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

Percentage Accurate: 90.5% → 94.9%

Time: 12.5s

Alternatives: 14

Speedup: 0.5×

• 47.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.5% 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: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(c \cdot t_1\right) \cdot i\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+270}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(-t_1\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - t_2\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(t_1 \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* c t_1) i)))
   (if (<= t_2 -5e+270)
     (* 2.0 (* c (* i (- t_1))))
     (if (<= t_2 5e+298)
       (* (- (+ (* z t) (* x y)) t_2) 2.0)
       (* 2.0 (- (* z t) (* c (* t_1 i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -5e+270) {
		tmp = 2.0 * (c * (i * -t_1));
	} else if (t_2 <= 5e+298) {
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (b * c)
    t_2 = (c * t_1) * i
    if (t_2 <= (-5d+270)) then
        tmp = 2.0d0 * (c * (i * -t_1))
    else if (t_2 <= 5d+298) then
        tmp = (((z * t) + (x * y)) - t_2) * 2.0d0
    else
        tmp = 2.0d0 * ((z * t) - (c * (t_1 * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (c * t_1) * i;
	double tmp;
	if (t_2 <= -5e+270) {
		tmp = 2.0 * (c * (i * -t_1));
	} else if (t_2 <= 5e+298) {
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	} else {
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (c * t_1) * i
	tmp = 0
	if t_2 <= -5e+270:
		tmp = 2.0 * (c * (i * -t_1))
	elif t_2 <= 5e+298:
		tmp = (((z * t) + (x * y)) - t_2) * 2.0
	else:
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(c * t_1) * i)
	tmp = 0.0
	if (t_2 <= -5e+270)
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(-t_1))));
	elseif (t_2 <= 5e+298)
		tmp = Float64(Float64(Float64(Float64(z * t) + Float64(x * y)) - t_2) * 2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(t_1 * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (c * t_1) * i;
	tmp = 0.0;
	if (t_2 <= -5e+270)
		tmp = 2.0 * (c * (i * -t_1));
	elseif (t_2 <= 5e+298)
		tmp = (((z * t) + (x * y)) - t_2) * 2.0;
	else
		tmp = 2.0 * ((z * t) - (c * (t_1 * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+270], N[(2.0 * N[(c * N[(i * (-t$95$1)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+298], N[(N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -4.99999999999999976e270

   1. Initial program 84.1%

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

   2. Taylor expanded in i around inf 98.0%

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

   if -4.99999999999999976e270 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000003e298

   1. Initial program 99.3%

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

   if 5.0000000000000003e298 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   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 x around 0 92.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq -5 \cdot 10^{+270}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(-\left(a + b \cdot c\right)\right)\right)\right)\\ \mathbf{elif}\;\left(c \cdot \left(a + b \cdot c\right)\right) \cdot i \leq 5 \cdot 10^{+298}:\\ \;\;\;\;\left(\left(z \cdot t + x \cdot y\right) - \left(c \cdot \left(a + b \cdot c\right)\right) \cdot i\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 2: 96.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(i * (-t$95$1)), $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 96.8%

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

      1. associate-*l* 98.4%

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

      2. fma-def 98.4%

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

   3. Simplified 98.4%

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

   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 78.0%

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

4. Final simplification 97.7%

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

Alternative 3: 96.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 - N[(N[(c * t$95$1), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(2.0 * N[(t$95$2 - N[(t$95$1 * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(c * N[(i * (-t$95$1)), $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 96.8%

