded in i around inf 92.4%

      \[\leadsto 2 \cdot \color{blue}{\left(-1 \cdot \left(c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -\infty:\\ \;\;\;\;2 \cdot \left(\mathsf{fma}\left(x, y, z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;c \cdot \left(a + b \cdot c\right) \leq 2 \cdot 10^{+266}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.9% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. fma-define 91.8%

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

   2. associate-*l* 95.8%

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

3. Simplified 95.8%

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

5. Final simplification 95.8%

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

Alternative 3: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := c \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+298} \lor \neg \left(t\_2 \leq 2 \cdot 10^{+266}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(t\_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* c t_1)))
   (if (or (<= t_2 -2e+298) (not (<= t_2 2e+266)))
     (* 2.0 (* c (* t_1 (- i))))
     (* 2.0 (- (+ (* x y) (* z t)) (* i t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = c * t_1;
	double tmp;
	if ((t_2 <= -2e+298) || !(t_2 <= 2e+266)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * t_2));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = c * t_1
    if ((t_2 <= (-2d+298)) .or. (.not. (t_2 <= 2d+266))) then
        tmp = 2.0d0 * (c * (t_1 * -i))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * 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;
	double tmp;
	if ((t_2 <= -2e+298) || !(t_2 <= 2e+266)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * 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
	tmp = 0
	if (t_2 <= -2e+298) or not (t_2 <= 2e+266):
		tmp = 2.0 * (c * (t_1 * -i))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * 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 * t_1)
	tmp = 0.0
	if ((t_2 <= -2e+298) || !(t_2 <= 2e+266))
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * 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;
	tmp = 0.0;
	if ((t_2 <= -2e+298) || ~((t_2 <= 2e+266)))
		tmp = 2.0 * (c * (t_1 * -i));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * 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 * t$95$1), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+298], N[Not[LessEqual[t$95$2, 2e+266]], $MachinePrecision]], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -1.9999999999999999e298 or 2.0000000000000001e266 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 69.6%

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

   3. Taylor expanded in i around inf 88.6%

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

   if -1.9999999999999999e298 < (*.f64 (+.f64 a (*.f64 b c)) c) < 2.0000000000000001e266

   1. Initial program 98.3%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot \left(a + b \cdot c\right) \leq -2 \cdot 10^{+298} \lor \neg \left(c \cdot \left(a + b \cdot c\right) \leq 2 \cdot 10^{+266}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(c \cdot \left(a + b \cdot c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \leq -112000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-79}:\\ \;\;\;\;2 \cdot \left(t\_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t\_1 - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (<= c -112000000000.0)
     (* 2.0 (* c (* (+ a (* b c)) (- i))))
     (if (<= c 4.7e-79)
       (* 2.0 (- t_1 (* i (* a c))))
       (* 2.0 (- t_1 (* (* b c) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -112000000000.0) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else if (c <= 4.7e-79) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    if (c <= (-112000000000.0d0)) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else if (c <= 4.7d-79) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else
        tmp = 2.0d0 * (t_1 - ((b * c) * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (c <= -112000000000.0) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else if (c <= 4.7e-79) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else {
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if c <= -112000000000.0:
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	elif c <= 4.7e-79:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	else:
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (c <= -112000000000.0)
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	elseif (c <= 4.7e-79)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(b * c) * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (c <= -112000000000.0)
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	elseif (c <= 4.7e-79)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	else
		tmp = 2.0 * (t_1 - ((b * c) * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -112000000000.0], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.7e-79], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(N[(b * c), $MachinePrecision] * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.12e11

