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

Percentage Accurate: 95.7% → 97.7%

Time: 13.1s

Alternatives: 17

Speedup: 0.5×

• 42.2% 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: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-def 98.0%

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

   3. associate-+l+ 98.0%

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

   4. fma-def 98.8%

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

   5. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 97.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-def 98.0%

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

   3. +-commutative 98.0%

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

   4. fma-def 98.4%

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

   5. fma-def 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 3: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-def 98.0%

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

   3. associate-+l+ 98.0%

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

   4. fma-def 98.8%

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

   5. fma-def 99.2%

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

3. Simplified 99.2%

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

   1. fma-udef 98.8%

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

5. Applied egg-rr 98.8%

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

6. Final simplification 98.8%

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

Alternative 4: 97.7% accurate, 0.1× speedup

Math

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

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 a b (* c i)))))

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(a, b, (c * i));
	}
	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(a, b, Float64(c * i));
	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[(a * b + N[(c * i), $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 z around 0 16.7%

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

   3. Taylor expanded in x around 0 50.0%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]
   4. Step-by-step derivation

      1. fma-def 66.7%

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

   5. Simplified 66.7%

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

4. Final simplification 99.2%

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

Alternative 5: 96.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-def 98.0%

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

   3. +-commutative 98.0%

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

   4. fma-def 98.4%

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

   5. fma-def 99.2%

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

3. Simplified 99.2%

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

   1. fma-udef 98.8%

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

   2. fma-udef 98.4%

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

   3. associate-+r+ 98.4%

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

   4. +-commutative 98.4%

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

   5. fma-def 97.6%

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

   6. +-commutative 97.6%

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

   7. associate-+r+ 97.6%

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

   8. fma-def 98.0%

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

5. Applied egg-rr 98.0%

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

6. Final simplification 98.0%

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

Alternative 6: 96.1% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-+l+ 97.6%

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

   2. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 7: 42.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -7.8 \cdot 10^{-162}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -6.2 \cdot 10^{-240}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.6 \cdot 10^{-308}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{-226}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.2 \cdot 10^{-170}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.6 \cdot 10^{+127}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -2.2e+128)
   (* a b)
   (if (<= (* a b) -3.4e-27)
     (* c i)
     (if (<= (* a b) -7.8e-162)
       (* x y)
       (if (<= (* a b) -6.2e-240)
         (* c i)
         (if (<= (* a b) 3.6e-308)
           (* x y)
           (if (<= (* a b) 3.2e-226)
             (* c i)
             (if (<= (* a b) 2.2e-170)
               (* z t)
               (if (<= (* a b) 4.6e+127) (* x y) (* a b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2.2e+128) {
		tmp = a * b;
	} else if ((a * b) <= -3.4e-27) {
		tmp = c * i;
	} else if ((a * b) <= -7.8e-162) {
		tmp = x * y;
	} else if ((a * b) <= -6.2e-240) {
		tmp = c * i;
	} else if ((a * b) <= 3.6e-308) {
		tmp = x * y;
	} else if ((a * b) <= 3.2e-226) {
		tmp = c * i;
	} else if ((a * b) <= 2.2e-170) {
		tmp = z * t;
	} else if ((a * b) <= 4.6e+127) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-2.2d+128)) then
        tmp = a * b
    else if ((a * b) <= (-3.4d-27)) then
        tmp = c * i
    else if ((a * b) <= (-7.8d-162)) then
        tmp = x * y
    else if ((a * b) <= (-6.2d-240)) then
        tmp = c * i
    else if ((a * b) <= 3.6d-308) then
        tmp = x * y
    else if ((a * b) <= 3.2d-226) then
        tmp = c * i
    else if ((a * b) <= 2.2d-170) then
        tmp = z * t
    else if ((a * b) <= 4.6d+127) then
        tmp = x * y
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -2.2e+128) {
		tmp = a * b;
	} else if ((a * b) <= -3.4e-27) {
		tmp = c * i;
	} else if ((a * b) <= -7.8e-162) {
		tmp = x * y;
	} else if ((a * b) <= -6.2e-240) {
		tmp = c * i;
	} else if ((a * b) <= 3.6e-308) {
		tmp = x * y;
	} else if ((a * b) <= 3.2e-226) {
		tmp = c * i;
	} else if ((a * b) <= 2.2e-170) {
		tmp = z * t;
	} else if ((a * b) <= 4.6e+127) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -2.2e+128:
		tmp = a * b
	elif (a * b) <= -3.4e-27:
		tmp = c * i
	elif (a * b) <= -7.8e-162:
		tmp = x * y
	elif (a * b) <= -6.2e-240:
		tmp = c * i
	elif (a * b) <= 3.6e-308:
		tmp = x * y
	elif (a * b) <= 3.2e-226:
		tmp = c * i
	elif (a * b) <= 2.2e-170:
		tmp = z * t
	elif (a * b) <= 4.6e+127:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -2.2e+128)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -3.4e-27)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= -7.8e-162)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= -6.2e-240)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 3.6e-308)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 3.2e-226)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 2.2e-170)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 4.6e+127)
		tmp = Float64(x * y);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -2.2e+128)
		tmp = a * b;
	elseif ((a * b) <= -3.4e-27)
		tmp = c * i;
	elseif ((a * b) <= -7.8e-162)
		tmp = x * y;
	elseif ((a * b) <= -6.2e-240)
		tmp = c * i;
	elseif ((a * b) <= 3.6e-308)
		tmp = x * y;
	elseif ((a * b) <= 3.2e-226)
		tmp = c * i;
	elseif ((a * b) <= 2.2e-170)
		tmp = z * t;
	elseif ((a * b) <= 4.6e+127)
		tmp = x * y;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -2.2e+128], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -3.4e-27], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -7.8e-162], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -6.2e-240], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.6e-308], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3.2e-226], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.2e-170], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 4.6e+127], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2.20000000000000017e128 or 4.6000000000000003e127 < (*.f64 a b)

