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

Percentage Accurate: 90.1% → 96.5%

Time: 13.1s

Alternatives: 13

Speedup: 0.5×

• 47.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))))
   (if (<= (- (+ (* x y) (* z t)) (* (* c t_1) i)) INFINITY)
     (* 2.0 (- (fma x y (* z t)) (* 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 tmp;
	if ((((x * y) + (z * t)) - ((c * t_1) * i)) <= ((double) INFINITY)) {
		tmp = 2.0 * (fma(x, y, (z * t)) - (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))
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(c * t_1) * i)) <= Inf)
		tmp = Float64(2.0 * Float64(fma(x, y, Float64(z * t)) - Float64(t_1 * Float64(c * i))));
	else
		tmp = Float64(2.0 * Float64(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]}, If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(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 95.6%

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

      1. associate-*l* 98.7%

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

      2. fma-def 98.7%

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

   3. Simplified 98.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around inf 80.3%

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

4. Final simplification 97.6%

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

Alternative 2: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+290}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(t_1 \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - t_2\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+290)))
     (* 2.0 (* c (* t_1 (- i))))
     (* (- (+ (* x y) (* z t)) t_2) 2.0))))

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 <= -((double) INFINITY)) || !(t_2 <= 5e+290)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	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 tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+290)) {
		tmp = 2.0 * (c * (t_1 * -i));
	} else {
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	}
	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 <= -math.inf) or not (t_2 <= 5e+290):
		tmp = 2.0 * (c * (t_1 * -i))
	else:
		tmp = (((x * y) + (z * t)) - t_2) * 2.0
	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 <= Float64(-Inf)) || !(t_2 <= 5e+290))
		tmp = Float64(2.0 * Float64(c * Float64(t_1 * Float64(-i))));
	else
		tmp = Float64(Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2) * 2.0);
	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 <= -Inf) || ~((t_2 <= 5e+290)))
		tmp = 2.0 * (c * (t_1 * -i));
	else
		tmp = (((x * y) + (z * t)) - t_2) * 2.0;
	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[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+290]], $MachinePrecision]], N[(2.0 * N[(c * N[(t$95$1 * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0 or 4.9999999999999998e290 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 75.7%

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

   2. Taylor expanded in i around inf 94.2%

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

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 4.9999999999999998e290

   1. Initial program 99.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -\infty \lor \neg \left(\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+290}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \end{array} \]

Alternative 3: 96.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (+ (* 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 * Float64(-i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (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 95.6%

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

      1. associate-*l* 98.7%

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

      2. fma-def 98.7%

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

   3. Simplified 98.7%

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

      1. fma-def 98.7%

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

      2. +-commutative 98.7%

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

   5. Applied egg-rr 98.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around inf 80.3%

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

4. Final simplification 97.6%

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

Alternative 4: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 22500:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.2e+122)
     t_2
     (if (<= c 22500.0)
       (* 2.0 (- t_1 (* i (* a c))))
       (if (<= c 1.5e+186) (* 2.0 (- t_1 (* c (* b (* c 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 = (x * y) + (z * t);
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.2e+122) {
		tmp = t_2;
	} else if (c <= 22500.0) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (c <= 1.5e+186) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.2d+122)) then
        tmp = t_2
    else if (c <= 22500.0d0) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else if (c <= 1.5d+186) then
        tmp = 2.0d0 * (t_1 - (c * (b * (c * i))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.2e+122) {
		tmp = t_2;
	} else if (c <= 22500.0) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (c <= 1.5e+186) {
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.2e+122:
		tmp = t_2
	elif c <= 22500.0:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	elif c <= 1.5e+186:
		tmp = 2.0 * (t_1 - (c * (b * (c * i))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.2e+122)
		tmp = t_2;
	elseif (c <= 22500.0)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	elseif (c <= 1.5e+186)
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(b * Float64(c * i)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.2e+122)
		tmp = t_2;
	elseif (c <= 22500.0)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	elseif (c <= 1.5e+186)
		tmp = 2.0 * (t_1 - (c * (b * (c * i))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.2e+122], t$95$2, If[LessEqual[c, 22500.0], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e+186], N[(2.0 * N[(t$95$1 - N[(c * N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.2000000000000001e122 or 1.49999999999999991e186 < c

