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

Percentage Accurate: 95.9% → 98.0%

Time: 12.1s

Alternatives: 17

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: 95.9% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. associate-+l+ 96.1%

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

   2. +-commutative 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 96.1%

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

   5. associate-+r+ 96.1%

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

   6. +-commutative 96.1%

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

   7. fma-def 97.6%

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

   8. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 97.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. +-commutative 96.1%

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

   2. associate-+l+ 96.1%

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

   3. fma-def 96.5%

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

   4. associate-+l+ 96.5%

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

   5. fma-def 98.4%

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

   6. +-commutative 98.4%

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

   7. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 95.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 4 \cdot 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right) + c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) 4e+73)
   (fma z t (+ (fma x y (* a b)) (* c i)))
   (fma c i (fma 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 ((x * y) <= 4e+73) {
		tmp = fma(z, t, (fma(x, y, (a * b)) + (c * i)));
	} else {
		tmp = fma(c, i, fma(x, y, (z * t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= 4e+73)
		tmp = fma(z, t, Float64(fma(x, y, Float64(a * b)) + Float64(c * i)));
	else
		tmp = fma(c, i, fma(x, y, Float64(z * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], 4e+73], N[(z * t + N[(N[(x * y + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * i + N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 3.99999999999999993e73

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. +-commutative 98.5%

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

      3. associate-+l+ 98.5%

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

      4. fma-def 98.5%

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

      5. associate-+r+ 98.5%

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

      6. +-commutative 98.5%

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

      7. fma-def 99.0%

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

      8. fma-def 99.5%

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

   3. Simplified 99.5%

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

      1. fma-udef 99.0%

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

      2. +-commutative 99.0%

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

   5. Applied egg-rr 99.0%

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

   if 3.99999999999999993e73 < (*.f64 x y)

   1. Initial program 85.1%

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

   2. Taylor expanded in a around 0 87.2%

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

      1. fma-def 91.5%

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

      2. *-commutative 91.5%

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

      3. +-commutative 91.5%

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

      4. fma-def 95.7%

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

      5. *-commutative 95.7%

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

   4. Simplified 95.7%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 4 \cdot 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right) + c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\\ \end{array} \]

Alternative 4: 97.1% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (+ (* c i) (+ (* a b) (+ (* x y) (* z t)))) INFINITY)
   (fma z t (+ (* a b) (+ (* x y) (* c i))))
   (+ (* 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 (((c * i) + ((a * b) + ((x * y) + (z * t)))) <= ((double) INFINITY)) {
		tmp = fma(z, t, ((a * b) + ((x * y) + (c * i))));
	} else {
		tmp = (c * i) + (z * t);
	}
	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 = fma(z, t, Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(c * i))));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	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[(z * t + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $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%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-+r+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   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. Taylor expanded in a around 0 10.0%

