Linear.V4:$cdot from linear-1.19.1.3, C

Percentage Accurate: 95.7% → 97.9%

Time: 9.3s

Alternatives: 13

Speedup: 0.5×

• 41.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 98.4%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 96.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. associate-+l+ 94.9%

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

   2. fma-udef 94.9%

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

   3. *-commutative 94.9%

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

   4. fma-def 97.3%

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

3. Applied egg-rr 97.3%

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

4. Final simplification 97.3%

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

Alternative 3: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 23.1%

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

      3. associate-+l+ 23.1%

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

      4. fma-def 69.2%

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

      5. fma-def 69.2%

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

   3. Simplified 69.2%

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

      1. fma-udef 23.1%

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

      2. fma-udef 23.1%

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

      3. associate-+l+ 23.1%

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

      4. +-commutative 23.1%

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

      5. associate-+r+ 23.1%

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

   5. Applied egg-rr 23.1%

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

      1. fma-udef 0.0%

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

      2. associate-+r+ 0.0%

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

      3. +-commutative 0.0%

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

      4. fma-def 30.8%

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

      5. *-commutative 30.8%

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

   7. Applied egg-rr 30.8%

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

   8. Taylor expanded in c around 0 23.1%

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

      1. +-commutative 23.1%

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

      2. fma-udef 53.8%

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

   10. Simplified 53.8%

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

4. Final simplification 97.6%

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

Alternative 4: 96.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 98.4%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 96.1%

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

   2. fma-udef 96.1%

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

   3. associate-+l+ 96.1%

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

   4. +-commutative 96.1%

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

   5. associate-+r+ 96.1%

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

5. Applied egg-rr 96.1%

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

   1. fma-udef 94.9%

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

   2. associate-+r+ 94.9%

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

   3. +-commutative 94.9%

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

   4. fma-def 96.5%

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

   5. *-commutative 96.5%

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

7. Applied egg-rr 96.5%

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

8. Final simplification 96.5%

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

Alternative 5: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + x \cdot y\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.12 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -4.9 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-239}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* x y))) (t_2 (+ (* c i) (* z t))))
   (if (<= (* a b) -3.5e+161)
     (* a b)
     (if (<= (* a b) -1.12e-45)
       t_1
       (if (<= (* a b) -4.9e-223)
         t_2
         (if (<= (* a b) -2.3e-298)
           t_1
           (if (<= (* a b) 2.3e-239)
             t_2
             (if (<= (* a b) 2.9e-130)
               t_1
               (if (<= (* a b) 8e+165) t_2 (* a b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (x * y);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -3.5e+161) {
		tmp = a * b;
	} else if ((a * b) <= -1.12e-45) {
		tmp = t_1;
	} else if ((a * b) <= -4.9e-223) {
		tmp = t_2;
	} else if ((a * b) <= -2.3e-298) {
		tmp = t_1;
	} else if ((a * b) <= 2.3e-239) {
		tmp = t_2;
	} else if ((a * b) <= 2.9e-130) {
		tmp = t_1;
	} else if ((a * b) <= 8e+165) {
		tmp = t_2;
	} else {
		tmp = a * b;
	}
	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 = (z * t) + (x * y)
    t_2 = (c * i) + (z * t)
    if ((a * b) <= (-3.5d+161)) then
        tmp = a * b
    else if ((a * b) <= (-1.12d-45)) then
        tmp = t_1
    else if ((a * b) <= (-4.9d-223)) then
        tmp = t_2
    else if ((a * b) <= (-2.3d-298)) then
        tmp = t_1
    else if ((a * b) <= 2.3d-239) then
        tmp = t_2
    else if ((a * b) <= 2.9d-130) then
        tmp = t_1
    else if ((a * b) <= 8d+165) then
        tmp = t_2
    else
        tmp = a * b
    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 = (z * t) + (x * y);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((a * b) <= -3.5e+161) {
		tmp = a * b;
	} else if ((a * b) <= -1.12e-45) {
		tmp = t_1;
	} else if ((a * b) <= -4.9e-223) {
		tmp = t_2;
	} else if ((a * b) <= -2.3e-298) {
		tmp = t_1;
	} else if ((a * b) <= 2.3e-239) {
		tmp = t_2;
	} else if ((a * b) <= 2.9e-130) {
		tmp = t_1;
	} else if ((a * b) <= 8e+165) {
		tmp = t_2;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (x * y)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if (a * b) <= -3.5e+161:
		tmp = a * b
	elif (a * b) <= -1.12e-45:
		tmp = t_1
	elif (a * b) <= -4.9e-223:
		tmp = t_2
	elif (a * b) <= -2.3e-298:
		tmp = t_1
	elif (a * b) <= 2.3e-239:
		tmp = t_2
	elif (a * b) <= 2.9e-130:
		tmp = t_1
	elif (a * b) <= 8e+165:
		tmp = t_2
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(x * y))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -3.5e+161)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.12e-45)
		tmp = t_1;
	elseif (Float64(a * b) <= -4.9e-223)
		tmp = t_2;
	elseif (Float64(a * b) <= -2.3e-298)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.3e-239)
		tmp = t_2;
	elseif (Float64(a * b) <= 2.9e-130)
		tmp = t_1;
	elseif (Float64(a * b) <= 8e+165)
		tmp = t_2;
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (x * y);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -3.5e+161)
		tmp = a * b;
	elseif ((a * b) <= -1.12e-45)
		tmp = t_1;
	elseif ((a * b) <= -4.9e-223)
		tmp = t_2;
	elseif ((a * b) <= -2.3e-298)
		tmp = t_1;
	elseif ((a * b) <= 2.3e-239)
		tmp = t_2;
	elseif ((a * b) <= 2.9e-130)
		tmp = t_1;
	elseif ((a * b) <= 8e+165)
		tmp = t_2;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3.5e+161], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.12e-45], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -4.9e-223], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2.3e-298], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.3e-239], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2.9e-130], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 8e+165], t$95$2, N[(a * b), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.49999999999999988e161 or 7.9999999999999992e165 < (*.f64 a b)