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

      1. associate-*l* 98.4%

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

      2. fma-def 98.4%

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

   3. Simplified 98.4%

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

      1. fma-def 98.4%

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

      2. +-commutative 98.4%

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

   5. Applied egg-rr 98.4%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around inf 78.0%

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

4. Final simplification 97.6%

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

Alternative 4: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{if}\;c \leq -2.05 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-97}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-111}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (- (* z t) (* c (* (+ a (* b c)) i))))))
   (if (<= c -2.05e-10)
     t_1
     (if (<= c -1.55e-97)
       (* 2.0 (- (* x y) (* a (* c i))))
       (if (<= c -3.2e-111)
         (* 2.0 (- (* z t) (* i (* a c))))
         (if (<= c 3.8e-24) (* (+ (* z t) (* x y)) 2.0) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	double tmp;
	if (c <= -2.05e-10) {
		tmp = t_1;
	} else if (c <= -1.55e-97) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= -3.2e-111) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= 3.8e-24) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * ((z * t) - (c * ((a + (b * c)) * i)))
    if (c <= (-2.05d-10)) then
        tmp = t_1
    else if (c <= (-1.55d-97)) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else if (c <= (-3.2d-111)) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if (c <= 3.8d-24) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	double tmp;
	if (c <= -2.05e-10) {
		tmp = t_1;
	} else if (c <= -1.55e-97) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= -3.2e-111) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= 3.8e-24) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)))
	tmp = 0
	if c <= -2.05e-10:
		tmp = t_1
	elif c <= -1.55e-97:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	elif c <= -3.2e-111:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif c <= 3.8e-24:
		tmp = ((z * t) + (x * y)) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(Float64(z * t) - Float64(c * Float64(Float64(a + Float64(b * c)) * i))))
	tmp = 0.0
	if (c <= -2.05e-10)
		tmp = t_1;
	elseif (c <= -1.55e-97)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	elseif (c <= -3.2e-111)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (c <= 3.8e-24)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * ((z * t) - (c * ((a + (b * c)) * i)));
	tmp = 0.0;
	if (c <= -2.05e-10)
		tmp = t_1;
	elseif (c <= -1.55e-97)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	elseif (c <= -3.2e-111)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif (c <= 3.8e-24)
		tmp = ((z * t) + (x * y)) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.05e-10], t$95$1, If[LessEqual[c, -1.55e-97], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.2e-111], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e-24], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.0499999999999999e-10 or 3.80000000000000026e-24 < c

   1. Initial program 87.6%

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

   2. Taylor expanded in x around 0 85.3%

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

   if -2.0499999999999999e-10 < c < -1.55000000000000001e-97

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 86.5%

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

   3. Taylor expanded in z around 0 65.3%

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

      1. associate-*r* 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*r* 65.3%

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

   5. Simplified 65.3%

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

   if -1.55000000000000001e-97 < c < -3.1999999999999998e-111

   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 84.8%

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

   3. Taylor expanded in x around 0 69.1%

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

      1. associate-*r* 84.7%

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

   5. Simplified 84.7%

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

   if -3.1999999999999998e-111 < c < 3.80000000000000026e-24

   1. Initial program 99.0%

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

   2. Taylor expanded in c around 0 88.6%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-97}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{-111}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 5: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-25} \lor \neg \left(z \cdot t \leq 10^{+18}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (or (<= (* z t) -5e-25) (not (<= (* z t) 1e+18)))
     (* 2.0 (- (* z t) t_1))
     (* 2.0 (- (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (((z * t) <= -5e-25) || !((z * t) <= 1e+18)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (((z * t) <= (-5d-25)) .or. (.not. ((z * t) <= 1d+18))) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (((z * t) <= -5e-25) || !((z * t) <= 1e+18)) {
		tmp = 2.0 * ((z * t) - t_1);
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if ((z * t) <= -5e-25) or not ((z * t) <= 1e+18):
		tmp = 2.0 * ((z * t) - t_1)
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if ((Float64(z * t) <= -5e-25) || !(Float64(z * t) <= 1e+18))
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (((z * t) <= -5e-25) || ~(((z * t) <= 1e+18)))
		tmp = 2.0 * ((z * t) - t_1);
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e-25], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+18]], $MachinePrecision]], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.99999999999999962e-25 or 1e18 < (*.f64 z t)