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

   3. Taylor expanded in x around 0 60.0%

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

4. Final simplification 98.4%

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

Alternative 5: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + z \cdot t\\ t_3 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.1 \cdot 10^{+131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \cdot i \leq -8.5 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -3 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t)))
        (t_2 (+ (* a b) (* z t)))
        (t_3 (+ (* c i) (* z t))))
   (if (<= (* c i) -1.1e+131)
     t_3
     (if (<= (* c i) -8.5e-71)
       t_1
       (if (<= (* c i) -3e-299)
         t_2
         (if (<= (* c i) 2e-143)
           t_1
           (if (<= (* c i) 1.22e+17)
             t_2
             (if (<= (* c i) 2.1e+133) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + (z * t);
	double t_3 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -1.1e+131) {
		tmp = t_3;
	} else if ((c * i) <= -8.5e-71) {
		tmp = t_1;
	} else if ((c * i) <= -3e-299) {
		tmp = t_2;
	} else if ((c * i) <= 2e-143) {
		tmp = t_1;
	} else if ((c * i) <= 1.22e+17) {
		tmp = t_2;
	} else if ((c * i) <= 2.1e+133) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = (a * b) + (z * t)
    t_3 = (c * i) + (z * t)
    if ((c * i) <= (-1.1d+131)) then
        tmp = t_3
    else if ((c * i) <= (-8.5d-71)) then
        tmp = t_1
    else if ((c * i) <= (-3d-299)) then
        tmp = t_2
    else if ((c * i) <= 2d-143) then
        tmp = t_1
    else if ((c * i) <= 1.22d+17) then
        tmp = t_2
    else if ((c * i) <= 2.1d+133) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (a * b) + (z * t);
	double t_3 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -1.1e+131) {
		tmp = t_3;
	} else if ((c * i) <= -8.5e-71) {
		tmp = t_1;
	} else if ((c * i) <= -3e-299) {
		tmp = t_2;
	} else if ((c * i) <= 2e-143) {
		tmp = t_1;
	} else if ((c * i) <= 1.22e+17) {
		tmp = t_2;
	} else if ((c * i) <= 2.1e+133) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (z * t)
	t_3 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -1.1e+131:
		tmp = t_3
	elif (c * i) <= -8.5e-71:
		tmp = t_1
	elif (c * i) <= -3e-299:
		tmp = t_2
	elif (c * i) <= 2e-143:
		tmp = t_1
	elif (c * i) <= 1.22e+17:
		tmp = t_2
	elif (c * i) <= 2.1e+133:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	t_3 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1.1e+131)
		tmp = t_3;
	elseif (Float64(c * i) <= -8.5e-71)
		tmp = t_1;
	elseif (Float64(c * i) <= -3e-299)
		tmp = t_2;
	elseif (Float64(c * i) <= 2e-143)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.22e+17)
		tmp = t_2;
	elseif (Float64(c * i) <= 2.1e+133)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = (a * b) + (z * t);
	t_3 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1.1e+131)
		tmp = t_3;
	elseif ((c * i) <= -8.5e-71)
		tmp = t_1;
	elseif ((c * i) <= -3e-299)
		tmp = t_2;
	elseif ((c * i) <= 2e-143)
		tmp = t_1;
	elseif ((c * i) <= 1.22e+17)
		tmp = t_2;
	elseif ((c * i) <= 2.1e+133)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.1e+131], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], -8.5e-71], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -3e-299], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 2e-143], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.22e+17], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 2.1e+133], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.0999999999999999e131 or 2.1e133 < (*.f64 c i)

   1. Initial program 88.4%

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

   2. Taylor expanded in a around 0 83.1%

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

   3. Taylor expanded in x around 0 80.9%

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

   if -1.0999999999999999e131 < (*.f64 c i) < -8.49999999999999988e-71 or -2.99999999999999984e-299 < (*.f64 c i) < 1.9999999999999999e-143 or 1.22e17 < (*.f64 c i) < 2.1e133

   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 a around 0 82.9%

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

   3. Taylor expanded in c around 0 77.5%

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

   if -8.49999999999999988e-71 < (*.f64 c i) < -2.99999999999999984e-299 or 1.9999999999999999e-143 < (*.f64 c i) < 1.22e17

   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 x around 0 83.8%

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

   3. Taylor expanded in c around 0 78.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.1 \cdot 10^{+131}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -8.5 \cdot 10^{-71}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -3 \cdot 10^{-299}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2 \cdot 10^{-143}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{+133}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 6: 97.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) t_1 (+ (* c i) (* 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) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	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 = (c * i) + (z * t);
	}
	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 = (c * i) + (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(x * y) + Float64(z * t))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	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)
	t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (c * i) + (z * t);
	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[(c * i), $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. Taylor expanded in a around 0 10.0%

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

   3. Taylor expanded in x around 0 60.0%

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

4. Final simplification 98.4%

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

Alternative 7: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -6.4 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -2.25 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -1.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 6.3:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* a b) -6.4e+119)
     t_2
     (if (<= (* a b) -2.25e-5)
       t_1
       (if (<= (* a b) -1.5e-28)
         (* x y)
         (if (<= (* a b) 2.9e-40)
           t_1
           (if (<= (* a b) 6.3) (+ (* a b) (* x y)) t_2)))))))

