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

Percentage Accurate: 95.8% → 98.2%

Time: 9.4s

Alternatives: 17

Speedup: 0.5×

• 41.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. associate-+l+ 93.3%

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

   2. associate-+l+ 93.3%

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

   3. fma-def 94.9%

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

   4. fma-def 96.1%

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

   5. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 97.8% 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 93.3%

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

   1. +-commutative 93.3%

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

   2. fma-def 94.5%

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

   3. associate-+l+ 94.5%

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

   4. fma-def 96.1%

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

   5. fma-def 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 3: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) + ((a * b) + ((z * t) + (x * y)))) <= ((double) INFINITY)) {
		tmp = (z * t) + (fma(a, b, (c * i)) + (x * y));
	} else {
		tmp = fma(y, x, (a * b));
	}
	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(z * t) + Float64(x * y)))) <= Inf)
		tmp = Float64(Float64(z * t) + Float64(fma(a, b, Float64(c * i)) + Float64(x * y)));
	else
		tmp = fma(y, x, Float64(a * b));
	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[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(z * t), $MachinePrecision] + N[(N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. fma-udef 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+r+ 100.0%

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

      9. fma-def 100.0%

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

   5. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-+l+ 0.0%

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

      3. fma-def 23.5%

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

      4. fma-def 41.2%

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

      5. fma-def 58.8%

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

   3. Simplified 58.8%

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

   4. Taylor expanded in z around 0 41.2%

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

   5. Taylor expanded in c around 0 41.2%

      \[\leadsto \color{blue}{a \cdot b + y \cdot x} \]
   6. Step-by-step derivation

      1. +-commutative 41.2%

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

      2. fma-def 58.9%

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

   7. Applied egg-rr 58.9%

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

4. Final simplification 97.2%

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

Alternative 4: 97.8% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* z t) (* x y))))))
   (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) + ((z * t) + (x * y)));
	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(z * t) + Float64(x * y))))
	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[(z * t), $MachinePrecision] + N[(x * y), $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 x around 0 23.5%

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

      1. fma-def 35.3%

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

   4. Simplified 35.3%

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

   5. Taylor expanded in t around 0 35.5%

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

      1. +-commutative 35.5%

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

      2. fma-def 53.2%

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

   7. Simplified 53.2%

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

4. Final simplification 96.9%

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

Alternative 5: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-+l+ 0.0%

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

      3. fma-def 23.5%

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

      4. fma-def 41.2%

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

      5. fma-def 58.8%

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

   3. Simplified 58.8%

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

   4. Taylor expanded in z around 0 41.2%

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

   5. Taylor expanded in c around 0 41.2%

      \[\leadsto \color{blue}{a \cdot b + y \cdot x} \]
   6. Step-by-step derivation

      1. +-commutative 41.2%

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

      2. fma-def 58.9%

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

   7. Applied egg-rr 58.9%

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

4. Final simplification 97.2%

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

Alternative 6: 96.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. associate-+l+ 0.0%