   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 79.2%

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

   if -2.20000000000000017e128 < (*.f64 a b) < -3.3999999999999997e-27 or -7.7999999999999999e-162 < (*.f64 a b) < -6.20000000000000034e-240 or 3.5999999999999999e-308 < (*.f64 a b) < 3.19999999999999982e-226

   1. Initial program 98.1%

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

   2. Taylor expanded in c around inf 53.1%

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

   if -3.3999999999999997e-27 < (*.f64 a b) < -7.7999999999999999e-162 or -6.20000000000000034e-240 < (*.f64 a b) < 3.5999999999999999e-308 or 2.20000000000000015e-170 < (*.f64 a b) < 4.6000000000000003e127

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 41.0%

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

   if 3.19999999999999982e-226 < (*.f64 a b) < 2.20000000000000015e-170

   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 z around inf 79.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3.4 \cdot 10^{-27}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -7.8 \cdot 10^{-162}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -6.2 \cdot 10^{-240}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3.6 \cdot 10^{-308}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 3.2 \cdot 10^{-226}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.2 \cdot 10^{-170}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.6 \cdot 10^{+127}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 8: 62.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -7.9 \cdot 10^{+135}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -3.4 \cdot 10^{-67}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2.15 \cdot 10^{-195}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{+197}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -7.9e+135)
     (* x y)
     (if (<= (* x y) -3e-45)
       t_1
       (if (<= (* x y) -3.4e-67)
         (* z t)
         (if (<= (* x y) -3.3e-126)
           t_1
           (if (<= (* x y) -2.15e-195)
             (* z t)
             (if (<= (* x y) 8.5e+197) t_1 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -7.9e+135) {
		tmp = x * y;
	} else if ((x * y) <= -3e-45) {
		tmp = t_1;
	} else if ((x * y) <= -3.4e-67) {
		tmp = z * t;
	} else if ((x * y) <= -3.3e-126) {
		tmp = t_1;
	} else if ((x * y) <= -2.15e-195) {
		tmp = z * t;
	} else if ((x * y) <= 8.5e+197) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((x * y) <= (-7.9d+135)) then
        tmp = x * y
    else if ((x * y) <= (-3d-45)) then
        tmp = t_1
    else if ((x * y) <= (-3.4d-67)) then
        tmp = z * t
    else if ((x * y) <= (-3.3d-126)) then
        tmp = t_1
    else if ((x * y) <= (-2.15d-195)) then
        tmp = z * t
    else if ((x * y) <= 8.5d+197) then
        tmp = t_1
    else
        tmp = 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 t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -7.9e+135) {
		tmp = x * y;
	} else if ((x * y) <= -3e-45) {
		tmp = t_1;
	} else if ((x * y) <= -3.4e-67) {
		tmp = z * t;
	} else if ((x * y) <= -3.3e-126) {
		tmp = t_1;
	} else if ((x * y) <= -2.15e-195) {
		tmp = z * t;
	} else if ((x * y) <= 8.5e+197) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -7.9e+135:
		tmp = x * y
	elif (x * y) <= -3e-45:
		tmp = t_1
	elif (x * y) <= -3.4e-67:
		tmp = z * t
	elif (x * y) <= -3.3e-126:
		tmp = t_1
	elif (x * y) <= -2.15e-195:
		tmp = z * t
	elif (x * y) <= 8.5e+197:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -7.9e+135)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3e-45)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.4e-67)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -3.3e-126)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.15e-195)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 8.5e+197)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -7.9e+135)
		tmp = x * y;
	elseif ((x * y) <= -3e-45)
		tmp = t_1;
	elseif ((x * y) <= -3.4e-67)
		tmp = z * t;
	elseif ((x * y) <= -3.3e-126)
		tmp = t_1;
	elseif ((x * y) <= -2.15e-195)
		tmp = z * t;
	elseif ((x * y) <= 8.5e+197)
		tmp = t_1;
	else
		tmp = x * y;
	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[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7.9e+135], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3e-45], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.4e-67], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.3e-126], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.15e-195], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.5e+197], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.90000000000000017e135 or 8.5000000000000001e197 < (*.f64 x y)

