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

Percentage Accurate: 95.8% → 98.0%

Time: 9.3s

Alternatives: 14

Speedup: 0.5×

• 41.2% 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: 95.8% 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: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(x * y + N[(z * t + N[(a * b + N[(c * i), $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. associate-+l+ 94.9%

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

   2. associate-+l+ 94.9%

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

   3. fma-def 95.7%

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

   4. fma-def 97.6%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 98.0% 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 96.5%

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

   3. associate-+l+ 96.5%

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

   4. fma-def 97.3%

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

   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 3: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(x * y + N[(z * t + N[(N[(c * i), $MachinePrecision] + 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. associate-+l+ 94.9%

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

   2. associate-+l+ 94.9%

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

   3. fma-def 95.7%

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

   4. fma-def 97.6%

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

   5. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 97.6%

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

   2. +-commutative 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 4: 97.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (+ (* c i) (+ (* a b) (+ (* x y) (* z t)))) INFINITY)
   (+ (+ (fma a b (* c i)) (* x y)) (* z t))
   (fma c i (+ (* a b) (* 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) + ((a * b) + ((x * y) + (z * t)))) <= ((double) INFINITY)) {
		tmp = (fma(a, b, (c * i)) + (x * y)) + (z * t);
	} else {
		tmp = fma(c, i, ((a * b) + (x * y)));
	}
	return tmp;
}

Julia

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

Wolfram

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

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. fma-udef 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+l+ 100.0%

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

      7. +-commutative 100.0%

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

      8. fma-udef 100.0%

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

      9. associate-+l+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   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 30.8%

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

      3. associate-+l+ 30.8%

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

      4. fma-def 46.2%

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

      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 53.8%

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

      2. fma-udef 30.8%

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

      3. associate-+l+ 30.8%

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

      4. +-commutative 30.8%

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

      5. associate-+r+ 30.8%

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

   5. Applied egg-rr 30.8%

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

   6. Taylor expanded in z around 0 69.2%

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

4. Final simplification 98.4%

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

Alternative 5: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

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) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(c, i, ((a * b) + (x * y)));
	}
	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(x * y) + Float64(z * t))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(c, i, Float64(Float64(a * b) + Float64(x * y)));
	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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * i + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $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 30.8%