   1. Initial program 77.8%

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

   3. Taylor expanded in i around inf 80.5%

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

   if -1.12e11 < c < 4.7000000000000002e-79

   1. Initial program 96.9%

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

   3. Taylor expanded in a around inf 95.5%

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

      1. *-commutative 95.5%

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

   5. Simplified 95.5%

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

   if 4.7000000000000002e-79 < c

   1. Initial program 88.5%

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

      1. associate-*r* 98.5%

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

      2. *-commutative 98.5%

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

      3. +-commutative 98.5%

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

      4. distribute-lft-in 87.7%

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

   4. Applied egg-rr 87.7%

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

      1. add-sqr-sqrt 49.9%

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

      2. sqrt-unprod 81.1%

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

      3. sqr-neg 81.1%

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

      4. sqrt-unprod 32.4%

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

      5. add-sqr-sqrt 75.3%

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

      6. distribute-rgt-neg-in 75.3%

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

      7. distribute-lft-neg-in 75.3%

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

      8. *-commutative 75.3%

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

      9. distribute-lft-neg-in 75.3%

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

      10. cancel-sign-sub-inv 75.3%

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

      11. *-commutative 75.3%

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

      12. distribute-rgt-out-- 83.4%

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

      13. *-commutative 83.4%

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

   6. Applied egg-rr 83.4%

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

   7. Taylor expanded in c around inf 87.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -112000000000:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{-79}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= z -1.1e+111)
     t_2
     (if (<= z -2.8e-257)
       t_1
       (if (<= z 4.7e-247)
         (* c (* i (* a -2.0)))
         (if (<= z 2.5e-65) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (z <= -1.1e+111) {
		tmp = t_2;
	} else if (z <= -2.8e-257) {
		tmp = t_1;
	} else if (z <= 4.7e-247) {
		tmp = c * (i * (a * -2.0));
	} else if (z <= 2.5e-65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (z <= (-1.1d+111)) then
        tmp = t_2
    else if (z <= (-2.8d-257)) then
        tmp = t_1
    else if (z <= 4.7d-247) then
        tmp = c * (i * (a * (-2.0d0)))
    else if (z <= 2.5d-65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (z <= -1.1e+111) {
		tmp = t_2;
	} else if (z <= -2.8e-257) {
		tmp = t_1;
	} else if (z <= 4.7e-247) {
		tmp = c * (i * (a * -2.0));
	} else if (z <= 2.5e-65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if z <= -1.1e+111:
		tmp = t_2
	elif z <= -2.8e-257:
		tmp = t_1
	elif z <= 4.7e-247:
		tmp = c * (i * (a * -2.0))
	elif z <= 2.5e-65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -1.1e+111)
		tmp = t_2;
	elseif (z <= -2.8e-257)
		tmp = t_1;
	elseif (z <= 4.7e-247)
		tmp = Float64(c * Float64(i * Float64(a * -2.0)));
	elseif (z <= 2.5e-65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (z <= -1.1e+111)
		tmp = t_2;
	elseif (z <= -2.8e-257)
		tmp = t_1;
	elseif (z <= 4.7e-247)
		tmp = c * (i * (a * -2.0));
	elseif (z <= 2.5e-65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+111], t$95$2, If[LessEqual[z, -2.8e-257], t$95$1, If[LessEqual[z, 4.7e-247], N[(c * N[(i * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999999e111 or 2.49999999999999991e-65 < z

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -1.09999999999999999e111 < z < -2.80000000000000001e-257 or 4.6999999999999998e-247 < z < 2.49999999999999991e-65