   1. Initial program 71.7%

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

   2. Taylor expanded in i around inf 92.6%

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

   if -1.2000000000000001e122 < c < 22500

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 91.8%

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

   if 22500 < c < 1.49999999999999991e186

   1. Initial program 89.3%

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

   2. Taylor expanded in a around 0 82.8%

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

      1. expm1-log1p-u 42.1%

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

      2. expm1-udef 42.1%

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

      3. associate-*l* 42.4%

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

      4. *-commutative 42.4%

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

   4. Applied egg-rr 42.4%

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

      1. expm1-def 42.4%

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

      2. expm1-log1p 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*r* 85.2%

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

      5. *-commutative 85.2%

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

      6. *-commutative 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{+122}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 22500:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(b \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 5: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 11200:\\ \;\;\;\;2 \cdot \left(t_1 - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.04 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -6.8e+124)
     t_2
     (if (<= c 11200.0)
       (* 2.0 (- t_1 (* i (* a c))))
       (if (<= c 1.04e+186) (* 2.0 (- t_1 (* c (* c (* b 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 = (x * y) + (z * t);
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -6.8e+124) {
		tmp = t_2;
	} else if (c <= 11200.0) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (c <= 1.04e+186) {
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-6.8d+124)) then
        tmp = t_2
    else if (c <= 11200.0d0) then
        tmp = 2.0d0 * (t_1 - (i * (a * c)))
    else if (c <= 1.04d+186) then
        tmp = 2.0d0 * (t_1 - (c * (c * (b * i))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -6.8e+124) {
		tmp = t_2;
	} else if (c <= 11200.0) {
		tmp = 2.0 * (t_1 - (i * (a * c)));
	} else if (c <= 1.04e+186) {
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -6.8e+124:
		tmp = t_2
	elif c <= 11200.0:
		tmp = 2.0 * (t_1 - (i * (a * c)))
	elif c <= 1.04e+186:
		tmp = 2.0 * (t_1 - (c * (c * (b * i))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -6.8e+124)
		tmp = t_2;
	elseif (c <= 11200.0)
		tmp = Float64(2.0 * Float64(t_1 - Float64(i * Float64(a * c))));
	elseif (c <= 1.04e+186)
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(c * Float64(b * i)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -6.8e+124)
		tmp = t_2;
	elseif (c <= 11200.0)
		tmp = 2.0 * (t_1 - (i * (a * c)));
	elseif (c <= 1.04e+186)
		tmp = 2.0 * (t_1 - (c * (c * (b * i))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.8e+124], t$95$2, If[LessEqual[c, 11200.0], N[(2.0 * N[(t$95$1 - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.04e+186], N[(2.0 * N[(t$95$1 - N[(c * N[(c * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.8e124 or 1.04e186 < c