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

      3. associate-+l+ 30.8%

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

      4. fma-def 46.2%

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

      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 53.8%

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

      2. fma-udef 30.8%

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

      3. associate-+l+ 30.8%

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

      4. +-commutative 30.8%

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

      5. associate-+r+ 30.8%

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

   5. Applied egg-rr 30.8%

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

   6. Taylor expanded in z around 0 69.2%

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

4. Final simplification 98.4%

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

Alternative 6: 62.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+157}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -6.5 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -1.35 \cdot 10^{-249}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 2.3 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* c i) -3.7e+157)
     (* c i)
     (if (<= (* c i) -6.5e-196)
       t_1
       (if (<= (* c i) -1.35e-249)
         t_2
         (if (<= (* c i) 0.0)
           t_1
           (if (<= (* c i) 3.7e-60)
             t_2
             (if (<= (* c i) 2.3e+76) t_1 (* c 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) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -3.7e+157) {
		tmp = c * i;
	} else if ((c * i) <= -6.5e-196) {
		tmp = t_1;
	} else if ((c * i) <= -1.35e-249) {
		tmp = t_2;
	} else if ((c * i) <= 0.0) {
		tmp = t_1;
	} else if ((c * i) <= 3.7e-60) {
		tmp = t_2;
	} else if ((c * i) <= 2.3e+76) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((c * i) <= (-3.7d+157)) then
        tmp = c * i
    else if ((c * i) <= (-6.5d-196)) then
        tmp = t_1
    else if ((c * i) <= (-1.35d-249)) then
        tmp = t_2
    else if ((c * i) <= 0.0d0) then
        tmp = t_1
    else if ((c * i) <= 3.7d-60) then
        tmp = t_2
    else if ((c * i) <= 2.3d+76) then
        tmp = t_1
    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 t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -3.7e+157) {
		tmp = c * i;
	} else if ((c * i) <= -6.5e-196) {
		tmp = t_1;
	} else if ((c * i) <= -1.35e-249) {
		tmp = t_2;
	} else if ((c * i) <= 0.0) {
		tmp = t_1;
	} else if ((c * i) <= 3.7e-60) {
		tmp = t_2;
	} else if ((c * i) <= 2.3e+76) {
		tmp = t_1;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (c * i) <= -3.7e+157:
		tmp = c * i
	elif (c * i) <= -6.5e-196:
		tmp = t_1
	elif (c * i) <= -1.35e-249:
		tmp = t_2
	elif (c * i) <= 0.0:
		tmp = t_1
	elif (c * i) <= 3.7e-60:
		tmp = t_2
	elif (c * i) <= 2.3e+76:
		tmp = t_1
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(c * i) <= -3.7e+157)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -6.5e-196)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.35e-249)
		tmp = t_2;
	elseif (Float64(c * i) <= 0.0)
		tmp = t_1;
	elseif (Float64(c * i) <= 3.7e-60)
		tmp = t_2;
	elseif (Float64(c * i) <= 2.3e+76)
		tmp = t_1;
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((c * i) <= -3.7e+157)
		tmp = c * i;
	elseif ((c * i) <= -6.5e-196)
		tmp = t_1;
	elseif ((c * i) <= -1.35e-249)
		tmp = t_2;
	elseif ((c * i) <= 0.0)
		tmp = t_1;
	elseif ((c * i) <= 3.7e-60)
		tmp = t_2;
	elseif ((c * i) <= 2.3e+76)
		tmp = t_1;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.7e+157], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -6.5e-196], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.35e-249], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 3.7e-60], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 2.3e+76], t$95$1, N[(c * i), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.6999999999999999e157 or 2.30000000000000001e76 < (*.f64 c i)

   1. Initial program 88.6%

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

   2. Taylor expanded in c around inf 67.1%

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

   if -3.6999999999999999e157 < (*.f64 c i) < -6.5000000000000004e-196 or -1.35e-249 < (*.f64 c i) < 0.0 or 3.70000000000000025e-60 < (*.f64 c i) < 2.30000000000000001e76

   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 0 83.4%

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

   3. Taylor expanded in c around 0 72.2%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if -6.5000000000000004e-196 < (*.f64 c i) < -1.35e-249 or 0.0 < (*.f64 c i) < 3.70000000000000025e-60

   1. Initial program 96.6%

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

   2. Taylor expanded in c around 0 95.0%

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

   3. Taylor expanded in t around 0 84.5%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+157}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -6.5 \cdot 10^{-196}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -1.35 \cdot 10^{-249}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.3 \cdot 10^{+76}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 7: 97.2% accurate, 0.5× speedup

Math

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

FPCore

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

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

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (a * b) + (x * y)
	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(x * y) + Float64(z * t))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (a * b) + (x * y);
	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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(x * y), $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. Taylor expanded in c around 0 30.8%

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

   3. Taylor expanded in t around 0 54.9%

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

4. Final simplification 97.7%

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

Alternative 8: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -2.8 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{-14}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* c i) -2.8e+149)
     t_1
     (if (<= (* c i) 0.0)
       (+ (* a b) (* z t))
       (if (<= (* c i) 9.2e-14) (+ (* a b) (* 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 * i) + (z * t);
	double tmp;
	if ((c * i) <= -2.8e+149) {
		tmp = t_1;
	} else if ((c * i) <= 0.0) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 9.2e-14) {
		tmp = (a * b) + (x * y);
	} 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 = (c * i) + (z * t)
    if ((c * i) <= (-2.8d+149)) then
        tmp = t_1
    else if ((c * i) <= 0.0d0) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 9.2d-14) then
        tmp = (a * b) + (x * y)
    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 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -2.8e+149) {
		tmp = t_1;
	} else if ((c * i) <= 0.0) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 9.2e-14) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -2.8e+149:
		tmp = t_1
	elif (c * i) <= 0.0:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 9.2e-14:
		tmp = (a * b) + (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -2.8e+149)
		tmp = t_1;
	elseif (Float64(c * i) <= 0.0)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 9.2e-14)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -2.8e+149)
		tmp = t_1;
	elseif ((c * i) <= 0.0)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 9.2e-14)
		tmp = (a * b) + (x * y);
	else
		tmp = t_1;
	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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.8e+149], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 0.0], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.2e-14], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.7999999999999999e149 or 9.19999999999999993e-14 < (*.f64 c i)