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf 37.0%

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

   if -2.80000000000000001e-257 < z < 4.6999999999999998e-247

   1. Initial program 93.1%

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

   3. Taylor expanded in a around inf 33.2%

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

      1. mul-1-neg 33.2%

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

      2. *-commutative 33.2%

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

      3. distribute-rgt-neg-in 33.2%

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

   5. Simplified 33.2%

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

   6. Taylor expanded in c around 0 33.2%

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

      1. associate-*r* 33.2%

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

      2. *-commutative 33.2%

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

      3. *-commutative 33.2%

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

   8. Simplified 33.2%

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

   9. Taylor expanded in c around 0 33.2%

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

       1. associate-*r* 33.2%

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

       2. *-commutative 33.2%

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

       3. *-commutative 33.2%

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

       4. associate-*r* 32.9%

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

   11. Simplified 32.9%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+111}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-257}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(i \cdot \left(a \cdot -2\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-247}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= z -6.8e+112)
     t_2
     (if (<= z -2.6e-257)
       t_1
       (if (<= z 4.7e-247)
         (* (* a c) (* i -2.0))
         (if (<= z 4e-64) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (z <= -6.8e+112) {
		tmp = t_2;
	} else if (z <= -2.6e-257) {
		tmp = t_1;
	} else if (z <= 4.7e-247) {
		tmp = (a * c) * (i * -2.0);
	} else if (z <= 4e-64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (z <= (-6.8d+112)) then
        tmp = t_2
    else if (z <= (-2.6d-257)) then
        tmp = t_1
    else if (z <= 4.7d-247) then
        tmp = (a * c) * (i * (-2.0d0))
    else if (z <= 4d-64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (z <= -6.8e+112) {
		tmp = t_2;
	} else if (z <= -2.6e-257) {
		tmp = t_1;
	} else if (z <= 4.7e-247) {
		tmp = (a * c) * (i * -2.0);
	} else if (z <= 4e-64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if z <= -6.8e+112:
		tmp = t_2
	elif z <= -2.6e-257:
		tmp = t_1
	elif z <= 4.7e-247:
		tmp = (a * c) * (i * -2.0)
	elif z <= 4e-64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -6.8e+112)
		tmp = t_2;
	elseif (z <= -2.6e-257)
		tmp = t_1;
	elseif (z <= 4.7e-247)
		tmp = Float64(Float64(a * c) * Float64(i * -2.0));
	elseif (z <= 4e-64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (z <= -6.8e+112)
		tmp = t_2;
	elseif (z <= -2.6e-257)
		tmp = t_1;
	elseif (z <= 4.7e-247)
		tmp = (a * c) * (i * -2.0);
	elseif (z <= 4e-64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e+112], t$95$2, If[LessEqual[z, -2.6e-257], t$95$1, If[LessEqual[z, 4.7e-247], N[(N[(a * c), $MachinePrecision] * N[(i * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999987e112 or 3.99999999999999986e-64 < z

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -6.79999999999999987e112 < z < -2.6000000000000001e-257 or 4.6999999999999998e-247 < z < 3.99999999999999986e-64

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf 37.0%

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

   if -2.6000000000000001e-257 < z < 4.6999999999999998e-247

   1. Initial program 93.1%

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

   3. Taylor expanded in a around inf 33.2%

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

      1. mul-1-neg 33.2%

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

      2. *-commutative 33.2%

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

      3. distribute-rgt-neg-in 33.2%

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

   5. Simplified 33.2%

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

   6. Taylor expanded in c around 0 33.2%

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

      1. mul-1-neg 33.2%

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

      2. *-commutative 33.2%

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

      3. associate-*r* 32.9%

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

      4. distribute-rgt-neg-in 32.9%

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

      5. *-commutative 32.9%

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

      6. distribute-rgt-neg-in 32.9%

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

   8. Simplified 32.9%

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

   9. Taylor expanded in c around 0 33.2%

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

       1. *-commutative 33.2%

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

       2. associate-*r* 33.0%

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

       3. associate-*l* 33.0%

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

   11. Simplified 33.0%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+112}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-257}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-247}:\\ \;\;\;\;\left(a \cdot c\right) \cdot \left(i \cdot -2\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-64}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-247}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;z \leq 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))) (t_2 (* 2.0 (* z t))))
   (if (<= z -1.05e+111)
     t_2
     (if (<= z -5.3e-128)
       t_1
       (if (<= z 4.9e-247)
         (* (* c i) (* a -2.0))
         (if (<= z 1e-64) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (z <= -1.05e+111) {
		tmp = t_2;
	} else if (z <= -5.3e-128) {
		tmp = t_1;
	} else if (z <= 4.9e-247) {
		tmp = (c * i) * (a * -2.0);
	} else if (z <= 1e-64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * (x * y)
    t_2 = 2.0d0 * (z * t)
    if (z <= (-1.05d+111)) then
        tmp = t_2
    else if (z <= (-5.3d-128)) then
        tmp = t_1
    else if (z <= 4.9d-247) then
        tmp = (c * i) * (a * (-2.0d0))
    else if (z <= 1d-64) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (x * y);
	double t_2 = 2.0 * (z * t);
	double tmp;
	if (z <= -1.05e+111) {
		tmp = t_2;
	} else if (z <= -5.3e-128) {
		tmp = t_1;
	} else if (z <= 4.9e-247) {
		tmp = (c * i) * (a * -2.0);
	} else if (z <= 1e-64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	t_2 = 2.0 * (z * t)
	tmp = 0
	if z <= -1.05e+111:
		tmp = t_2
	elif z <= -5.3e-128:
		tmp = t_1
	elif z <= 4.9e-247:
		tmp = (c * i) * (a * -2.0)
	elif z <= 1e-64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	t_2 = Float64(2.0 * Float64(z * t))
	tmp = 0.0
	if (z <= -1.05e+111)
		tmp = t_2;
	elseif (z <= -5.3e-128)
		tmp = t_1;
	elseif (z <= 4.9e-247)
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	elseif (z <= 1e-64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (x * y);
	t_2 = 2.0 * (z * t);
	tmp = 0.0;
	if (z <= -1.05e+111)
		tmp = t_2;
	elseif (z <= -5.3e-128)
		tmp = t_1;
	elseif (z <= 4.9e-247)
		tmp = (c * i) * (a * -2.0);
	elseif (z <= 1e-64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+111], t$95$2, If[LessEqual[z, -5.3e-128], t$95$1, If[LessEqual[z, 4.9e-247], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999997e111 or 9.99999999999999965e-65 < z