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 73.6%

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

   if -7.90000000000000017e135 < (*.f64 x y) < -3.00000000000000011e-45 or -3.4000000000000001e-67 < (*.f64 x y) < -3.3000000000000001e-126 or -2.1500000000000002e-195 < (*.f64 x y) < 8.5000000000000001e197

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 78.7%

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

   3. Taylor expanded in x around 0 67.1%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -3.00000000000000011e-45 < (*.f64 x y) < -3.4000000000000001e-67 or -3.3000000000000001e-126 < (*.f64 x y) < -2.1500000000000002e-195

   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 z around inf 90.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.9 \cdot 10^{+135}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3 \cdot 10^{-45}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -3.4 \cdot 10^{-67}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{-126}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq -2.15 \cdot 10^{-195}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.5 \cdot 10^{+197}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 97.2% accurate, 0.5× speedup

Math

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

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 33.3%

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

   3. Taylor expanded in x around 0 66.7%

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

4. Final simplification 99.2%

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

Alternative 10: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.1 \cdot 10^{+152} \lor \neg \left(c \cdot i \leq -5.4 \cdot 10^{-24}\right) \land \left(c \cdot i \leq -4.3 \cdot 10^{-106} \lor \neg \left(c \cdot i \leq 3.2 \cdot 10^{+133}\right)\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -4.1e+152)
         (and (not (<= (* c i) -5.4e-24))
              (or (<= (* c i) -4.3e-106) (not (<= (* c i) 3.2e+133)))))
   (+ (* c i) (* z t))
   (+ (* 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) <= -4.1e+152) || (!((c * i) <= -5.4e-24) && (((c * i) <= -4.3e-106) || !((c * i) <= 3.2e+133)))) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + (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) <= (-4.1d+152)) .or. (.not. ((c * i) <= (-5.4d-24))) .and. ((c * i) <= (-4.3d-106)) .or. (.not. ((c * i) <= 3.2d+133))) then
        tmp = (c * i) + (z * t)
    else
        tmp = (a * b) + (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) <= -4.1e+152) || (!((c * i) <= -5.4e-24) && (((c * i) <= -4.3e-106) || !((c * i) <= 3.2e+133)))) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -4.1e+152) or (not ((c * i) <= -5.4e-24) and (((c * i) <= -4.3e-106) or not ((c * i) <= 3.2e+133))):
		tmp = (c * i) + (z * t)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -4.1e+152) || (!(Float64(c * i) <= -5.4e-24) && ((Float64(c * i) <= -4.3e-106) || !(Float64(c * i) <= 3.2e+133))))
		tmp = Float64(Float64(c * i) + Float64(z * t));
	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)
	tmp = 0.0;
	if (((c * i) <= -4.1e+152) || (~(((c * i) <= -5.4e-24)) && (((c * i) <= -4.3e-106) || ~(((c * i) <= 3.2e+133)))))
		tmp = (c * i) + (z * t);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -4.1e+152], And[N[Not[LessEqual[N[(c * i), $MachinePrecision], -5.4e-24]], $MachinePrecision], Or[LessEqual[N[(c * i), $MachinePrecision], -4.3e-106], N[Not[LessEqual[N[(c * i), $MachinePrecision], 3.2e+133]], $MachinePrecision]]]], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -4.0999999999999998e152 or -5.40000000000000014e-24 < (*.f64 c i) < -4.3000000000000002e-106 or 3.19999999999999997e133 < (*.f64 c i)