   1. Initial program 71.7%

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

   2. Taylor expanded in i around inf 92.6%

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

   if -6.8e124 < c < 11200

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 91.8%

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

   if 11200 < c < 1.04e186

   1. Initial program 89.3%

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

   2. Taylor expanded in a around 0 82.9%

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

      1. unpow2 82.9%

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

      2. associate-*r* 87.2%

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

   4. Simplified 87.2%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{+124}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq 11200:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 1.04 \cdot 10^{+186}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(c \cdot \left(b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 6: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := 2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{if}\;c \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-75}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0))
        (t_2 (* 2.0 (* c (* (+ a (* b c)) (- i))))))
   (if (<= c -1.95e+48)
     t_2
     (if (<= c -2e-37)
       t_1
       (if (<= c -5.4e-53)
         t_2
         (if (<= c -9e-75)
           (* 2.0 (- (* z t) (* i (* a c))))
           (if (<= c 2.7e-13) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.95e+48) {
		tmp = t_2;
	} else if (c <= -2e-37) {
		tmp = t_1;
	} else if (c <= -5.4e-53) {
		tmp = t_2;
	} else if (c <= -9e-75) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= 2.7e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = 2.0d0 * (c * ((a + (b * c)) * -i))
    if (c <= (-1.95d+48)) then
        tmp = t_2
    else if (c <= (-2d-37)) then
        tmp = t_1
    else if (c <= (-5.4d-53)) then
        tmp = t_2
    else if (c <= (-9d-75)) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if (c <= 2.7d-13) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	double tmp;
	if (c <= -1.95e+48) {
		tmp = t_2;
	} else if (c <= -2e-37) {
		tmp = t_1;
	} else if (c <= -5.4e-53) {
		tmp = t_2;
	} else if (c <= -9e-75) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= 2.7e-13) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = 2.0 * (c * ((a + (b * c)) * -i))
	tmp = 0
	if c <= -1.95e+48:
		tmp = t_2
	elif c <= -2e-37:
		tmp = t_1
	elif c <= -5.4e-53:
		tmp = t_2
	elif c <= -9e-75:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif c <= 2.7e-13:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(2.0 * Float64(c * Float64(Float64(a + Float64(b * c)) * Float64(-i))))
	tmp = 0.0
	if (c <= -1.95e+48)
		tmp = t_2;
	elseif (c <= -2e-37)
		tmp = t_1;
	elseif (c <= -5.4e-53)
		tmp = t_2;
	elseif (c <= -9e-75)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (c <= 2.7e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = 2.0 * (c * ((a + (b * c)) * -i));
	tmp = 0.0;
	if (c <= -1.95e+48)
		tmp = t_2;
	elseif (c <= -2e-37)
		tmp = t_1;
	elseif (c <= -5.4e-53)
		tmp = t_2;
	elseif (c <= -9e-75)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif (c <= 2.7e-13)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.95e+48], t$95$2, If[LessEqual[c, -2e-37], t$95$1, If[LessEqual[c, -5.4e-53], t$95$2, If[LessEqual[c, -9e-75], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.7e-13], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.95e48 or -2.00000000000000013e-37 < c < -5.3999999999999998e-53 or 2.70000000000000011e-13 < c

   1. Initial program 81.3%

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

   2. Taylor expanded in i around inf 82.3%

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

   if -1.95e48 < c < -2.00000000000000013e-37 or -9.0000000000000006e-75 < c < 2.70000000000000011e-13

   1. Initial program 99.1%

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

   2. Taylor expanded in c around 0 77.9%

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

   if -5.3999999999999998e-53 < c < -9.0000000000000006e-75

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 100.0%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. associate-*r* 85.8%

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

      2. *-commutative 85.8%

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

      3. *-commutative 85.8%

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

      4. *-commutative 85.8%

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

   5. Simplified 85.8%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+48}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -2 \cdot 10^{-37}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-53}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-75}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 7: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+122} \lor \neg \left(c \leq 10^{+41}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -3e+122) (not (<= c 1e+41)))
   (* 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 <= -3e+122) || !(c <= 1e+41)) {
		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 <= (-3d+122)) .or. (.not. (c <= 1d+41))) 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 <= -3e+122) || !(c <= 1e+41)) {
		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 <= -3e+122) or not (c <= 1e+41):
		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 <= -3e+122) || !(c <= 1e+41))
		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 <= -3e+122) || ~((c <= 1e+41)))
		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, -3e+122], N[Not[LessEqual[c, 1e+41]], $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 < -2.99999999999999986e122 or 1.00000000000000001e41 < c

   1. Initial program 76.8%

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

   2. Taylor expanded in i around inf 84.8%

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

   if -2.99999999999999986e122 < c < 1.00000000000000001e41

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 90.4%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+122} \lor \neg \left(c \leq 10^{+41}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a + b \cdot c\right) \cdot \left(-i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \left(a \cdot c\right)\right)\\ \end{array} \]