   1. Initial program 90.7%

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

   2. Taylor expanded in x around 0 80.2%

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

   if -4.99999999999999962e-25 < (*.f64 z t) < 1e18

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 87.9%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-25} \lor \neg \left(z \cdot t \leq 10^{+18}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 6: 67.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-111}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(-b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* 2.0 (* c (* i (* b (- c)))))))
   (if (<= c -4.2e+95)
     t_1
     (if (<= c -2.3e+33)
       (* 2.0 (- (* z t) (* i (* a c))))
       (if (<= c -1.05e+23)
         t_1
         (if (<= c -1e-111)
           (* 2.0 (- (* x y) (* a (* c i))))
           (if (<= c 3.7e+58)
             (* (+ (* z t) (* x y)) 2.0)
             (* 2.0 (* c (* c (- (* b i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * (i * (b * -c)));
	double tmp;
	if (c <= -4.2e+95) {
		tmp = t_1;
	} else if (c <= -2.3e+33) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= -1.05e+23) {
		tmp = t_1;
	} else if (c <= -1e-111) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= 3.7e+58) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = 2.0 * (c * (c * -(b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (c * (i * (b * -c)))
    if (c <= (-4.2d+95)) then
        tmp = t_1
    else if (c <= (-2.3d+33)) then
        tmp = 2.0d0 * ((z * t) - (i * (a * c)))
    else if (c <= (-1.05d+23)) then
        tmp = t_1
    else if (c <= (-1d-111)) then
        tmp = 2.0d0 * ((x * y) - (a * (c * i)))
    else if (c <= 3.7d+58) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else
        tmp = 2.0d0 * (c * (c * -(b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 2.0 * (c * (i * (b * -c)));
	double tmp;
	if (c <= -4.2e+95) {
		tmp = t_1;
	} else if (c <= -2.3e+33) {
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	} else if (c <= -1.05e+23) {
		tmp = t_1;
	} else if (c <= -1e-111) {
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	} else if (c <= 3.7e+58) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = 2.0 * (c * (c * -(b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 2.0 * (c * (i * (b * -c)))
	tmp = 0
	if c <= -4.2e+95:
		tmp = t_1
	elif c <= -2.3e+33:
		tmp = 2.0 * ((z * t) - (i * (a * c)))
	elif c <= -1.05e+23:
		tmp = t_1
	elif c <= -1e-111:
		tmp = 2.0 * ((x * y) - (a * (c * i)))
	elif c <= 3.7e+58:
		tmp = ((z * t) + (x * y)) * 2.0
	else:
		tmp = 2.0 * (c * (c * -(b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(2.0 * Float64(c * Float64(i * Float64(b * Float64(-c)))))
	tmp = 0.0
	if (c <= -4.2e+95)
		tmp = t_1;
	elseif (c <= -2.3e+33)
		tmp = Float64(2.0 * Float64(Float64(z * t) - Float64(i * Float64(a * c))));
	elseif (c <= -1.05e+23)
		tmp = t_1;
	elseif (c <= -1e-111)
		tmp = Float64(2.0 * Float64(Float64(x * y) - Float64(a * Float64(c * i))));
	elseif (c <= 3.7e+58)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(c * Float64(c * Float64(-Float64(b * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 2.0 * (c * (i * (b * -c)));
	tmp = 0.0;
	if (c <= -4.2e+95)
		tmp = t_1;
	elseif (c <= -2.3e+33)
		tmp = 2.0 * ((z * t) - (i * (a * c)));
	elseif (c <= -1.05e+23)
		tmp = t_1;
	elseif (c <= -1e-111)
		tmp = 2.0 * ((x * y) - (a * (c * i)));
	elseif (c <= 3.7e+58)
		tmp = ((z * t) + (x * y)) * 2.0;
	else
		tmp = 2.0 * (c * (c * -(b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(2.0 * N[(c * N[(i * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+95], t$95$1, If[LessEqual[c, -2.3e+33], N[(2.0 * N[(N[(z * t), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.05e+23], t$95$1, If[LessEqual[c, -1e-111], N[(2.0 * N[(N[(x * y), $MachinePrecision] - N[(a * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.7e+58], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(c * N[(c * (-N[(b * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.2e95 or -2.30000000000000011e33 < c < -1.0500000000000001e23