   1. Initial program 94.5%

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

   2. Taylor expanded in a around 0 84.9%

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

   3. Taylor expanded in x around 0 80.0%

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

   if -4.0999999999999998e152 < (*.f64 c i) < -5.40000000000000014e-24 or -4.3000000000000002e-106 < (*.f64 c i) < 3.19999999999999997e133

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. fma-def 99.4%

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

      3. associate-+l+ 99.4%

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

      4. fma-def 99.4%

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

      5. fma-def 99.4%

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

   3. Simplified 99.4%

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

      1. fma-udef 99.4%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in z around 0 79.4%

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

   7. Taylor expanded in c around 0 72.7%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.1 \cdot 10^{+152} \lor \neg \left(c \cdot i \leq -5.4 \cdot 10^{-24}\right) \land \left(c \cdot i \leq -4.3 \cdot 10^{-106} \lor \neg \left(c \cdot i \leq 3.2 \cdot 10^{+133}\right)\right):\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 11: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -1.2 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq -5.4 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -5.2 \cdot 10^{-79}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -1.2e+149)
     t_2
     (if (<= (* c i) -5.4e-24)
       t_1
       (if (<= (* c i) -5.2e-79)
         (* z t)
         (if (<= (* c i) 2.1e+137) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.2e+149) {
		tmp = t_2;
	} else if ((c * i) <= -5.4e-24) {
		tmp = t_1;
	} else if ((c * i) <= -5.2e-79) {
		tmp = z * t;
	} else if ((c * i) <= 2.1e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-1.2d+149)) then
        tmp = t_2
    else if ((c * i) <= (-5.4d-24)) then
        tmp = t_1
    else if ((c * i) <= (-5.2d-79)) then
        tmp = z * t
    else if ((c * i) <= 2.1d+137) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.2e+149) {
		tmp = t_2;
	} else if ((c * i) <= -5.4e-24) {
		tmp = t_1;
	} else if ((c * i) <= -5.2e-79) {
		tmp = z * t;
	} else if ((c * i) <= 2.1e+137) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -1.2e+149:
		tmp = t_2
	elif (c * i) <= -5.4e-24:
		tmp = t_1
	elif (c * i) <= -5.2e-79:
		tmp = z * t
	elif (c * i) <= 2.1e+137:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -1.2e+149)
		tmp = t_2;
	elseif (Float64(c * i) <= -5.4e-24)
		tmp = t_1;
	elseif (Float64(c * i) <= -5.2e-79)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 2.1e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -1.2e+149)
		tmp = t_2;
	elseif ((c * i) <= -5.4e-24)
		tmp = t_1;
	elseif ((c * i) <= -5.2e-79)
		tmp = z * t;
	elseif ((c * i) <= 2.1e+137)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.2e+149], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -5.4e-24], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -5.2e-79], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.1e+137], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.20000000000000006e149 or 2.0999999999999999e137 < (*.f64 c i)

   1. Initial program 94.5%

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

   2. Taylor expanded in z around 0 81.9%

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

   3. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{a \cdot b + c \cdot i} \]

   if -1.20000000000000006e149 < (*.f64 c i) < -5.40000000000000014e-24 or -5.19999999999999987e-79 < (*.f64 c i) < 2.0999999999999999e137

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. fma-def 99.4%

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

      3. associate-+l+ 99.4%

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

      4. fma-def 99.4%

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

      5. fma-def 99.4%

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

   3. Simplified 99.4%

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

      1. fma-udef 99.4%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in z around 0 78.6%