Alternative 8: 68.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z \cdot t\right) \cdot 2\\ t_2 := c \cdot \left(b \cdot \left(\left(c \cdot i\right) \cdot -2\right)\right)\\ \mathbf{if}\;c \leq -3.25 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -92000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-75}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) (* z t)) 2.0)) (t_2 (* c (* b (* (* c i) -2.0)))))
   (if (<= c -3.25e+122)
     t_2
     (if (<= c -92000000000.0)
       t_1
       (if (<= c -8.8e-75)
         (* 2.0 (- (* z t) (* i (* a c))))
         (if (<= c 4.6e+41) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = c * (b * ((c * i) * -2.0));
	double tmp;
	if (c <= -3.25e+122) {
		tmp = t_2;
	} else if (c <= -92000000000.0) {
		tmp = t_1;
	} else if (c <= -8.8e-75) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= 4.6e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + (z * t)) * 2.0d0
    t_2 = c * (b * ((c * i) * (-2.0d0)))
    if (c <= (-3.25d+122)) then
        tmp = t_2
    else if (c <= (-92000000000.0d0)) then
        tmp = t_1
    else if (c <= (-8.8d-75)) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if (c <= 4.6d+41) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((x * y) + (z * t)) * 2.0;
	double t_2 = c * (b * ((c * i) * -2.0));
	double tmp;
	if (c <= -3.25e+122) {
		tmp = t_2;
	} else if (c <= -92000000000.0) {
		tmp = t_1;
	} else if (c <= -8.8e-75) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= 4.6e+41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((x * y) + (z * t)) * 2.0
	t_2 = c * (b * ((c * i) * -2.0))
	tmp = 0
	if c <= -3.25e+122:
		tmp = t_2
	elif c <= -92000000000.0:
		tmp = t_1
	elif c <= -8.8e-75:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif c <= 4.6e+41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0)
	t_2 = Float64(c * Float64(b * Float64(Float64(c * i) * -2.0)))
	tmp = 0.0
	if (c <= -3.25e+122)
		tmp = t_2;
	elseif (c <= -92000000000.0)
		tmp = t_1;
	elseif (c <= -8.8e-75)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (c <= 4.6e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((x * y) + (z * t)) * 2.0;
	t_2 = c * (b * ((c * i) * -2.0));
	tmp = 0.0;
	if (c <= -3.25e+122)
		tmp = t_2;
	elseif (c <= -92000000000.0)
		tmp = t_1;
	elseif (c <= -8.8e-75)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif (c <= 4.6e+41)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(b * N[(N[(c * i), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.25e+122], t$95$2, If[LessEqual[c, -92000000000.0], t$95$1, If[LessEqual[c, -8.8e-75], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e+41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.24999999999999982e122 or 4.5999999999999997e41 < c

   1. Initial program 76.8%

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

      1. associate-*l* 85.1%

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

      2. fma-def 87.1%

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

   3. Simplified 87.1%

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

      1. fma-def 85.1%

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

      2. +-commutative 85.1%

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

   5. Applied egg-rr 85.1%

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

   6. Taylor expanded in b around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

      4. unpow2 67.4%

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

      5. distribute-rgt-neg-in 67.4%

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

   8. Simplified 67.4%

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

   9. Taylor expanded in i around 0 67.4%

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

       1. *-commutative 67.4%

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

       2. unpow2 67.4%

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

       3. associate-*r* 68.8%

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

       4. associate-*l* 72.4%

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

       5. associate-*r* 72.4%

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

       6. *-commutative 72.4%

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

       7. associate-*l* 72.4%

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

       8. *-commutative 72.4%

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

       9. *-commutative 72.4%

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

       10. associate-*r* 71.5%

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

   11. Simplified 71.5%

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

   12. Taylor expanded in c around 0 67.4%

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

       1. *-commutative 67.4%

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

       2. unpow2 67.4%

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

       3. associate-*l* 70.4%

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

       4. associate-*r* 72.4%

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

       5. *-commutative 72.4%

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

       6. associate-*r* 71.5%

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

       7. associate-*r* 71.5%

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

       8. *-commutative 71.5%

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

       9. associate-*r* 72.4%

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

       10. *-commutative 72.4%

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

       11. associate-*r* 72.4%

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

   14. Simplified 72.4%

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

   if -3.24999999999999982e122 < c < -9.2e10 or -8.80000000000000022e-75 < c < 4.5999999999999997e41