   1. Initial program 86.6%

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

   2. Taylor expanded in a around inf 83.8%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -3.49999999999999988e161 < (*.f64 a b) < -1.1199999999999999e-45 or -4.9e-223 < (*.f64 a b) < -2.3000000000000001e-298 or 2.2999999999999999e-239 < (*.f64 a b) < 2.9e-130

   1. Initial program 98.7%

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

      1. associate-+l+ 98.7%

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

      2. fma-udef 98.7%

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

      3. *-commutative 98.7%

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

      4. fma-def 98.7%

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

   3. Applied egg-rr 98.7%

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

   4. Taylor expanded in a around 0 91.0%

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

   5. Taylor expanded in c around 0 76.0%

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if -1.1199999999999999e-45 < (*.f64 a b) < -4.9e-223 or -2.3000000000000001e-298 < (*.f64 a b) < 2.2999999999999999e-239 or 2.9e-130 < (*.f64 a b) < 7.9999999999999992e165

   1. Initial program 96.7%

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

      1. associate-+l+ 96.7%

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

      2. fma-udef 96.7%

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

      3. *-commutative 96.7%

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

      4. fma-def 97.5%

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

   3. Applied egg-rr 97.5%

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

   4. Taylor expanded in a around 0 87.8%

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

   5. Taylor expanded in t around inf 71.2%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.5 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.12 \cdot 10^{-45}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -4.9 \cdot 10^{-223}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-298}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{-239}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8 \cdot 10^{+165}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 6: 96.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around inf 39.4%