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

   7. Taylor expanded in c around 0 72.0%

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

   if -5.40000000000000014e-24 < (*.f64 c i) < -5.19999999999999987e-79

   1. Initial program 93.2%

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

   2. Taylor expanded in z around inf 67.2%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.2 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -5.4 \cdot 10^{-24}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -5.2 \cdot 10^{-79}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{+137}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 12: 42.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.1 \cdot 10^{-305}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.4 \cdot 10^{-122}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+128}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4.2e+128)
   (* a b)
   (if (<= (* a b) -2.1e-305)
     (* c i)
     (if (<= (* a b) 2.4e-122)
       (* z t)
       (if (<= (* a b) 2.5e+128) (* c i) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -4.2e+128) {
		tmp = a * b;
	} else if ((a * b) <= -2.1e-305) {
		tmp = c * i;
	} else if ((a * b) <= 2.4e-122) {
		tmp = z * t;
	} else if ((a * b) <= 2.5e+128) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-4.2d+128)) then
        tmp = a * b
    else if ((a * b) <= (-2.1d-305)) then
        tmp = c * i
    else if ((a * b) <= 2.4d-122) then
        tmp = z * t
    else if ((a * b) <= 2.5d+128) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -4.2e+128) {
		tmp = a * b;
	} else if ((a * b) <= -2.1e-305) {
		tmp = c * i;
	} else if ((a * b) <= 2.4e-122) {
		tmp = z * t;
	} else if ((a * b) <= 2.5e+128) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -4.2e+128:
		tmp = a * b
	elif (a * b) <= -2.1e-305:
		tmp = c * i
	elif (a * b) <= 2.4e-122:
		tmp = z * t
	elif (a * b) <= 2.5e+128:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -4.2e+128)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.1e-305)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 2.4e-122)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 2.5e+128)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -4.2e+128)
		tmp = a * b;
	elseif ((a * b) <= -2.1e-305)
		tmp = c * i;
	elseif ((a * b) <= 2.4e-122)
		tmp = z * t;
	elseif ((a * b) <= 2.5e+128)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -4.2e+128], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.1e-305], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.4e-122], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.5e+128], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.1999999999999999e128 or 2.5e128 < (*.f64 a b)

   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 79.2%

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

   if -4.1999999999999999e128 < (*.f64 a b) < -2.1e-305 or 2.39999999999999987e-122 < (*.f64 a b) < 2.5e128

   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 inf 38.2%

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

   if -2.1e-305 < (*.f64 a b) < 2.39999999999999987e-122

   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 z around inf 45.4%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.2 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.1 \cdot 10^{-305}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 2.4 \cdot 10^{-122}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.5 \cdot 10^{+128}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 13: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -1.1 \cdot 10^{+135} \lor \neg \left(a \cdot b \leq 4.6 \cdot 10^{+74}\right):\\ \;\;\;\;a \cdot b + t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))))
   (if (or (<= (* a b) -1.1e+135) (not (<= (* a b) 4.6e+74)))
     (+ (* a b) t_1)
     (+ (* c i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double tmp;
	if (((a * b) <= -1.1e+135) || !((a * b) <= 4.6e+74)) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + 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 = (x * y) + (z * t)
    if (((a * b) <= (-1.1d+135)) .or. (.not. ((a * b) <= 4.6d+74))) then
        tmp = (a * b) + t_1
    else
        tmp = (c * i) + 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 = (x * y) + (z * t);
	double tmp;
	if (((a * b) <= -1.1e+135) || !((a * b) <= 4.6e+74)) {
		tmp = (a * b) + t_1;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	tmp = 0
	if ((a * b) <= -1.1e+135) or not ((a * b) <= 4.6e+74):
		tmp = (a * b) + t_1
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if ((Float64(a * b) <= -1.1e+135) || !(Float64(a * b) <= 4.6e+74))
		tmp = Float64(Float64(a * b) + t_1);
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	tmp = 0.0;
	if (((a * b) <= -1.1e+135) || ~(((a * b) <= 4.6e+74)))
		tmp = (a * b) + t_1;
	else
		tmp = (c * i) + t_1;
	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]}, If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.1e+135], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.6e+74]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.1e135 or 4.5999999999999997e74 < (*.f64 a b)