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

      3. fma-def 23.5%

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

      4. fma-def 41.2%

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

      5. fma-def 58.8%

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

   3. Simplified 58.8%

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

   4. Taylor expanded in z around 0 41.2%

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

   5. Taylor expanded in a around inf 41.7%

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

4. Final simplification 96.1%

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

Alternative 7: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.9 \cdot 10^{+90}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.1 \cdot 10^{+16} \lor \neg \left(c \cdot i \leq 2.4 \cdot 10^{+69}\right) \land c \cdot i \leq 6 \cdot 10^{+179}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.9e+90)
   (+ (* c i) (* a b))
   (if (or (<= (* c i) 3.1e+16)
           (and (not (<= (* c i) 2.4e+69)) (<= (* c i) 6e+179)))
     (+ (* a b) (* 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 ((c * i) <= -2.9e+90) {
		tmp = (c * i) + (a * b);
	} else if (((c * i) <= 3.1e+16) || (!((c * i) <= 2.4e+69) && ((c * i) <= 6e+179))) {
		tmp = (a * b) + (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 ((c * i) <= (-2.9d+90)) then
        tmp = (c * i) + (a * b)
    else if (((c * i) <= 3.1d+16) .or. (.not. ((c * i) <= 2.4d+69)) .and. ((c * i) <= 6d+179)) then
        tmp = (a * b) + (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 ((c * i) <= -2.9e+90) {
		tmp = (c * i) + (a * b);
	} else if (((c * i) <= 3.1e+16) || (!((c * i) <= 2.4e+69) && ((c * i) <= 6e+179))) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.9e+90:
		tmp = (c * i) + (a * b)
	elif ((c * i) <= 3.1e+16) or (not ((c * i) <= 2.4e+69) and ((c * i) <= 6e+179)):
		tmp = (a * b) + (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 (Float64(c * i) <= -2.9e+90)
		tmp = Float64(Float64(c * i) + Float64(a * b));
	elseif ((Float64(c * i) <= 3.1e+16) || (!(Float64(c * i) <= 2.4e+69) && (Float64(c * i) <= 6e+179)))
		tmp = Float64(Float64(a * b) + 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 ((c * i) <= -2.9e+90)
		tmp = (c * i) + (a * b);
	elseif (((c * i) <= 3.1e+16) || (~(((c * i) <= 2.4e+69)) && ((c * i) <= 6e+179)))
		tmp = (a * b) + (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[N[(c * i), $MachinePrecision], -2.9e+90], N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(c * i), $MachinePrecision], 3.1e+16], And[N[Not[LessEqual[N[(c * i), $MachinePrecision], 2.4e+69]], $MachinePrecision], LessEqual[N[(c * i), $MachinePrecision], 6e+179]]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.9000000000000001e90

   1. Initial program 88.6%

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

   2. Taylor expanded in a around inf 79.4%

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

   if -2.9000000000000001e90 < (*.f64 c i) < 3.1e16 or 2.4000000000000002e69 < (*.f64 c i) < 5.9999999999999996e179

   1. Initial program 95.9%

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

      1. associate-+l+ 95.9%

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

      2. associate-+l+ 95.9%

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

      3. fma-def 97.6%

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

      4. fma-def 98.8%

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

      5. fma-def 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around 0 79.4%

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

   5. Taylor expanded in c around 0 70.8%

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

   if 3.1e16 < (*.f64 c i) < 2.4000000000000002e69 or 5.9999999999999996e179 < (*.f64 c i)

   1. Initial program 87.5%

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

   2. Taylor expanded in z around inf 76.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.9 \cdot 10^{+90}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.1 \cdot 10^{+16} \lor \neg \left(c \cdot i \leq 2.4 \cdot 10^{+69}\right) \land c \cdot i \leq 6 \cdot 10^{+179}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 8: 65.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -7.5 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 8.8 \cdot 10^{-79}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.1 \cdot 10^{-8}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.6 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* a b) -7.5e-15)
     t_1
     (if (<= (* a b) 8.8e-79)
       (+ (* c i) (* x y))
       (if (<= (* a b) 1.1e-8)
         (+ (* c i) (* z t))
         (if (<= (* a b) 6.6e+90) t_1 (+ (* c i) (* a b))))))))

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 tmp;
	if ((a * b) <= -7.5e-15) {
		tmp = t_1;
	} else if ((a * b) <= 8.8e-79) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 1.1e-8) {
		tmp = (c * i) + (z * t);
	} else if ((a * b) <= 6.6e+90) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    if ((a * b) <= (-7.5d-15)) then
        tmp = t_1
    else if ((a * b) <= 8.8d-79) then
        tmp = (c * i) + (x * y)
    else if ((a * b) <= 1.1d-8) then
        tmp = (c * i) + (z * t)
    else if ((a * b) <= 6.6d+90) then
        tmp = t_1
    else
        tmp = (c * i) + (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -7.5e-15) {
		tmp = t_1;
	} else if ((a * b) <= 8.8e-79) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 1.1e-8) {
		tmp = (c * i) + (z * t);
	} else if ((a * b) <= 6.6e+90) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if (a * b) <= -7.5e-15:
		tmp = t_1
	elif (a * b) <= 8.8e-79:
		tmp = (c * i) + (x * y)
	elif (a * b) <= 1.1e-8:
		tmp = (c * i) + (z * t)
	elif (a * b) <= 6.6e+90:
		tmp = t_1
	else:
		tmp = (c * i) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -7.5e-15)
		tmp = t_1;
	elseif (Float64(a * b) <= 8.8e-79)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(a * b) <= 1.1e-8)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(a * b) <= 6.6e+90)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * i) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	tmp = 0.0;
	if ((a * b) <= -7.5e-15)
		tmp = t_1;
	elseif ((a * b) <= 8.8e-79)
		tmp = (c * i) + (x * y);
	elseif ((a * b) <= 1.1e-8)
		tmp = (c * i) + (z * t);
	elseif ((a * b) <= 6.6e+90)
		tmp = t_1;
	else
		tmp = (c * i) + (a * b);
	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]}, If[LessEqual[N[(a * b), $MachinePrecision], -7.5e-15], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 8.8e-79], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.1e-8], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6.6e+90], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -7.4999999999999996e-15 or 1.0999999999999999e-8 < (*.f64 a b) < 6.60000000000000016e90