   1. Initial program 87.6%

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

      1. associate-*l* 89.8%

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

      2. fma-def 89.8%

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

   3. Simplified 89.8%

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

      1. fma-def 89.8%

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

      2. +-commutative 89.8%

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

   5. Applied egg-rr 89.8%

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

   6. Taylor expanded in a around 0 85.9%

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

      1. expm1-log1p-u 51.8%

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

      2. expm1-udef 51.8%

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

      3. associate-*l* 51.8%

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

   8. Applied egg-rr 51.8%

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

      1. expm1-def 51.8%

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

      2. expm1-log1p 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-*l* 80.0%

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

   10. Simplified 80.0%

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

   11. Taylor expanded in b around inf 75.7%

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

       1. mul-1-neg 75.7%

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

       2. *-commutative 75.7%

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

       3. unpow2 75.7%

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

       4. associate-*r* 78.0%

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

       5. distribute-rgt-neg-in 78.0%

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

       6. associate-*r* 78.1%

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

       7. distribute-rgt-neg-in 78.1%

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

   13. Simplified 78.1%

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

   if -4.2e95 < c < -2.30000000000000011e33

   1. Initial program 94.8%

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

   2. Taylor expanded in a around inf 80.5%

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

   3. Taylor expanded in x around 0 56.5%

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

      1. associate-*r* 56.4%

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

   5. Simplified 56.4%

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

   if -1.0500000000000001e23 < c < -1.00000000000000009e-111

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 86.2%

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

   3. Taylor expanded in z around 0 62.0%

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

      1. associate-*r* 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-*r* 64.7%

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

   5. Simplified 64.7%

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

   if -1.00000000000000009e-111 < c < 3.7000000000000002e58

   1. Initial program 98.2%

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

   2. Taylor expanded in c around 0 85.5%

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

   if 3.7000000000000002e58 < c

   1. Initial program 81.2%

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

      1. associate-*l* 90.2%

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

      2. fma-def 92.7%

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

   3. Simplified 92.7%

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

      1. fma-def 90.2%

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

      2. +-commutative 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in a around 0 76.2%

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

      1. expm1-log1p-u 43.5%

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

      2. expm1-udef 43.5%

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

      3. associate-*l* 43.5%

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

   8. Applied egg-rr 43.5%

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

      1. expm1-def 43.5%

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

      2. expm1-log1p 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*l* 76.2%

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

   10. Simplified 76.2%

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

   11. Taylor expanded in b around inf 69.0%

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

       1. mul-1-neg 69.0%

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

       2. *-commutative 69.0%

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

       3. unpow2 69.0%

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

       4. associate-*r* 73.7%

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

       5. distribute-rgt-neg-in 73.7%

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

       6. distribute-lft-neg-in 73.7%

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

       7. *-commutative 73.7%

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

   13. Simplified 73.7%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+95}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;2 \cdot \left(z \cdot t - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-111}:\\ \;\;\;\;2 \cdot \left(x \cdot y - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(-b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 7: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\\ \mathbf{if}\;c \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(z \cdot t - t_1\right)\\ \mathbf{elif}\;c \leq 6.1 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* c (* (+ a (* b c)) i))))
   (if (<= c -6.5e+20)
     (* 2.0 (- (* z t) t_1))
     (if (<= c 6.1e+53)
       (* 2.0 (- (+ (* z t) (* x y)) (* i (* a c))))
       (* 2.0 (- (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -6.5e+20) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 6.1e+53) {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a + (b * c)) * i)
    if (c <= (-6.5d+20)) then
        tmp = 2.0d0 * ((z * t) - t_1)
    else if (c <= 6.1d+53) then
        tmp = 2.0d0 * (((z * t) + (x * y)) - (i * (a * c)))
    else
        tmp = 2.0d0 * ((x * y) - t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c * ((a + (b * c)) * i);
	double tmp;
	if (c <= -6.5e+20) {
		tmp = 2.0 * ((z * t) - t_1);
	} else if (c <= 6.1e+53) {
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	} else {
		tmp = 2.0 * ((x * y) - t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c * ((a + (b * c)) * i)
	tmp = 0
	if c <= -6.5e+20:
		tmp = 2.0 * ((z * t) - t_1)
	elif c <= 6.1e+53:
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)))
	else:
		tmp = 2.0 * ((x * y) - t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c * Float64(Float64(a + Float64(b * c)) * i))
	tmp = 0.0
	if (c <= -6.5e+20)
		tmp = Float64(2.0 * Float64(Float64(z * t) - t_1));
	elseif (c <= 6.1e+53)
		tmp = Float64(2.0 * Float64(Float64(Float64(z * t) + Float64(x * y)) - Float64(i * Float64(a * c))));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) - t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c * ((a + (b * c)) * i);
	tmp = 0.0;
	if (c <= -6.5e+20)
		tmp = 2.0 * ((z * t) - t_1);
	elseif (c <= 6.1e+53)
		tmp = 2.0 * (((z * t) + (x * y)) - (i * (a * c)));
	else
		tmp = 2.0 * ((x * y) - t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c * N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.5e+20], N[(2.0 * N[(N[(z * t), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.1e+53], N[(2.0 * N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.5e20