   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 c around 0 92.0%

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

   if -1.1e135 < (*.f64 a b) < 4.5999999999999997e74

   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 a around 0 91.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.1 \cdot 10^{+135} \lor \neg \left(a \cdot b \leq 4.6 \cdot 10^{+74}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 14: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.05 \cdot 10^{+153}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+248}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.05e+153)
   (+ (* c i) (* z t))
   (if (<= (* c i) 5e+248)
     (+ (* a b) (+ (* 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) {
	double tmp;
	if ((c * i) <= -3.05e+153) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 5e+248) {
		tmp = (a * b) + ((x * y) + (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 ((c * i) <= (-3.05d+153)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 5d+248) then
        tmp = (a * b) + ((x * y) + (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 ((c * i) <= -3.05e+153) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 5e+248) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.05e+153:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 5e+248:
		tmp = (a * b) + ((x * y) + (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 (Float64(c * i) <= -3.05e+153)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 5e+248)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + 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 ((c * i) <= -3.05e+153)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 5e+248)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.05e+153], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e+248], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.0499999999999999e153

   1. Initial program 95.0%

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

   2. Taylor expanded in a around 0 87.9%

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

   3. Taylor expanded in x around 0 87.2%

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

   if -3.0499999999999999e153 < (*.f64 c i) < 4.9999999999999996e248

   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 c around 0 90.0%

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

   if 4.9999999999999996e248 < (*.f64 c i)

   1. Initial program 88.2%

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

   2. Taylor expanded in z around 0 88.2%

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

   3. Taylor expanded in x around 0 94.1%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.05 \cdot 10^{+153}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{+248}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 15: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+267}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-37}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.3e+267)
   (* z t)
   (if (<= z 2e-37) (+ (* a b) (+ (* c i) (* x y))) (+ (* 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 (z <= -2.3e+267) {
		tmp = z * t;
	} else if (z <= 2e-37) {
		tmp = (a * b) + ((c * i) + (x * y));
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.3d+267)) then
        tmp = z * t
    else if (z <= 2d-37) then
        tmp = (a * b) + ((c * i) + (x * y))
    else
        tmp = (c * i) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.3e+267) {
		tmp = z * t;
	} else if (z <= 2e-37) {
		tmp = (a * b) + ((c * i) + (x * y));
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.3e+267:
		tmp = z * t
	elif z <= 2e-37:
		tmp = (a * b) + ((c * i) + (x * y))
	else:
		tmp = (c * i) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.3e+267)
		tmp = Float64(z * t);
	elseif (z <= 2e-37)
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.3e+267)
		tmp = z * t;
	elseif (z <= 2e-37)
		tmp = (a * b) + ((c * i) + (x * y));
	else
		tmp = (c * i) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.3e+267], N[(z * t), $MachinePrecision], If[LessEqual[z, 2e-37], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000021e267

   1. Initial program 88.9%

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

   2. Taylor expanded in z around inf 100.0%

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

   if -2.30000000000000021e267 < z < 2.00000000000000013e-37

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 86.3%

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

   if 2.00000000000000013e-37 < z

   1. Initial program 93.0%

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

   2. Taylor expanded in a around 0 72.3%

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

   3. Taylor expanded in x around 0 59.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+267}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-37}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 16: 43.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+126} \lor \neg \left(a \cdot b \leq 3.3 \cdot 10^{+127}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.15e+126) (not (<= (* a b) 3.3e+127))) (* 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) <= -1.15e+126) || !((a * b) <= 3.3e+127)) {
		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) <= (-1.15d+126)) .or. (.not. ((a * b) <= 3.3d+127))) 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) <= -1.15e+126) || !((a * b) <= 3.3e+127)) {
		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) <= -1.15e+126) or not ((a * b) <= 3.3e+127):
		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) <= -1.15e+126) || !(Float64(a * b) <= 3.3e+127))
		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) <= -1.15e+126) || ~(((a * b) <= 3.3e+127)))
		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], -1.15e+126], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3.3e+127]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.15e126 or 3.29999999999999977e127 < (*.f64 a b)

   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 79.2%

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

   if -1.15e126 < (*.f64 a b) < 3.29999999999999977e127

   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 inf 34.3%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+126} \lor \neg \left(a \cdot b \leq 3.3 \cdot 10^{+127}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 17: 27.5% 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 97.6%

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

2. Taylor expanded in a around inf 30.3%

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

3. Final simplification 30.3%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023333 
(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)))