      \[\leadsto \color{blue}{a \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

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

Alternative 7: 43.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.5 \cdot 10^{+80}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -1.08 \cdot 10^{-275}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.5e+80)
   (* c i)
   (if (<= (* c i) -2.5e-62)
     (* a b)
     (if (<= (* c i) -1.08e-275)
       (* x y)
       (if (<= (* c i) 8.5e-111)
         (* z t)
         (if (<= (* c i) 2.3e+25) (* a b) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4.5e+80) {
		tmp = c * i;
	} else if ((c * i) <= -2.5e-62) {
		tmp = a * b;
	} else if ((c * i) <= -1.08e-275) {
		tmp = x * y;
	} else if ((c * i) <= 8.5e-111) {
		tmp = z * t;
	} else if ((c * i) <= 2.3e+25) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-4.5d+80)) then
        tmp = c * i
    else if ((c * i) <= (-2.5d-62)) then
        tmp = a * b
    else if ((c * i) <= (-1.08d-275)) then
        tmp = x * y
    else if ((c * i) <= 8.5d-111) then
        tmp = z * t
    else if ((c * i) <= 2.3d+25) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4.5e+80) {
		tmp = c * i;
	} else if ((c * i) <= -2.5e-62) {
		tmp = a * b;
	} else if ((c * i) <= -1.08e-275) {
		tmp = x * y;
	} else if ((c * i) <= 8.5e-111) {
		tmp = z * t;
	} else if ((c * i) <= 2.3e+25) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.5e+80:
		tmp = c * i
	elif (c * i) <= -2.5e-62:
		tmp = a * b
	elif (c * i) <= -1.08e-275:
		tmp = x * y
	elif (c * i) <= 8.5e-111:
		tmp = z * t
	elif (c * i) <= 2.3e+25:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4.5e+80)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.5e-62)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= -1.08e-275)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 8.5e-111)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 2.3e+25)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -4.5e+80)
		tmp = c * i;
	elseif ((c * i) <= -2.5e-62)
		tmp = a * b;
	elseif ((c * i) <= -1.08e-275)
		tmp = x * y;
	elseif ((c * i) <= 8.5e-111)
		tmp = z * t;
	elseif ((c * i) <= 2.3e+25)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4.5e+80], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.5e-62], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.08e-275], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.5e-111], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.3e+25], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -4.50000000000000007e80 or 2.2999999999999998e25 < (*.f64 c i)

   1. Initial program 91.7%

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

   2. Taylor expanded in c around inf 60.6%

      \[\leadsto \color{blue}{c \cdot i} \]

   if -4.50000000000000007e80 < (*.f64 c i) < -2.5000000000000001e-62 or 8.5000000000000003e-111 < (*.f64 c i) < 2.2999999999999998e25

   1. Initial program 95.4%

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

   2. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -2.5000000000000001e-62 < (*.f64 c i) < -1.07999999999999994e-275

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 54.6%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -1.07999999999999994e-275 < (*.f64 c i) < 8.5000000000000003e-111

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 46.4%

      \[\leadsto \color{blue}{t \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.5 \cdot 10^{+80}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.5 \cdot 10^{-62}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -1.08 \cdot 10^{-275}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.3 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 8: 43.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.6 \cdot 10^{+81}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.3 \cdot 10^{-85}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5.8 \cdot 10^{-122}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.6 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.6e+81)
   (* c i)
   (if (<= (* c i) -2.3e-85)
     (* a b)
     (if (<= (* c i) 5.8e-122)
       (* z t)
       (if (<= (* c i) 2.6e+25) (* a b) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.6e+81) {
		tmp = c * i;
	} else if ((c * i) <= -2.3e-85) {
		tmp = a * b;
	} else if ((c * i) <= 5.8e-122) {
		tmp = z * t;
	} else if ((c * i) <= 2.6e+25) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2.6d+81)) then
        tmp = c * i
    else if ((c * i) <= (-2.3d-85)) then
        tmp = a * b
    else if ((c * i) <= 5.8d-122) then
        tmp = z * t
    else if ((c * i) <= 2.6d+25) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.6e+81) {
		tmp = c * i;
	} else if ((c * i) <= -2.3e-85) {
		tmp = a * b;
	} else if ((c * i) <= 5.8e-122) {
		tmp = z * t;
	} else if ((c * i) <= 2.6e+25) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.6e+81:
		tmp = c * i
	elif (c * i) <= -2.3e-85:
		tmp = a * b
	elif (c * i) <= 5.8e-122:
		tmp = z * t
	elif (c * i) <= 2.6e+25:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.6e+81)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.3e-85)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 5.8e-122)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 2.6e+25)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2.6e+81)
		tmp = c * i;
	elseif ((c * i) <= -2.3e-85)
		tmp = a * b;
	elseif ((c * i) <= 5.8e-122)
		tmp = z * t;
	elseif ((c * i) <= 2.6e+25)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2.6e+81], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.3e-85], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.8e-122], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.6e+25], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.59999999999999992e81 or 2.5999999999999998e25 < (*.f64 c i)