   1. Initial program 99.2%

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

   2. Taylor expanded in c around 0 75.4%

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

   if -9.2e10 < c < -8.80000000000000022e-75

   1. Initial program 95.0%

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

   2. Taylor expanded in a around inf 81.1%

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

   3. Taylor expanded in x around 0 72.2%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

      3. *-commutative 68.1%

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

      4. *-commutative 68.1%

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

   5. Simplified 68.1%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.25 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(b \cdot \left(\left(c \cdot i\right) \cdot -2\right)\right)\\ \mathbf{elif}\;c \leq -92000000000:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-75}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+41}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(b \cdot \left(\left(c \cdot i\right) \cdot -2\right)\right)\\ \end{array} \]

Alternative 9: 68.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.7 \cdot 10^{+123} \lor \neg \left(c \leq 9.2 \cdot 10^{+43}\right):\\ \;\;\;\;c \cdot \left(b \cdot \left(\left(c \cdot i\right) \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.7e+123) (not (<= c 9.2e+43)))
   (* c (* b (* (* c i) -2.0)))
   (* (+ (* x y) (* z t)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.7e+123) || !(c <= 9.2e+43)) {
		tmp = c * (b * ((c * i) * -2.0));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.7d+123)) .or. (.not. (c <= 9.2d+43))) then
        tmp = c * (b * ((c * i) * (-2.0d0)))
    else
        tmp = ((x * y) + (z * t)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.7e+123) || !(c <= 9.2e+43)) {
		tmp = c * (b * ((c * i) * -2.0));
	} else {
		tmp = ((x * y) + (z * t)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.7e+123) or not (c <= 9.2e+43):
		tmp = c * (b * ((c * i) * -2.0))
	else:
		tmp = ((x * y) + (z * t)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.7e+123) || !(c <= 9.2e+43))
		tmp = Float64(c * Float64(b * Float64(Float64(c * i) * -2.0)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.7e+123) || ~((c <= 9.2e+43)))
		tmp = c * (b * ((c * i) * -2.0));
	else
		tmp = ((x * y) + (z * t)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.7e+123], N[Not[LessEqual[c, 9.2e+43]], $MachinePrecision]], N[(c * N[(b * N[(N[(c * i), $MachinePrecision] * -2.0), $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 < -2.70000000000000013e123 or 9.200000000000001e43 < c

   1. Initial program 76.8%

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

      1. associate-*l* 85.1%

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

      2. fma-def 87.1%

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

   3. Simplified 87.1%

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

      1. fma-def 85.1%

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

      2. +-commutative 85.1%

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

   5. Applied egg-rr 85.1%

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

   6. Taylor expanded in b around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. *-commutative 67.4%

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

      3. distribute-rgt-neg-in 67.4%

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

      4. unpow2 67.4%

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

      5. distribute-rgt-neg-in 67.4%

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

   8. Simplified 67.4%

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

   9. Taylor expanded in i around 0 67.4%

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

       1. *-commutative 67.4%

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

       2. unpow2 67.4%

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

       3. associate-*r* 68.8%

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

       4. associate-*l* 72.4%

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

       5. associate-*r* 72.4%

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

       6. *-commutative 72.4%

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

       7. associate-*l* 72.4%

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

       8. *-commutative 72.4%

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

       9. *-commutative 72.4%

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

       10. associate-*r* 71.5%

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

   11. Simplified 71.5%

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

   12. Taylor expanded in c around 0 67.4%

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

       1. *-commutative 67.4%

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

       2. unpow2 67.4%

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

       3. associate-*l* 70.4%

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

       4. associate-*r* 72.4%

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

       5. *-commutative 72.4%

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

       6. associate-*r* 71.5%

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

       7. associate-*r* 71.5%

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

       8. *-commutative 71.5%

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

       9. associate-*r* 72.4%

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

       10. *-commutative 72.4%

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

       11. associate-*r* 72.4%

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

   14. Simplified 72.4%

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

   if -2.70000000000000013e123 < c < 9.200000000000001e43

   1. Initial program 98.6%

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

   2. Taylor expanded in c around 0 71.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.7 \cdot 10^{+123} \lor \neg \left(c \leq 9.2 \cdot 10^{+43}\right):\\ \;\;\;\;c \cdot \left(b \cdot \left(\left(c \cdot i\right) \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \end{array} \]