   1. Initial program 93.4%

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

      1. associate-+l+ 93.4%

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

      2. associate-+l+ 93.4%

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

      3. fma-def 94.5%

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

      4. fma-def 95.6%

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

      5. fma-def 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in z around 0 84.2%

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

   5. Taylor expanded in c around 0 72.3%

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

   if -7.4999999999999996e-15 < (*.f64 a b) < 8.7999999999999995e-79

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 74.6%

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

   if 8.7999999999999995e-79 < (*.f64 a b) < 1.0999999999999999e-8

   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 82.8%

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

   if 6.60000000000000016e90 < (*.f64 a b)

   1. Initial program 85.7%

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

   2. Taylor expanded in a around inf 82.9%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.5 \cdot 10^{-15}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.8 \cdot 10^{-79}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.1 \cdot 10^{-8}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.6 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 9: 43.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.75 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.8 \cdot 10^{-213}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{-91}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.7 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.75e+94)
   (* c i)
   (if (<= (* c i) 2.8e-213)
     (* a b)
     (if (<= (* c i) 2.1e-91)
       (* z t)
       (if (<= (* c i) 4.7e+140) (* a b) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.75e+94) {
		tmp = c * i;
	} else if ((c * i) <= 2.8e-213) {
		tmp = a * b;
	} else if ((c * i) <= 2.1e-91) {
		tmp = z * t;
	} else if ((c * i) <= 4.7e+140) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2.75d+94)) then
        tmp = c * i
    else if ((c * i) <= 2.8d-213) then
        tmp = a * b
    else if ((c * i) <= 2.1d-91) then
        tmp = z * t
    else if ((c * i) <= 4.7d+140) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.75e+94) {
		tmp = c * i;
	} else if ((c * i) <= 2.8e-213) {
		tmp = a * b;
	} else if ((c * i) <= 2.1e-91) {
		tmp = z * t;
	} else if ((c * i) <= 4.7e+140) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.75e+94:
		tmp = c * i
	elif (c * i) <= 2.8e-213:
		tmp = a * b
	elif (c * i) <= 2.1e-91:
		tmp = z * t
	elif (c * i) <= 4.7e+140:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.75e+94)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 2.8e-213)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.1e-91)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 4.7e+140)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2.75e+94)
		tmp = c * i;
	elseif ((c * i) <= 2.8e-213)
		tmp = a * b;
	elseif ((c * i) <= 2.1e-91)
		tmp = z * t;
	elseif ((c * i) <= 4.7e+140)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2.75e+94], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.8e-213], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.1e-91], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.7e+140], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.7499999999999999e94 or 4.7000000000000003e140 < (*.f64 c i)

   1. Initial program 87.3%

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

   2. Taylor expanded in c around inf 69.7%

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

   if -2.7499999999999999e94 < (*.f64 c i) < 2.8e-213 or 2.0999999999999999e-91 < (*.f64 c i) < 4.7000000000000003e140