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 t_2 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -6.4e+119) {
		tmp = t_2;
	} else if ((a * b) <= -2.25e-5) {
		tmp = t_1;
	} else if ((a * b) <= -1.5e-28) {
		tmp = x * y;
	} else if ((a * b) <= 2.9e-40) {
		tmp = t_1;
	} else if ((a * b) <= 6.3) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (a * b) + (z * t)
    if ((a * b) <= (-6.4d+119)) then
        tmp = t_2
    else if ((a * b) <= (-2.25d-5)) then
        tmp = t_1
    else if ((a * b) <= (-1.5d-28)) then
        tmp = x * y
    else if ((a * b) <= 2.9d-40) then
        tmp = t_1
    else if ((a * b) <= 6.3d0) then
        tmp = (a * b) + (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -6.4e+119) {
		tmp = t_2;
	} else if ((a * b) <= -2.25e-5) {
		tmp = t_1;
	} else if ((a * b) <= -1.5e-28) {
		tmp = x * y;
	} else if ((a * b) <= 2.9e-40) {
		tmp = t_1;
	} else if ((a * b) <= 6.3) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (a * b) <= -6.4e+119:
		tmp = t_2
	elif (a * b) <= -2.25e-5:
		tmp = t_1
	elif (a * b) <= -1.5e-28:
		tmp = x * y
	elif (a * b) <= 2.9e-40:
		tmp = t_1
	elif (a * b) <= 6.3:
		tmp = (a * b) + (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -6.4e+119)
		tmp = t_2;
	elseif (Float64(a * b) <= -2.25e-5)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.5e-28)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 2.9e-40)
		tmp = t_1;
	elseif (Float64(a * b) <= 6.3)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -6.4e+119)
		tmp = t_2;
	elseif ((a * b) <= -2.25e-5)
		tmp = t_1;
	elseif ((a * b) <= -1.5e-28)
		tmp = x * y;
	elseif ((a * b) <= 2.9e-40)
		tmp = t_1;
	elseif ((a * b) <= 6.3)
		tmp = (a * b) + (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -6.4e+119], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2.25e-5], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.5e-28], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.9e-40], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 6.3], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -6.39999999999999979e119 or 6.29999999999999982 < (*.f64 a b)

   1. Initial program 92.0%

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

   2. Taylor expanded in x around 0 84.6%

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

   3. Taylor expanded in c around 0 81.0%

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

   if -6.39999999999999979e119 < (*.f64 a b) < -2.25000000000000014e-5 or -1.50000000000000001e-28 < (*.f64 a b) < 2.8999999999999999e-40

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0 95.3%

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

   3. Taylor expanded in x around 0 69.7%

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

   if -2.25000000000000014e-5 < (*.f64 a b) < -1.50000000000000001e-28

   1. Initial program 80.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   if 2.8999999999999999e-40 < (*.f64 a b) < 6.29999999999999982

   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 z around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. *-commutative 86.0%

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

      3. fma-def 86.0%

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

   4. Applied egg-rr 86.0%

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

   5. Taylor expanded in c around 0 70.6%

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.4 \cdot 10^{+119}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -2.25 \cdot 10^{-5}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -1.5 \cdot 10^{-28}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{-40}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.3:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 8: 42.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.65 \cdot 10^{+128}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.18 \cdot 10^{-256}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{+140}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.65e+128)
   (* c i)
   (if (<= (* c i) -8.2e-268)
     (* z t)
     (if (<= (* c i) 1.18e-256)
       (* a b)
       (if (<= (* c i) 2.5e+140) (* 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 ((c * i) <= -1.65e+128) {
		tmp = c * i;
	} else if ((c * i) <= -8.2e-268) {
		tmp = z * t;
	} else if ((c * i) <= 1.18e-256) {
		tmp = a * b;
	} else if ((c * i) <= 2.5e+140) {
		tmp = 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 ((c * i) <= (-1.65d+128)) then
        tmp = c * i
    else if ((c * i) <= (-8.2d-268)) then
        tmp = z * t
    else if ((c * i) <= 1.18d-256) then
        tmp = a * b
    else if ((c * i) <= 2.5d+140) then
        tmp = 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 ((c * i) <= -1.65e+128) {
		tmp = c * i;
	} else if ((c * i) <= -8.2e-268) {
		tmp = z * t;
	} else if ((c * i) <= 1.18e-256) {
		tmp = a * b;
	} else if ((c * i) <= 2.5e+140) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.65e+128:
		tmp = c * i
	elif (c * i) <= -8.2e-268:
		tmp = z * t
	elif (c * i) <= 1.18e-256:
		tmp = a * b
	elif (c * i) <= 2.5e+140:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.65e+128)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -8.2e-268)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.18e-256)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.5e+140)
		tmp = 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 ((c * i) <= -1.65e+128)
		tmp = c * i;
	elseif ((c * i) <= -8.2e-268)
		tmp = z * t;
	elseif ((c * i) <= 1.18e-256)
		tmp = a * b;
	elseif ((c * i) <= 2.5e+140)
		tmp = z * t;
	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], -1.65e+128], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -8.2e-268], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.18e-256], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.5e+140], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.65e128 or 2.50000000000000004e140 < (*.f64 c i)