Alternative 10: 56.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{+142}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -4.8e+125)
   (* (* i (* a c)) (- 2.0))
   (if (<= c 1.08e+142) (* (+ (* x y) (* z t)) 2.0) (* a (* (* c i) -2.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -4.8e+125) {
		tmp = (i * (a * c)) * -2.0;
	} else if (c <= 1.08e+142) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = a * ((c * i) * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-4.8d+125)) then
        tmp = (i * (a * c)) * -2.0d0
    else if (c <= 1.08d+142) then
        tmp = ((x * y) + (z * t)) * 2.0d0
    else
        tmp = a * ((c * i) * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -4.8e+125) {
		tmp = (i * (a * c)) * -2.0;
	} else if (c <= 1.08e+142) {
		tmp = ((x * y) + (z * t)) * 2.0;
	} else {
		tmp = a * ((c * i) * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -4.8e+125:
		tmp = (i * (a * c)) * -2.0
	elif c <= 1.08e+142:
		tmp = ((x * y) + (z * t)) * 2.0
	else:
		tmp = a * ((c * i) * -2.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -4.8e+125)
		tmp = Float64(Float64(i * Float64(a * c)) * Float64(-2.0));
	elseif (c <= 1.08e+142)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) * 2.0);
	else
		tmp = Float64(a * Float64(Float64(c * i) * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -4.8e+125)
		tmp = (i * (a * c)) * -2.0;
	elseif (c <= 1.08e+142)
		tmp = ((x * y) + (z * t)) * 2.0;
	else
		tmp = a * ((c * i) * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -4.8e+125], N[(N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision] * (-2.0)), $MachinePrecision], If[LessEqual[c, 1.08e+142], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(a * N[(N[(c * i), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.7999999999999999e125

   1. Initial program 74.2%

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

      1. associate-*l* 84.0%

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

      2. fma-def 89.3%

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

   3. Simplified 89.3%

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

      1. fma-def 84.0%

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

      2. +-commutative 84.0%

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

   5. Applied egg-rr 84.0%

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

   6. Taylor expanded in a around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. *-commutative 38.1%

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

      3. associate-*r* 38.3%

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

      4. *-commutative 38.3%

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

      5. distribute-lft-neg-out 38.3%

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

      6. *-commutative 38.3%

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

      7. distribute-rgt-neg-in 38.3%

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

   8. Simplified 38.3%

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

   if -4.7999999999999999e125 < c < 1.08e142

   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. Taylor expanded in c around 0 66.4%

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

   if 1.08e142 < c

   1. Initial program 77.3%

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

   2. Taylor expanded in a around inf 35.4%

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

   3. Taylor expanded in z around 0 36.1%

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

      1. associate-*r* 31.2%

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

      2. *-commutative 31.2%

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

      3. *-commutative 31.2%

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

      4. *-commutative 31.2%

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

   5. Simplified 31.2%

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

   6. Taylor expanded in y around 0 25.7%

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

      1. mul-1-neg 25.7%

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

      2. associate-*r* 32.9%

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

      3. distribute-rgt-neg-in 32.9%

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

      4. *-commutative 32.9%

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

      5. associate-*r* 23.3%

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

   8. Simplified 23.3%

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

   9. Taylor expanded in i around 0 25.7%

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

       1. *-commutative 25.7%

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

       2. associate-*r* 23.3%

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

       3. *-commutative 23.3%

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

       4. associate-*r* 32.9%

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

       5. associate-*l* 32.9%

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

   11. Simplified 32.9%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{+125}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot \left(-2\right)\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{+142}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \end{array} \]