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -1.04999999999999997e111 < z < -5.2999999999999999e-128 or 4.9e-247 < z < 9.99999999999999965e-65

   1. Initial program 91.5%

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

   3. Taylor expanded in x around inf 33.7%

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

   if -5.2999999999999999e-128 < z < 4.9e-247

   1. Initial program 95.1%

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

   3. Taylor expanded in a around inf 32.1%

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

      1. mul-1-neg 32.1%

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

      2. *-commutative 32.1%

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

      3. distribute-rgt-neg-in 32.1%

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

   5. Simplified 32.1%

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

   6. Taylor expanded in c around 0 32.1%

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

      1. associate-*r* 32.1%

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

      2. *-commutative 32.1%

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

      3. *-commutative 32.1%

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

   8. Simplified 32.1%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+111}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-128}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-247}:\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{elif}\;z \leq 10^{-64}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1850 \lor \neg \left(x \cdot y \leq 1.15 \cdot 10^{-11}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1850.0) (not (<= (* x y) 1.15e-11)))
   (* 2.0 (+ (* x y) (* z t)))
   (* 2.0 (- (* z t) (* a (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1850.0) || !((x * y) <= 1.15e-11)) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1850.0d0)) .or. (.not. ((x * y) <= 1.15d-11))) then
        tmp = 2.0d0 * ((x * y) + (z * t))
    else
        tmp = 2.0d0 * ((z * t) - (a * (c * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1850.0) || !((x * y) <= 1.15e-11)) {
		tmp = 2.0 * ((x * y) + (z * t));
	} else {
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1850.0) or not ((x * y) <= 1.15e-11):
		tmp = 2.0 * ((x * y) + (z * t))
	else:
		tmp = 2.0 * ((z * t) - (a * (c * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1850.0) || !(Float64(x * y) <= 1.15e-11))
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(a * Float64(c * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1850.0) || ~(((x * y) <= 1.15e-11)))
		tmp = 2.0 * ((x * y) + (z * t));
	else
		tmp = 2.0 * ((z * t) - (a * (c * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1850.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.15e-11]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1850 or 1.15000000000000007e-11 < (*.f64 x y)

   1. Initial program 91.0%

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

   3. Taylor expanded in c around 0 75.1%

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

   if -1850 < (*.f64 x y) < 1.15000000000000007e-11

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf 67.0%

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

      1. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in x around 0 64.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1850 \lor \neg \left(x \cdot y \leq 1.15 \cdot 10^{-11}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - a \cdot \left(c \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -112000000000 \lor \neg \left(c \leq 2.7 \cdot 10^{+110}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -112000000000.0) (not (<= c 2.7e+110)))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* 2.0 (- (+ (* x y) (* z t)) (* i (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -112000000000.0) || !(c <= 2.7e+110)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-112000000000.0d0)) .or. (.not. (c <= 2.7d+110))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = 2.0d0 * (((x * y) + (z * t)) - (i * (a * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -112000000000.0) || !(c <= 2.7e+110)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -112000000000.0) or not (c <= 2.7e+110):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -112000000000.0) || !(c <= 2.7e+110))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(i * Float64(a * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -112000000000.0) || ~((c <= 2.7e+110)))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = 2.0 * (((x * y) + (z * t)) - (i * (a * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -112000000000.0], N[Not[LessEqual[c, 2.7e+110]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.12e11 or 2.7000000000000001e110 < c