   1. Initial program 91.7%

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

   2. Taylor expanded in c around inf 60.6%

      \[\leadsto \color{blue}{c \cdot i} \]

   if -2.59999999999999992e81 < (*.f64 c i) < -2.3e-85 or 5.8000000000000005e-122 < (*.f64 c i) < 2.5999999999999998e25

   1. Initial program 96.3%

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

   2. Taylor expanded in a around inf 48.9%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -2.3e-85 < (*.f64 c i) < 5.8000000000000005e-122

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 43.8%

      \[\leadsto \color{blue}{t \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.6 \cdot 10^{+81}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.3 \cdot 10^{-85}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 5.8 \cdot 10^{-122}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.6 \cdot 10^{+25}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 9: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.1 \cdot 10^{+161} \lor \neg \left(a \cdot b \leq 1.5 \cdot 10^{+165}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -4.1e+161) (not (<= (* a b) 1.5e+165)))
   (* a b)
   (+ (* c i) (+ (* z t) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -4.1e+161) || !((a * b) <= 1.5e+165)) {
		tmp = a * b;
	} else {
		tmp = (c * i) + ((z * t) + (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 (((a * b) <= (-4.1d+161)) .or. (.not. ((a * b) <= 1.5d+165))) then
        tmp = a * b
    else
        tmp = (c * i) + ((z * t) + (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 (((a * b) <= -4.1e+161) || !((a * b) <= 1.5e+165)) {
		tmp = a * b;
	} else {
		tmp = (c * i) + ((z * t) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -4.1e+161) or not ((a * b) <= 1.5e+165):
		tmp = a * b
	else:
		tmp = (c * i) + ((z * t) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -4.1e+161) || !(Float64(a * b) <= 1.5e+165))
		tmp = Float64(a * b);
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -4.1e+161) || ~(((a * b) <= 1.5e+165)))
		tmp = a * b;
	else
		tmp = (c * i) + ((z * t) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -4.1e+161], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.5e+165]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.1000000000000001e161 or 1.49999999999999995e165 < (*.f64 a b)

   1. Initial program 86.6%

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

   2. Taylor expanded in a around inf 83.8%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -4.1000000000000001e161 < (*.f64 a b) < 1.49999999999999995e165

   1. Initial program 97.4%

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

   2. Taylor expanded in a around 0 89.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.1 \cdot 10^{+161} \lor \neg \left(a \cdot b \leq 1.5 \cdot 10^{+165}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \end{array} \]

Alternative 10: 64.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+154} \lor \neg \left(a \cdot b \leq 1.85 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -4.2e+154) (not (<= (* a b) 1.85e+166)))
   (* a b)
   (+ (* c i) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -4.2e+154) || !((a * b) <= 1.85e+166)) {
		tmp = a * b;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((a * b) <= (-4.2d+154)) .or. (.not. ((a * b) <= 1.85d+166))) then
        tmp = a * b
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -4.2e+154) || !((a * b) <= 1.85e+166)) {
		tmp = a * b;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -4.2e+154) or not ((a * b) <= 1.85e+166):
		tmp = a * b
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -4.2e+154) || !(Float64(a * b) <= 1.85e+166))
		tmp = Float64(a * b);
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -4.2e+154) || ~(((a * b) <= 1.85e+166)))
		tmp = a * b;
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -4.2e+154], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.85e+166]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.19999999999999989e154 or 1.85000000000000011e166 < (*.f64 a b)