Alternative 11: 37.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+78}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* x y))))
   (if (<= y -1.75e-136)
     t_1
     (if (<= y 7.5e-143)
       (* a (* (* c i) -2.0))
       (if (<= y 1.75e+78) (* 2.0 (* z t)) 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 * (x * y);
	double tmp;
	if (y <= -1.75e-136) {
		tmp = t_1;
	} else if (y <= 7.5e-143) {
		tmp = a * ((c * i) * -2.0);
	} else if (y <= 1.75e+78) {
		tmp = 2.0 * (z * t);
	} 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 * (x * y)
    if (y <= (-1.75d-136)) then
        tmp = t_1
    else if (y <= 7.5d-143) then
        tmp = a * ((c * i) * (-2.0d0))
    else if (y <= 1.75d+78) then
        tmp = 2.0d0 * (z * t)
    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 * (x * y);
	double tmp;
	if (y <= -1.75e-136) {
		tmp = t_1;
	} else if (y <= 7.5e-143) {
		tmp = a * ((c * i) * -2.0);
	} else if (y <= 1.75e+78) {
		tmp = 2.0 * (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (x * y)
	tmp = 0
	if y <= -1.75e-136:
		tmp = t_1
	elif y <= 7.5e-143:
		tmp = a * ((c * i) * -2.0)
	elif y <= 1.75e+78:
		tmp = 2.0 * (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -1.75e-136)
		tmp = t_1;
	elseif (y <= 7.5e-143)
		tmp = Float64(a * Float64(Float64(c * i) * -2.0));
	elseif (y <= 1.75e+78)
		tmp = Float64(2.0 * Float64(z * t));
	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 * (x * y);
	tmp = 0.0;
	if (y <= -1.75e-136)
		tmp = t_1;
	elseif (y <= 7.5e-143)
		tmp = a * ((c * i) * -2.0);
	elseif (y <= 1.75e+78)
		tmp = 2.0 * (z * t);
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-136], t$95$1, If[LessEqual[y, 7.5e-143], N[(a * N[(N[(c * i), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+78], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75000000000000015e-136 or 1.7500000000000001e78 < y

   1. Initial program 87.1%

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

   2. Taylor expanded in x around inf 45.9%

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

   if -1.75000000000000015e-136 < y < 7.5000000000000003e-143

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 64.6%

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

   3. Taylor expanded in z around 0 37.4%

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

      1. associate-*r* 41.5%

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

      2. *-commutative 41.5%

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

      3. *-commutative 41.5%

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

      4. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in y around 0 30.5%

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

      1. mul-1-neg 30.5%

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

      2. associate-*r* 40.0%

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

      3. distribute-rgt-neg-in 40.0%

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

      4. *-commutative 40.0%

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

      5. associate-*r* 34.5%

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

   8. Simplified 34.5%

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

   9. Taylor expanded in i around 0 30.5%

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

       1. *-commutative 30.5%

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

       2. associate-*r* 34.5%

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

       3. *-commutative 34.5%

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

       4. associate-*r* 40.0%

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

       5. associate-*l* 40.0%

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

   11. Simplified 40.0%

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

   if 7.5000000000000003e-143 < y < 1.7500000000000001e78

   1. Initial program 92.2%

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

   2. Taylor expanded in z around inf 30.4%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-136}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-143}:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+78}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 12: 38.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-136} \lor \neg \left(y \leq 2 \cdot 10^{+78}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.3e-136) (not (<= y 2e+78))) (* 2.0 (* x y)) (* 2.0 (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.3e-136) || !(y <= 2e+78)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.3d-136)) .or. (.not. (y <= 2d+78))) then
        tmp = 2.0d0 * (x * y)
    else
        tmp = 2.0d0 * (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.3e-136) || !(y <= 2e+78)) {
		tmp = 2.0 * (x * y);
	} else {
		tmp = 2.0 * (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.3e-136) or not (y <= 2e+78):
		tmp = 2.0 * (x * y)
	else:
		tmp = 2.0 * (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.3e-136) || !(y <= 2e+78))
		tmp = Float64(2.0 * Float64(x * y));
	else
		tmp = Float64(2.0 * Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.3e-136) || ~((y <= 2e+78)))
		tmp = 2.0 * (x * y);
	else
		tmp = 2.0 * (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.3e-136], N[Not[LessEqual[y, 2e+78]], $MachinePrecision]], N[(2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.3e-136 or 2.00000000000000002e78 < y

   1. Initial program 87.1%

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

   2. Taylor expanded in x around inf 45.9%

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

   if -4.3e-136 < y < 2.00000000000000002e78

   1. Initial program 93.5%

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

   2. Taylor expanded in z around inf 29.1%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-136} \lor \neg \left(y \leq 2 \cdot 10^{+78}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 13: 28.9% 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 90.0%

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

2. Taylor expanded in z around inf 24.1%

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

3. Final simplification 24.1%

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

Developer target: 94.4% 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 2023196 
(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))))