   1. Initial program 79.0%

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

   3. Taylor expanded in i around inf 81.1%

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

   if -1.12e11 < c < 2.7000000000000001e110

   1. Initial program 97.4%

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

   3. Taylor expanded in a around inf 91.6%

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

      1. *-commutative 91.6%

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

   5. Simplified 91.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -112000000000 \lor \neg \left(c \leq 2.7 \cdot 10^{+110}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{-23} \lor \neg \left(c \leq 8.5 \cdot 10^{+110}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -1.45e-23) (not (<= c 8.5e+110)))
   (* 2.0 (* c (* (+ a (* b c)) (- i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.45e-23) || !(c <= 8.5e+110)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-1.45d-23)) .or. (.not. (c <= 8.5d+110))) then
        tmp = 2.0d0 * (c * ((a + (b * c)) * -i))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -1.45e-23) || !(c <= 8.5e+110)) {
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -1.45e-23) or not (c <= 8.5e+110):
		tmp = 2.0 * (c * ((a + (b * c)) * -i))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -1.45e-23) || !(c <= 8.5e+110))
		tmp = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -1.45e-23) || ~((c <= 8.5e+110)))
		tmp = 2.0 * (c * ((a + (b * c)) * -i));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -1.45e-23], N[Not[LessEqual[c, 8.5e+110]], $MachinePrecision]], N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.4500000000000001e-23 or 8.5000000000000004e110 < c

   1. Initial program 79.6%

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

   3. Taylor expanded in i around inf 79.7%

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

   if -1.4500000000000001e-23 < c < 8.5000000000000004e110

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 77.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{-23} \lor \neg \left(c \leq 8.5 \cdot 10^{+110}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -112000000000 \lor \neg \left(c \leq 8.2 \cdot 10^{+154}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(a - b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -112000000000.0) (not (<= c 8.2e+154)))
   (* 2.0 (* c (* i (- a (* b c)))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -112000000000.0) || !(c <= 8.2e+154)) {
		tmp = 2.0 * (c * (i * (a - (b * c))));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-112000000000.0d0)) .or. (.not. (c <= 8.2d+154))) then
        tmp = 2.0d0 * (c * (i * (a - (b * c))))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -112000000000.0) || !(c <= 8.2e+154)) {
		tmp = 2.0 * (c * (i * (a - (b * c))));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -112000000000.0) or not (c <= 8.2e+154):
		tmp = 2.0 * (c * (i * (a - (b * c))))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -112000000000.0) || !(c <= 8.2e+154))
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(a - Float64(b * c)))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -112000000000.0) || ~((c <= 8.2e+154)))
		tmp = 2.0 * (c * (i * (a - (b * c))));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -112000000000.0], N[Not[LessEqual[c, 8.2e+154]], $MachinePrecision]], N[(2.0 * N[(c * N[(i * N[(a - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.12e11 or 8.2e154 < c

   1. Initial program 78.8%

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

      1. associate-*r* 90.7%

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

      2. *-commutative 90.7%

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

      3. +-commutative 90.7%

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

      4. distribute-lft-in 73.1%

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

   4. Applied egg-rr 73.1%

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

      1. add-sqr-sqrt 41.3%

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

      2. sqrt-unprod 60.2%

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

      3. sqr-neg 60.2%

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

      4. sqrt-unprod 20.0%

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

      5. add-sqr-sqrt 54.3%

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

      6. distribute-rgt-neg-in 54.3%

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

      7. distribute-lft-neg-in 54.3%

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

      8. *-commutative 54.3%

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

      9. distribute-lft-neg-in 54.3%

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

      10. cancel-sign-sub-inv 54.3%

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

      11. *-commutative 54.3%

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

      12. distribute-rgt-out-- 66.1%

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

      13. *-commutative 66.1%

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

   6. Applied egg-rr 66.1%

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

   7. Taylor expanded in i around inf 58.5%

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

      1. mul-1-neg 58.5%

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

      2. *-commutative 58.5%

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

      3. unsub-neg 58.5%

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

      4. fma-define 58.5%

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

      5. distribute-rgt-neg-in 58.5%

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

      6. distribute-rgt-neg-in 58.5%

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

      7. neg-sub0 58.5%

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

      8. fma-define 58.5%

         \[\leadsto 2 \cdot \left(c \cdot \left(i \cdot \left(0 - \color{blue}{\left(c \cdot b + \left(-a\right)\right)}\right)\right)\right) \]

      9. +-commutative 58.5%

         \[\leadsto 2 \cdot \left(c \cdot \left(i \cdot \left(0 - \color{blue}{\left(\left(-a\right) + c \cdot b\right)}\right)\right)\right) \]