   1. Initial program 89.8%

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

   2. Taylor expanded in x around 0 85.5%

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

   if -6.5e20 < c < 6.1000000000000002e53

   1. Initial program 98.5%

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

   2. Taylor expanded in a around inf 93.3%

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

   if 6.1000000000000002e53 < c

   1. Initial program 81.6%

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

   2. Taylor expanded in z around 0 90.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.1 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot \left(\left(z \cdot t + x \cdot y\right) - i \cdot \left(a \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternative 8: 75.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -48000000 \lor \neg \left(c \leq 8.6 \cdot 10^{+38}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(-\left(a + b \cdot c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -48000000.0) (not (<= c 8.6e+38)))
   (* 2.0 (* c (* i (- (+ a (* b c))))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -48000000.0) || !(c <= 8.6e+38)) {
		tmp = 2.0 * (c * (i * -(a + (b * c))));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-48000000.0d0)) .or. (.not. (c <= 8.6d+38))) then
        tmp = 2.0d0 * (c * (i * -(a + (b * c))))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -48000000.0) || !(c <= 8.6e+38)) {
		tmp = 2.0 * (c * (i * -(a + (b * c))));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -48000000.0) or not (c <= 8.6e+38):
		tmp = 2.0 * (c * (i * -(a + (b * c))))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -48000000.0) || !(c <= 8.6e+38))
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(-Float64(a + Float64(b * c))))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -48000000.0) || ~((c <= 8.6e+38)))
		tmp = 2.0 * (c * (i * -(a + (b * c))));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -48000000.0], N[Not[LessEqual[c, 8.6e+38]], $MachinePrecision]], N[(2.0 * N[(c * N[(i * (-N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.8e7 or 8.5999999999999994e38 < c

   1. Initial program 86.5%

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

   2. Taylor expanded in i around inf 78.4%

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

   if -4.8e7 < c < 8.5999999999999994e38

   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 80.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -48000000 \lor \neg \left(c \leq 8.6 \cdot 10^{+38}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(-\left(a + b \cdot c\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 9: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+101} \lor \neg \left(c \leq 1.5 \cdot 10^{+59}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(-b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= c -2.2e+101) (not (<= c 1.5e+59)))
   (* 2.0 (* c (* c (- (* b i)))))
   (* (+ (* z t) (* x y)) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.2e+101) || !(c <= 1.5e+59)) {
		tmp = 2.0 * (c * (c * -(b * i)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c <= (-2.2d+101)) .or. (.not. (c <= 1.5d+59))) then
        tmp = 2.0d0 * (c * (c * -(b * i)))
    else
        tmp = ((z * t) + (x * y)) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c <= -2.2e+101) || !(c <= 1.5e+59)) {
		tmp = 2.0 * (c * (c * -(b * i)));
	} else {
		tmp = ((z * t) + (x * y)) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c <= -2.2e+101) or not (c <= 1.5e+59):
		tmp = 2.0 * (c * (c * -(b * i)))
	else:
		tmp = ((z * t) + (x * y)) * 2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((c <= -2.2e+101) || !(c <= 1.5e+59))
		tmp = Float64(2.0 * Float64(c * Float64(c * Float64(-Float64(b * i)))));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c <= -2.2e+101) || ~((c <= 1.5e+59)))
		tmp = 2.0 * (c * (c * -(b * i)));
	else
		tmp = ((z * t) + (x * y)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[c, -2.2e+101], N[Not[LessEqual[c, 1.5e+59]], $MachinePrecision]], N[(2.0 * N[(c * N[(c * (-N[(b * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.2000000000000001e101 or 1.5e59 < c

   1. Initial program 83.8%

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

      1. associate-*l* 90.5%

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

      2. fma-def 91.7%

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

   3. Simplified 91.7%

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

      1. fma-def 90.5%

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

      2. +-commutative 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in a around 0 81.4%