   1. Initial program 90.1%

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

   2. Taylor expanded in x around 0 85.1%

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

   3. Taylor expanded in a around 0 76.1%

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

   if -2.7999999999999999e149 < (*.f64 c i) < 0.0

   1. Initial program 98.9%

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

   2. Taylor expanded in x around 0 76.7%

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

   3. Taylor expanded in c around 0 70.1%

      \[\leadsto \color{blue}{a \cdot b + t \cdot z} \]

   if 0.0 < (*.f64 c i) < 9.19999999999999993e-14

   1. Initial program 98.0%

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

   2. Taylor expanded in c around 0 93.8%

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

   3. Taylor expanded in t around 0 79.8%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.8 \cdot 10^{+149}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{-14}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 9: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.55 \cdot 10^{+44} \lor \neg \left(c \cdot i \leq 2.8 \cdot 10^{-45}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -1.55e+44) (not (<= (* c i) 2.8e-45)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* a b) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.55e+44) || !((c * i) <= 2.8e-45)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-1.55d+44)) .or. (.not. ((c * i) <= 2.8d-45))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (a * b) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -1.55e+44) || !((c * i) <= 2.8e-45)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -1.55e+44) or not ((c * i) <= 2.8e-45):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -1.55e+44) || !(Float64(c * i) <= 2.8e-45))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -1.55e+44) || ~(((c * i) <= 2.8e-45)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -1.55e+44], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.8e-45]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.54999999999999998e44 or 2.8000000000000001e-45 < (*.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 x around 0 86.0%

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

   if -1.54999999999999998e44 < (*.f64 c i) < 2.8000000000000001e-45

   1. Initial program 98.4%

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

   2. Taylor expanded in c around 0 95.8%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.55 \cdot 10^{+44} \lor \neg \left(c \cdot i \leq 2.8 \cdot 10^{-45}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 10: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.8e+150)
   (+ (* c i) (* z t))
   (if (<= (* c i) 2.7e+157)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* 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) <= -3.8e+150) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 2.7e+157) {
		tmp = (a * b) + ((x * y) + (z * t));
	} 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) <= (-3.8d+150)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 2.7d+157) then
        tmp = (a * b) + ((x * y) + (z * t))
    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) <= -3.8e+150) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 2.7e+157) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.8e+150:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 2.7e+157:
		tmp = (a * b) + ((x * y) + (z * t))
	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) <= -3.8e+150)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 2.7e+157)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	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) <= -3.8e+150)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 2.7e+157)
		tmp = (a * b) + ((x * y) + (z * t));
	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], -3.8e+150], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.7e+157], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.79999999999999989e150

   1. Initial program 82.9%

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

   2. Taylor expanded in x around 0 85.3%

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

   3. Taylor expanded in a around 0 74.8%

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

   if -3.79999999999999989e150 < (*.f64 c i) < 2.7e157

   1. Initial program 98.8%

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

   2. Taylor expanded in c around 0 88.8%

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

   if 2.7e157 < (*.f64 c i)

   1. Initial program 90.4%

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

   2. Taylor expanded in z around 0 84.0%

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

   3. Taylor expanded in a around 0 86.4%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+157}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]