   1. Initial program 88.4%

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

   2. Taylor expanded in c around inf 67.4%

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

   if -1.65e128 < (*.f64 c i) < -8.1999999999999998e-268 or 1.18e-256 < (*.f64 c i) < 2.50000000000000004e140

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 42.1%

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

   if -8.1999999999999998e-268 < (*.f64 c i) < 1.18e-256

   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 a around inf 42.9%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.65 \cdot 10^{+128}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.18 \cdot 10^{-256}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{+140}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 9: 85.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+118} \lor \neg \left(a \cdot b \leq 1.85 \cdot 10^{+118}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -8e+118) (not (<= (* a b) 1.85e+118)))
   (+ (* a b) (* z t))
   (+ (* c i) (+ (* 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 (((a * b) <= -8e+118) || !((a * b) <= 1.85e+118)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (c * i) + ((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 (((a * b) <= (-8d+118)) .or. (.not. ((a * b) <= 1.85d+118))) then
        tmp = (a * b) + (z * t)
    else
        tmp = (c * i) + ((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 (((a * b) <= -8e+118) || !((a * b) <= 1.85e+118)) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (c * i) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -8e+118) or not ((a * b) <= 1.85e+118):
		tmp = (a * b) + (z * t)
	else:
		tmp = (c * i) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -8e+118) || !(Float64(a * b) <= 1.85e+118))
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = Float64(Float64(c * i) + 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 (((a * b) <= -8e+118) || ~(((a * b) <= 1.85e+118)))
		tmp = (a * b) + (z * t);
	else
		tmp = (c * i) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -8e+118], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.85e+118]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -7.99999999999999973e118 or 1.84999999999999993e118 < (*.f64 a b)

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 84.6%

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

   3. Taylor expanded in c around 0 83.1%

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

   if -7.99999999999999973e118 < (*.f64 a b) < 1.84999999999999993e118

   1. Initial program 98.3%

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

   2. Taylor expanded in a around 0 92.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+118} \lor \neg \left(a \cdot b \leq 1.85 \cdot 10^{+118}\right):\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 10: 87.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+78} \lor \neg \left(x \cdot y \leq 2.7 \cdot 10^{+31}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -3.8e+78) (not (<= (* x y) 2.7e+31)))
   (+ (* c i) (+ (* x y) (* z t)))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -3.8e+78) || !((x * y) <= 2.7e+31)) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (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 (((x * y) <= (-3.8d+78)) .or. (.not. ((x * y) <= 2.7d+31))) then
        tmp = (c * i) + ((x * y) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (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 (((x * y) <= -3.8e+78) || !((x * y) <= 2.7e+31)) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -3.8e+78) or not ((x * y) <= 2.7e+31):
		tmp = (c * i) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -3.8e+78) || !(Float64(x * y) <= 2.7e+31))
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -3.8e+78) || ~(((x * y) <= 2.7e+31)))
		tmp = (c * i) + ((x * y) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.8e+78], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.7e+31]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.7999999999999999e78 or 2.69999999999999986e31 < (*.f64 x y)

   1. Initial program 91.0%

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

   2. Taylor expanded in a around 0 87.5%

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

   if -3.7999999999999999e78 < (*.f64 x y) < 2.69999999999999986e31

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 96.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+78} \lor \neg \left(x \cdot y \leq 2.7 \cdot 10^{+31}\right):\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 11: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+59} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.05e+59) (not (<= (* x y) 5e+45)))
   (* 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 tmp;
	if (((x * y) <= -1.05e+59) || !((x * y) <= 5e+45)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (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 (((x * y) <= (-1.05d+59)) .or. (.not. ((x * y) <= 5d+45))) then
        tmp = x * y
    else
        tmp = (a * b) + (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 (((x * y) <= -1.05e+59) || !((x * y) <= 5e+45)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.05e+59) or not ((x * y) <= 5e+45):
		tmp = x * y
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.05e+59) || !(Float64(x * y) <= 5e+45))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.05e+59) || ~(((x * y) <= 5e+45)))
		tmp = x * y;
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.05e+59], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+45]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.04999999999999992e59 or 5e45 < (*.f64 x y)