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

      1. expm1-log1p-u 46.1%

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

      2. expm1-udef 46.1%

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

      3. associate-*l* 46.1%

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

   8. Applied egg-rr 46.1%

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

      1. expm1-def 46.1%

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

      2. expm1-log1p 82.5%

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

      3. *-commutative 82.5%

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

      4. associate-*l* 79.2%

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

   10. Simplified 79.2%

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

   11. Taylor expanded in b around inf 72.2%

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

       1. mul-1-neg 72.2%

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

       2. *-commutative 72.2%

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

       3. unpow2 72.2%

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

       4. associate-*r* 75.8%

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

       5. distribute-rgt-neg-in 75.8%

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

       6. distribute-lft-neg-in 75.8%

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

       7. *-commutative 75.8%

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

   13. Simplified 75.8%

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

   if -2.2000000000000001e101 < c < 1.5e59

   1. Initial program 98.2%

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

   2. Taylor expanded in c around 0 73.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.2 \cdot 10^{+101} \lor \neg \left(c \leq 1.5 \cdot 10^{+59}\right):\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(-b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \end{array} \]

Alternative 10: 68.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(-b \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.9e+101)
   (* 2.0 (* c (* i (* b (- c)))))
   (if (<= c 1.7e+58)
     (* (+ (* z t) (* x y)) 2.0)
     (* 2.0 (* c (* c (- (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.9e+101) {
		tmp = 2.0 * (c * (i * (b * -c)));
	} else if (c <= 1.7e+58) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = 2.0 * (c * (c * -(b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-1.9d+101)) then
        tmp = 2.0d0 * (c * (i * (b * -c)))
    else if (c <= 1.7d+58) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else
        tmp = 2.0d0 * (c * (c * -(b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.9e+101) {
		tmp = 2.0 * (c * (i * (b * -c)));
	} else if (c <= 1.7e+58) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = 2.0 * (c * (c * -(b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.9e+101:
		tmp = 2.0 * (c * (i * (b * -c)))
	elif c <= 1.7e+58:
		tmp = ((z * t) + (x * y)) * 2.0
	else:
		tmp = 2.0 * (c * (c * -(b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.9e+101)
		tmp = Float64(2.0 * Float64(c * Float64(i * Float64(b * Float64(-c)))));
	elseif (c <= 1.7e+58)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	else
		tmp = Float64(2.0 * Float64(c * Float64(c * Float64(-Float64(b * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1.9e+101)
		tmp = 2.0 * (c * (i * (b * -c)));
	elseif (c <= 1.7e+58)
		tmp = ((z * t) + (x * y)) * 2.0;
	else
		tmp = 2.0 * (c * (c * -(b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.9e+101], N[(2.0 * N[(c * N[(i * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e+58], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(2.0 * N[(c * N[(c * (-N[(b * i), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.8999999999999999e101

   1. Initial program 86.2%

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

      1. associate-*l* 90.8%

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

      2. fma-def 90.8%

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

   3. Simplified 90.8%

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

      1. fma-def 90.8%

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

      2. +-commutative 90.8%

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

   5. Applied egg-rr 90.8%

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

   6. Taylor expanded in a around 0 86.4%

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

      1. expm1-log1p-u 48.5%

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

      2. expm1-udef 48.5%

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

      3. associate-*l* 48.5%

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

   8. Applied egg-rr 48.5%

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

      1. expm1-def 48.5%

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

      2. expm1-log1p 86.4%

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

      3. *-commutative 86.4%

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

      4. associate-*l* 82.0%

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

   10. Simplified 82.0%

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

   11. Taylor expanded in b around inf 75.3%

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

       1. mul-1-neg 75.3%

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

       2. *-commutative 75.3%

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

       3. unpow2 75.3%

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

       4. associate-*r* 77.8%

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

       5. distribute-rgt-neg-in 77.8%

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

       6. associate-*r* 77.8%

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

       7. distribute-rgt-neg-in 77.8%

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

   13. Simplified 77.8%

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

   if -1.8999999999999999e101 < c < 1.7e58

   1. Initial program 98.2%

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

   2. Taylor expanded in c around 0 73.6%

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

   if 1.7e58 < c

   1. Initial program 81.2%

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

      1. associate-*l* 90.2%

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

      2. fma-def 92.7%

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

   3. Simplified 92.7%

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

      1. fma-def 90.2%

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

      2. +-commutative 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in a around 0 76.2%