      10. associate--r+ 58.5%

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

      11. neg-sub0 58.5%

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

      12. remove-double-neg 58.5%

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

      13. *-commutative 58.5%

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

   9. Simplified 58.5%

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

   if -1.12e11 < c < 8.2e154

   1. Initial program 96.5%

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

   3. Taylor expanded in c around 0 73.8%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -112000000000 \lor \neg \left(c \leq 8.2 \cdot 10^{+154}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(a - b \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1040000 \lor \neg \left(i \leq 1.6 \cdot 10^{+120}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1040000.0) (not (<= i 1.6e+120)))
   (* 2.0 (- (* x y) (* a (* c i))))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1040000.0) || !(i <= 1.6e+120)) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1040000.0d0)) .or. (.not. (i <= 1.6d+120))) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1040000.0) || !(i <= 1.6e+120)) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1040000.0) or not (i <= 1.6e+120):
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1040000.0) || !(i <= 1.6e+120))
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1040000.0) || ~((i <= 1.6e+120)))
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1040000.0], N[Not[LessEqual[i, 1.6e+120]], $MachinePrecision]], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.04e6 or 1.59999999999999991e120 < i

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf 69.5%

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

      1. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in z around 0 69.1%

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

   if -1.04e6 < i < 1.59999999999999991e120

   1. Initial program 89.5%

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

   3. Taylor expanded in c around 0 71.4%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1040000 \lor \neg \left(i \leq 1.6 \cdot 10^{+120}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+53} \lor \neg \left(c \leq 1.3 \cdot 10^{+164}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -7e+53) (not (<= c 1.3e+164)))
   (* (* c i) (* a -2.0))
   (* 2.0 (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -7e+53) || !(c <= 1.3e+164)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-7d+53)) .or. (.not. (c <= 1.3d+164))) then
        tmp = (c * i) * (a * (-2.0d0))
    else
        tmp = 2.0d0 * ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -7e+53) || !(c <= 1.3e+164)) {
		tmp = (c * i) * (a * -2.0);
	} else {
		tmp = 2.0 * ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -7e+53) or not (c <= 1.3e+164):
		tmp = (c * i) * (a * -2.0)
	else:
		tmp = 2.0 * ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -7e+53) || !(c <= 1.3e+164))
		tmp = Float64(Float64(c * i) * Float64(a * -2.0));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -7e+53) || ~((c <= 1.3e+164)))
		tmp = (c * i) * (a * -2.0);
	else
		tmp = 2.0 * ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -7e+53], N[Not[LessEqual[c, 1.3e+164]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.00000000000000038e53 or 1.3e164 < c

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 45.3%

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

      1. mul-1-neg 45.3%

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

      2. *-commutative 45.3%

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

      3. distribute-rgt-neg-in 45.3%

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

   5. Simplified 45.3%

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

   6. Taylor expanded in c around 0 45.3%

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

      1. associate-*r* 45.3%

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

      2. *-commutative 45.3%

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

      3. *-commutative 45.3%

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

   8. Simplified 45.3%

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

   if -7.00000000000000038e53 < c < 1.3e164

   1. Initial program 96.2%

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

   3. Taylor expanded in c around 0 71.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+53} \lor \neg \left(c \leq 1.3 \cdot 10^{+164}\right):\\ \;\;\;\;\left(c \cdot i\right) \cdot \left(a \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+111} \lor \neg \left(z \leq 9 \cdot 10^{-64}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -1.1e+111) (not (<= z 9e-64))) (* 2.0 (* z t)) (* 2.0 (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -1.1e+111) || !(z <= 9e-64)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-1.1d+111)) .or. (.not. (z <= 9d-64))) then
        tmp = 2.0d0 * (z * t)
    else
        tmp = 2.0d0 * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -1.1e+111) || !(z <= 9e-64)) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = 2.0 * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -1.1e+111) or not (z <= 9e-64):
		tmp = 2.0 * (z * t)
	else:
		tmp = 2.0 * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -1.1e+111) || !(z <= 9e-64))
		tmp = Float64(2.0 * Float64(z * t));
	else
		tmp = Float64(2.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -1.1e+111) || ~((z <= 9e-64)))
		tmp = 2.0 * (z * t);
	else
		tmp = 2.0 * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -1.1e+111], N[Not[LessEqual[z, 9e-64]], $MachinePrecision]], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999999e111 or 9.00000000000000019e-64 < z

   1. Initial program 87.8%

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

   3. Taylor expanded in z around inf 50.0%

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

   if -1.09999999999999999e111 < z < 9.00000000000000019e-64

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf 35.8%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+111} \lor \neg \left(z \leq 9 \cdot 10^{-64}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.2% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

3. Taylor expanded in z around inf 29.9%

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

4. Final simplification 29.9%

   \[\leadsto 2 \cdot \left(z \cdot t\right) \]
5. Add Preprocessing

Developer target: 93.6% 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 2024045 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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