   1. Initial program 91.0%

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

   2. Taylor expanded in x around inf 62.6%

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

   if -1.04999999999999992e59 < (*.f64 x y) < 5e45

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 95.3%

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

   3. Taylor expanded in c around 0 70.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+59} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+45}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 12: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+56} \lor \neg \left(x \cdot y \leq 2.2 \cdot 10^{+22}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4.5e+56) (not (<= (* x y) 2.2e+22)))
   (+ (* a b) (* 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 tmp;
	if (((x * y) <= -4.5e+56) || !((x * y) <= 2.2e+22)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (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 (((x * y) <= (-4.5d+56)) .or. (.not. ((x * y) <= 2.2d+22))) then
        tmp = (a * b) + (x * y)
    else
        tmp = (a * b) + (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 (((x * y) <= -4.5e+56) || !((x * y) <= 2.2e+22)) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -4.5e+56) or not ((x * y) <= 2.2e+22):
		tmp = (a * b) + (x * y)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -4.5e+56) || !(Float64(x * y) <= 2.2e+22))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -4.5e+56) || ~(((x * y) <= 2.2e+22)))
		tmp = (a * b) + (x * y);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4.5e+56], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.2e+22]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.5000000000000003e56 or 2.2e22 < (*.f64 x y)

   1. Initial program 91.4%

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

   2. Taylor expanded in z around 0 81.3%

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

      1. +-commutative 81.3%

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

      2. *-commutative 81.3%

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

      3. fma-def 83.2%

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

   4. Applied egg-rr 83.2%

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

   5. Taylor expanded in c around 0 69.3%

      \[\leadsto \color{blue}{a \cdot b + x \cdot y} \]

   if -4.5000000000000003e56 < (*.f64 x y) < 2.2e22

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 96.5%

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

   3. Taylor expanded in c around 0 71.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.5 \cdot 10^{+56} \lor \neg \left(x \cdot y \leq 2.2 \cdot 10^{+22}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 13: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.4 \cdot 10^{+53} \lor \neg \left(x \cdot y \leq 2.2 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4.4e+53) (not (<= (* x y) 2.2e+31)))
   (+ (* x y) (* c i))
   (+ (* a b) (* z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -4.4e+53) || !((x * y) <= 2.2e+31)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (a * b) + (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 (((x * y) <= (-4.4d+53)) .or. (.not. ((x * y) <= 2.2d+31))) then
        tmp = (x * y) + (c * i)
    else
        tmp = (a * b) + (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 (((x * y) <= -4.4e+53) || !((x * y) <= 2.2e+31)) {
		tmp = (x * y) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -4.4e+53) or not ((x * y) <= 2.2e+31):
		tmp = (x * y) + (c * i)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -4.4e+53) || !(Float64(x * y) <= 2.2e+31))
		tmp = Float64(Float64(x * y) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -4.4e+53) || ~(((x * y) <= 2.2e+31)))
		tmp = (x * y) + (c * i);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4.4e+53], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.2e+31]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.39999999999999997e53 or 2.2000000000000001e31 < (*.f64 x y)

   1. Initial program 91.2%

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

      1. associate-+l+ 91.2%

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

      2. +-commutative 91.2%

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

      3. associate-+l+ 91.2%

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

      4. fma-def 91.2%

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

      5. associate-+r+ 91.2%

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

      6. +-commutative 91.2%

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

      7. fma-def 94.2%

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

      8. fma-def 96.1%

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

   3. Simplified 96.1%

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

      1. fma-udef 93.2%

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

      2. +-commutative 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in a around 0 87.9%