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

      1. expm1-log1p-u 43.5%

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

      2. expm1-udef 43.5%

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

      3. associate-*l* 43.5%

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

   8. Applied egg-rr 43.5%

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

      1. expm1-def 43.5%

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

      2. expm1-log1p 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*l* 76.2%

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

   10. Simplified 76.2%

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

   11. Taylor expanded in b around inf 69.0%

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

       1. mul-1-neg 69.0%

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

       2. *-commutative 69.0%

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

       3. unpow2 69.0%

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

       4. associate-*r* 73.7%

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

       5. distribute-rgt-neg-in 73.7%

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

       6. distribute-lft-neg-in 73.7%

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

       7. *-commutative 73.7%

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

   13. Simplified 73.7%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(i \cdot \left(b \cdot \left(-c\right)\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+58}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(c \cdot \left(-b \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 11: 37.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \left(x \cdot y\right)\\ t_2 := 2 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -1.42 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-103}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot -2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (<= t -1.42e-192)
     t_2
     (if (<= t 9.8e-129)
       t_1
       (if (<= t 2.5e-103)
         (* (* i (* a c)) -2.0)
         (if (<= t 2.6e+135) 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 (t <= -1.42e-192) {
		tmp = t_2;
	} else if (t <= 9.8e-129) {
		tmp = t_1;
	} else if (t <= 2.5e-103) {
		tmp = (i * (a * c)) * -2.0;
	} else if (t <= 2.6e+135) {
		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 (t <= (-1.42d-192)) then
        tmp = t_2
    else if (t <= 9.8d-129) then
        tmp = t_1
    else if (t <= 2.5d-103) then
        tmp = (i * (a * c)) * (-2.0d0)
    else if (t <= 2.6d+135) 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 (t <= -1.42e-192) {
		tmp = t_2;
	} else if (t <= 9.8e-129) {
		tmp = t_1;
	} else if (t <= 2.5e-103) {
		tmp = (i * (a * c)) * -2.0;
	} else if (t <= 2.6e+135) {
		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 t <= -1.42e-192:
		tmp = t_2
	elif t <= 9.8e-129:
		tmp = t_1
	elif t <= 2.5e-103:
		tmp = (i * (a * c)) * -2.0
	elif t <= 2.6e+135:
		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 (t <= -1.42e-192)
		tmp = t_2;
	elseif (t <= 9.8e-129)
		tmp = t_1;
	elseif (t <= 2.5e-103)
		tmp = Float64(Float64(i * Float64(a * c)) * -2.0);
	elseif (t <= 2.6e+135)
		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 (t <= -1.42e-192)
		tmp = t_2;
	elseif (t <= 9.8e-129)
		tmp = t_1;
	elseif (t <= 2.5e-103)
		tmp = (i * (a * c)) * -2.0;
	elseif (t <= 2.6e+135)
		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[t, -1.42e-192], t$95$2, If[LessEqual[t, 9.8e-129], t$95$1, If[LessEqual[t, 2.5e-103], N[(N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t, 2.6e+135], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4200000000000001e-192 or 2.6e135 < t

   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 42.4%

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

   if -1.4200000000000001e-192 < t < 9.80000000000000004e-129 or 2.49999999999999983e-103 < t < 2.6e135

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 38.3%

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

   if 9.80000000000000004e-129 < t < 2.49999999999999983e-103

   1. Initial program 99.5%

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

   2. Taylor expanded in a around inf 79.2%

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

   3. Taylor expanded in x around 0 47.7%

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

      1. associate-*r* 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in t around 0 47.7%