   1. Initial program 87.1%

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

   2. Taylor expanded in a around inf 81.2%

      \[\leadsto \color{blue}{a \cdot b} \]

   if -4.19999999999999989e154 < (*.f64 a b) < 1.85000000000000011e166

   1. Initial program 97.4%

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

      1. associate-+l+ 97.4%

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

      2. fma-udef 97.4%

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

      3. *-commutative 97.4%

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

      4. fma-def 97.9%

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

   3. Applied egg-rr 97.9%

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

   4. Taylor expanded in a around 0 89.0%

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

   5. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+154} \lor \neg \left(a \cdot b \leq 1.85 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 11: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+74}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.2e+92)
   (+ (* c i) (* z t))
   (if (<= (* c i) 5e+74) (+ (* z t) (* x y)) (+ (* c i) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.2e+92) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 5e+74) {
		tmp = (z * t) + (x * y);
	} else {
		tmp = (c * i) + (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 ((c * i) <= (-3.2d+92)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 5d+74) then
        tmp = (z * t) + (x * y)
    else
        tmp = (c * i) + (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 ((c * i) <= -3.2e+92) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 5e+74) {
		tmp = (z * t) + (x * y);
	} else {
		tmp = (c * i) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.2e+92:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 5e+74:
		tmp = (z * t) + (x * y)
	else:
		tmp = (c * i) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.2e+92)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 5e+74)
		tmp = Float64(Float64(z * t) + Float64(x * y));
	else
		tmp = Float64(Float64(c * i) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.2e+92)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 5e+74)
		tmp = (z * t) + (x * y);
	else
		tmp = (c * i) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.2e+92], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+74], N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.20000000000000025e92

   1. Initial program 87.5%

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

      1. associate-+l+ 87.5%

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

      2. fma-udef 87.5%

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

      3. *-commutative 87.5%

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

      4. fma-def 91.6%

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

   3. Applied egg-rr 91.6%

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

   4. Taylor expanded in a around 0 73.4%

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

   5. Taylor expanded in t around inf 71.7%

      \[\leadsto \color{blue}{t \cdot z} + c \cdot i \]

   if -3.20000000000000025e92 < (*.f64 c i) < 4.99999999999999963e74

   1. Initial program 97.5%

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

      1. associate-+l+ 97.5%

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

      2. fma-udef 97.5%

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

      3. *-commutative 97.5%

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

      4. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in a around 0 67.6%

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

   5. Taylor expanded in c around 0 63.9%

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]

   if 4.99999999999999963e74 < (*.f64 c i)

   1. Initial program 93.9%

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

      1. associate-+l+ 93.9%

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

      2. fma-udef 93.9%

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

      3. *-commutative 93.9%

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

      4. fma-def 93.9%

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

   3. Applied egg-rr 93.9%

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

   4. Taylor expanded in a around 0 81.8%

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

   5. Taylor expanded in t around 0 81.8%

      \[\leadsto \color{blue}{x \cdot y} + c \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+74}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]

Alternative 12: 43.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.1 \cdot 10^{+81} \lor \neg \left(c \cdot i \leq 4.8 \cdot 10^{+29}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.1e+81) (not (<= (* c i) 4.8e+29))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.1e+81) || !((c * i) <= 4.8e+29)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	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 * i) <= (-1.1d+81)) .or. (.not. ((c * i) <= 4.8d+29))) then
        tmp = c * i
    else
        tmp = a * b
    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 * i) <= -1.1e+81) || !((c * i) <= 4.8e+29)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.1e+81) or not ((c * i) <= 4.8e+29):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.1e+81) || !(Float64(c * i) <= 4.8e+29))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.1e+81) || ~(((c * i) <= 4.8e+29)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.1e+81], N[Not[LessEqual[N[(c * i), $MachinePrecision], 4.8e+29]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.09999999999999993e81 or 4.8000000000000002e29 < (*.f64 c i)

   1. Initial program 91.7%

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

   2. Taylor expanded in c around inf 60.6%

      \[\leadsto \color{blue}{c \cdot i} \]

   if -1.09999999999999993e81 < (*.f64 c i) < 4.8000000000000002e29

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf 37.1%

      \[\leadsto \color{blue}{a \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.1 \cdot 10^{+81} \lor \neg \left(c \cdot i \leq 4.8 \cdot 10^{+29}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 13: 28.0% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ a \cdot b \end{array} \]

FPCore

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

C

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

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 = a * b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

2. Taylor expanded in a around inf 28.0%

   \[\leadsto \color{blue}{a \cdot b} \]

3. Final simplification 28.0%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023332 
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3, C"
  :precision binary64
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))