Alternative 11: 42.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.5 \cdot 10^{+122}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.75 \cdot 10^{-308}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 12000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -7.5e+122)
   (* c i)
   (if (<= (* c i) 2.75e-308)
     (* z t)
     (if (<= (* c i) 12000.0) (* x y) (* 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) <= -7.5e+122) {
		tmp = c * i;
	} else if ((c * i) <= 2.75e-308) {
		tmp = z * t;
	} else if ((c * i) <= 12000.0) {
		tmp = x * y;
	} 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) <= (-7.5d+122)) then
        tmp = c * i
    else if ((c * i) <= 2.75d-308) then
        tmp = z * t
    else if ((c * i) <= 12000.0d0) then
        tmp = x * y
    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) <= -7.5e+122) {
		tmp = c * i;
	} else if ((c * i) <= 2.75e-308) {
		tmp = z * t;
	} else if ((c * i) <= 12000.0) {
		tmp = x * y;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -7.5e+122:
		tmp = c * i
	elif (c * i) <= 2.75e-308:
		tmp = z * t
	elif (c * i) <= 12000.0:
		tmp = x * y
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -7.5e+122)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 2.75e-308)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 12000.0)
		tmp = Float64(x * y);
	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) <= -7.5e+122)
		tmp = c * i;
	elseif ((c * i) <= 2.75e-308)
		tmp = z * t;
	elseif ((c * i) <= 12000.0)
		tmp = x * y;
	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], -7.5e+122], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.75e-308], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 12000.0], N[(x * y), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -7.5000000000000002e122 or 12000 < (*.f64 c i)

   1. Initial program 90.4%

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

   2. Taylor expanded in c around inf 61.6%

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

   if -7.5000000000000002e122 < (*.f64 c i) < 2.75e-308

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 39.3%

      \[\leadsto \color{blue}{t \cdot z} \]

   if 2.75e-308 < (*.f64 c i) < 12000

   1. Initial program 98.0%

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

   2. Taylor expanded in x around inf 46.2%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.5 \cdot 10^{+122}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.75 \cdot 10^{-308}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 12000:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 12: 42.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.1 \cdot 10^{+117}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.5 \cdot 10^{+74}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.1e+117) (* c i) (if (<= (* c i) 6.5e+74) (* 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) <= -2.1e+117) {
		tmp = c * i;
	} else if ((c * i) <= 6.5e+74) {
		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) <= (-2.1d+117)) then
        tmp = c * i
    else if ((c * i) <= 6.5d+74) 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) <= -2.1e+117) {
		tmp = c * i;
	} else if ((c * i) <= 6.5e+74) {
		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) <= -2.1e+117:
		tmp = c * i
	elif (c * i) <= 6.5e+74:
		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) <= -2.1e+117)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 6.5e+74)
		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) <= -2.1e+117)
		tmp = c * i;
	elseif ((c * i) <= 6.5e+74)
		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], -2.1e+117], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 6.5e+74], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.1000000000000001e117 or 6.49999999999999962e74 < (*.f64 c i)

   1. Initial program 89.5%

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

   2. Taylor expanded in c around inf 64.5%

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

   if -2.1000000000000001e117 < (*.f64 c i) < 6.49999999999999962e74

   1. Initial program 98.7%

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

   2. Taylor expanded in a around inf 36.7%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.1 \cdot 10^{+117}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 6.5 \cdot 10^{+74}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 13: 55.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+179}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.65e+58)
   (* c i)
   (if (<= i 5.8e+179) (+ (* a b) (* z t)) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.65e+58) {
		tmp = c * i;
	} else if (i <= 5.8e+179) {
		tmp = (a * b) + (z * t);
	} 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 (i <= (-1.65d+58)) then
        tmp = c * i
    else if (i <= 5.8d+179) then
        tmp = (a * b) + (z * t)
    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 (i <= -1.65e+58) {
		tmp = c * i;
	} else if (i <= 5.8e+179) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.65e+58:
		tmp = c * i
	elif i <= 5.8e+179:
		tmp = (a * b) + (z * t)
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.65e+58)
		tmp = Float64(c * i);
	elseif (i <= 5.8e+179)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	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 (i <= -1.65e+58)
		tmp = c * i;
	elseif (i <= 5.8e+179)
		tmp = (a * b) + (z * t);
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.65e+58], N[(c * i), $MachinePrecision], If[LessEqual[i, 5.8e+179], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.64999999999999991e58 or 5.80000000000000038e179 < i

   1. Initial program 89.2%

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

   2. Taylor expanded in c around inf 62.1%

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

   if -1.64999999999999991e58 < i < 5.80000000000000038e179

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 72.4%

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

   3. Taylor expanded in c around 0 59.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;i \leq 5.8 \cdot 10^{+179}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 14: 26.5% 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 28.2%

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

3. Final simplification 28.2%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023290 
(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)))