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

      1. associate-*r* 47.7%

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

      2. *-commutative 47.7%

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

      3. *-commutative 47.7%

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

      4. *-commutative 47.7%

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

      5. *-commutative 47.7%

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

   8. Simplified 47.7%

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

   9. Taylor expanded in i around 0 47.7%

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

       1. associate-*r* 78.1%

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

       2. *-commutative 78.1%

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

   11. Simplified 78.1%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{-192}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-129}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-103}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot -2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+135}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 12: 57.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+202}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+168}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.7e+202)
   (* (* a i) (* c -2.0))
   (if (<= c 1.4e+168) (* (+ (* z t) (* x y)) 2.0) (* (* i (* a c)) -2.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.7e+202) {
		tmp = (a * i) * (c * -2.0);
	} else if (c <= 1.4e+168) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = (i * (a * c)) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (c <= (-1.7d+202)) then
        tmp = (a * i) * (c * (-2.0d0))
    else if (c <= 1.4d+168) then
        tmp = ((z * t) + (x * y)) * 2.0d0
    else
        tmp = (i * (a * c)) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (c <= -1.7e+202) {
		tmp = (a * i) * (c * -2.0);
	} else if (c <= 1.4e+168) {
		tmp = ((z * t) + (x * y)) * 2.0;
	} else {
		tmp = (i * (a * c)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.7e+202:
		tmp = (a * i) * (c * -2.0)
	elif c <= 1.4e+168:
		tmp = ((z * t) + (x * y)) * 2.0
	else:
		tmp = (i * (a * c)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.7e+202)
		tmp = Float64(Float64(a * i) * Float64(c * -2.0));
	elseif (c <= 1.4e+168)
		tmp = Float64(Float64(Float64(z * t) + Float64(x * y)) * 2.0);
	else
		tmp = Float64(Float64(i * Float64(a * c)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (c <= -1.7e+202)
		tmp = (a * i) * (c * -2.0);
	elseif (c <= 1.4e+168)
		tmp = ((z * t) + (x * y)) * 2.0;
	else
		tmp = (i * (a * c)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.7e+202], N[(N[(a * i), $MachinePrecision] * N[(c * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e+168], N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(i * N[(a * c), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.7e202

   1. Initial program 85.7%

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

   2. Taylor expanded in a around inf 48.8%

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

   3. Taylor expanded in x around 0 48.6%

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

      1. associate-*r* 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in t around 0 48.8%

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

      1. associate-*r* 48.8%

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

      2. *-commutative 48.8%

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

      3. *-commutative 48.8%

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

      4. *-commutative 48.8%

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

      5. *-commutative 48.8%

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

   8. Simplified 48.8%

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

   if -1.7e202 < c < 1.39999999999999995e168

   1. Initial program 96.1%

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

   2. Taylor expanded in c around 0 67.8%

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

   if 1.39999999999999995e168 < c

   1. Initial program 82.2%

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

   2. Taylor expanded in a around inf 40.2%

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

   3. Taylor expanded in x around 0 43.0%

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

      1. associate-*r* 43.0%

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

   5. Simplified 43.0%

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

   6. Taylor expanded in t around 0 39.9%

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

      1. associate-*r* 39.9%

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

      2. *-commutative 39.9%

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

      3. *-commutative 39.9%

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

      4. *-commutative 39.9%

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

      5. *-commutative 39.9%

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

   8. Simplified 39.9%

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

   9. Taylor expanded in i around 0 39.9%

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

       1. associate-*r* 40.1%

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

       2. *-commutative 40.1%

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

   11. Simplified 40.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+202}:\\ \;\;\;\;\left(a \cdot i\right) \cdot \left(c \cdot -2\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+168}:\\ \;\;\;\;\left(z \cdot t + x \cdot y\right) \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot \left(a \cdot c\right)\right) \cdot -2\\ \end{array} \]

Alternative 13: 37.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-192} \lor \neg \left(t \leq 2.6 \cdot 10^{+135}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= t -1.6e-192) (not (<= t 2.6e+135)))
   (* 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 ((t <= -1.6e-192) || !(t <= 2.6e+135)) {
		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 ((t <= (-1.6d-192)) .or. (.not. (t <= 2.6d+135))) 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 ((t <= -1.6e-192) || !(t <= 2.6e+135)) {
		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 (t <= -1.6e-192) or not (t <= 2.6e+135):
		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 ((t <= -1.6e-192) || !(t <= 2.6e+135))
		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 ((t <= -1.6e-192) || ~((t <= 2.6e+135)))
		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[t, -1.6e-192], N[Not[LessEqual[t, 2.6e+135]], $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 t < -1.6000000000000001e-192 or 2.6e135 < t

   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 42.4%

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

   if -1.6000000000000001e-192 < t < 2.6e135

   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. Taylor expanded in x around inf 36.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-192} \lor \neg \left(t \leq 2.6 \cdot 10^{+135}\right):\\ \;\;\;\;2 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 14: 29.7% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

2. Taylor expanded in z around inf 31.6%

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

3. Final simplification 31.6%

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

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 2023213 
(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))))