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

      1. fma-def 89.8%

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

   8. Simplified 89.8%

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

      1. fma-udef 89.8%

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

      2. *-commutative 89.8%

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

      3. +-commutative 89.8%

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

      4. *-commutative 89.8%

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

   10. Applied egg-rr 89.8%

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

   11. Taylor expanded in z around 0 76.6%

       \[\leadsto \color{blue}{c \cdot i + x \cdot y} \]

   if -4.39999999999999997e53 < (*.f64 x y) < 2.2000000000000001e31

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 95.9%

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

   3. Taylor expanded in c around 0 71.5%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.4 \cdot 10^{+53} \lor \neg \left(x \cdot y \leq 2.2 \cdot 10^{+31}\right):\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 14: 43.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.5 \cdot 10^{+117} \lor \neg \left(a \cdot b \leq 6 \cdot 10^{-13}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -8.5e+117) (not (<= (* a b) 6e-13))) (* 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 (((a * b) <= -8.5e+117) || !((a * b) <= 6e-13)) {
		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 (((a * b) <= (-8.5d+117)) .or. (.not. ((a * b) <= 6d-13))) 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 (((a * b) <= -8.5e+117) || !((a * b) <= 6e-13)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -8.5e+117) or not ((a * b) <= 6e-13):
		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(a * b) <= -8.5e+117) || !(Float64(a * b) <= 6e-13))
		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 (((a * b) <= -8.5e+117) || ~(((a * b) <= 6e-13)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -8.5e+117], N[Not[LessEqual[N[(a * b), $MachinePrecision], 6e-13]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -8.49999999999999966e117 or 5.99999999999999968e-13 < (*.f64 a b)

   1. Initial program 91.4%

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

   2. Taylor expanded in a around inf 56.5%

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

   if -8.49999999999999966e117 < (*.f64 a b) < 5.99999999999999968e-13

   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 c around inf 32.1%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8.5 \cdot 10^{+117} \lor \neg \left(a \cdot b \leq 6 \cdot 10^{-13}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 15: 43.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.8 \cdot 10^{+58} \lor \neg \left(x \cdot y \leq 3.5 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -9.8e+58) (not (<= (* x y) 3.5e+22))) (* 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 (((x * y) <= -9.8e+58) || !((x * y) <= 3.5e+22)) {
		tmp = x * y;
	} else {
		tmp = 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 (((x * y) <= (-9.8d+58)) .or. (.not. ((x * y) <= 3.5d+22))) then
        tmp = x * y
    else
        tmp = 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 (((x * y) <= -9.8e+58) || !((x * y) <= 3.5e+22)) {
		tmp = x * y;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -9.8e+58) or not ((x * y) <= 3.5e+22):
		tmp = x * y
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -9.8e+58) || !(Float64(x * y) <= 3.5e+22))
		tmp = Float64(x * y);
	else
		tmp = Float64(z * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -9.8e+58) || ~(((x * y) <= 3.5e+22)))
		tmp = x * y;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -9.8e+58], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.5e+22]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(z * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.80000000000000037e58 or 3.5e22 < (*.f64 x y)

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 61.6%

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

   if -9.80000000000000037e58 < (*.f64 x y) < 3.5e22

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 43.8%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.8 \cdot 10^{+58} \lor \neg \left(x \cdot y \leq 3.5 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 16: 52.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+100} \lor \neg \left(z \leq 1.65 \cdot 10^{-33}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -5.8e+100) (not (<= z 1.65e-33))) (* 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) {
	double tmp;
	if ((z <= -5.8e+100) || !(z <= 1.65e-33)) {
		tmp = z * t;
	} else {
		tmp = (a * b) + (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 ((z <= (-5.8d+100)) .or. (.not. (z <= 1.65d-33))) then
        tmp = z * t
    else
        tmp = (a * b) + (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 ((z <= -5.8e+100) || !(z <= 1.65e-33)) {
		tmp = z * t;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -5.8e+100) or not (z <= 1.65e-33):
		tmp = z * t
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -5.8e+100) || !(z <= 1.65e-33))
		tmp = Float64(z * t);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -5.8e+100) || ~((z <= 1.65e-33)))
		tmp = z * t;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -5.8e+100], N[Not[LessEqual[z, 1.65e-33]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000001e100 or 1.6500000000000001e-33 < z

   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 z around inf 46.6%

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

   if -5.8000000000000001e100 < z < 1.6500000000000001e-33

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 70.5%

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

   3. Taylor expanded in t around 0 54.3%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+100} \lor \neg \left(z \leq 1.65 \cdot 10^{-33}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 17: 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 96.1%

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

2. Taylor expanded in a around inf 24.1%

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

3. Final simplification 24.1%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023306 
(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)))