   1. Initial program 95.6%

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

      1. associate-+l+ 95.6%

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

      2. associate-+l+ 95.6%

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

      3. fma-def 97.5%

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

      4. fma-def 98.7%

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

      5. fma-def 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 79.6%

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

   5. Taylor expanded in a around inf 40.1%

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

   if 2.8e-213 < (*.f64 c i) < 2.0999999999999999e-91

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 54.7%

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

      1. fma-def 54.7%

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

   4. Simplified 54.7%

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

      1. fma-udef 54.7%

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

      2. *-commutative 54.7%

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

      3. +-commutative 54.7%

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

   6. Applied egg-rr 54.7%

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

   7. Taylor expanded in z around inf 47.7%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.75 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.8 \cdot 10^{-213}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.1 \cdot 10^{-91}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.7 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 10: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 4.6 \cdot 10^{-79}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* a b))))
   (if (<= (* c i) -8.5e-9)
     t_1
     (if (<= (* c i) 4.6e-79)
       (+ (* a b) (* z t))
       (if (<= (* c i) 1.05e-34) (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (a * b);
	double tmp;
	if ((c * i) <= -8.5e-9) {
		tmp = t_1;
	} else if ((c * i) <= 4.6e-79) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 1.05e-34) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (a * b)
    if ((c * i) <= (-8.5d-9)) then
        tmp = t_1
    else if ((c * i) <= 4.6d-79) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 1.05d-34) then
        tmp = x * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (a * b);
	double tmp;
	if ((c * i) <= -8.5e-9) {
		tmp = t_1;
	} else if ((c * i) <= 4.6e-79) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 1.05e-34) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (a * b)
	tmp = 0
	if (c * i) <= -8.5e-9:
		tmp = t_1
	elif (c * i) <= 4.6e-79:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 1.05e-34:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(a * b))
	tmp = 0.0
	if (Float64(c * i) <= -8.5e-9)
		tmp = t_1;
	elseif (Float64(c * i) <= 4.6e-79)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 1.05e-34)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (a * b);
	tmp = 0.0;
	if ((c * i) <= -8.5e-9)
		tmp = t_1;
	elseif ((c * i) <= 4.6e-79)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 1.05e-34)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -8.5e-9], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 4.6e-79], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.05e-34], N[(x * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -8.5e-9 or 1.05e-34 < (*.f64 c i)

   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 a around inf 65.9%

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

   if -8.5e-9 < (*.f64 c i) < 4.60000000000000023e-79

   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 x around 0 66.4%

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

      1. fma-def 67.3%

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

   4. Simplified 67.3%

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

      1. fma-udef 66.4%

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

      2. *-commutative 66.4%

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

      3. +-commutative 66.4%

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

   6. Applied egg-rr 66.4%

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

   7. Taylor expanded in c around 0 64.3%

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

   if 4.60000000000000023e-79 < (*.f64 c i) < 1.05e-34

   1. Initial program 85.7%

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

      1. associate-+l+ 85.7%

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

      2. associate-+l+ 85.7%

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

      3. fma-def 92.9%

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

      4. fma-def 92.9%

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

      5. fma-def 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 93.6%

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

   5. Taylor expanded in x around inf 79.6%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.6 \cdot 10^{-79}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{-34}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 11: 87.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+135} \lor \neg \left(z \cdot t \leq 1\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -1e+135) (not (<= (* z t) 1.0)))
   (+ (* c i) (+ (* a b) (* z t)))
   (+ (* c i) (+ (* a b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -1e+135) || !((z * t) <= 1.0)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((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 (((z * t) <= (-1d+135)) .or. (.not. ((z * t) <= 1.0d0))) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((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 (((z * t) <= -1e+135) || !((z * t) <= 1.0)) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((z * t) <= -1e+135) or not ((z * t) <= 1.0):
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(z * t) <= -1e+135) || !(Float64(z * t) <= 1.0))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + 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 (((z * t) <= -1e+135) || ~(((z * t) <= 1.0)))
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -1e+135], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.99999999999999962e134 or 1 < (*.f64 z t)

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0 80.3%

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

   if -9.99999999999999962e134 < (*.f64 z t) < 1

   1. Initial program 97.0%

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

   2. Taylor expanded in z around 0 95.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+135} \lor \neg \left(z \cdot t \leq 1\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]

Alternative 12: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+92}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{+185}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -6.5e+92)
   (+ (* c i) (* a b))
   (if (<= (* c i) 3.6e+185) (+ (* a b) (* x y)) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -6.5e+92) {
		tmp = (c * i) + (a * b);
	} else if ((c * i) <= 3.6e+185) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-6.5d+92)) then
        tmp = (c * i) + (a * b)
    else if ((c * i) <= 3.6d+185) then
        tmp = (a * b) + (x * y)
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -6.5e+92) {
		tmp = (c * i) + (a * b);
	} else if ((c * i) <= 3.6e+185) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -6.5e+92:
		tmp = (c * i) + (a * b)
	elif (c * i) <= 3.6e+185:
		tmp = (a * b) + (x * y)
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -6.5e+92)
		tmp = Float64(Float64(c * i) + Float64(a * b));
	elseif (Float64(c * i) <= 3.6e+185)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -6.5e+92)
		tmp = (c * i) + (a * b);
	elseif ((c * i) <= 3.6e+185)
		tmp = (a * b) + (x * y);
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -6.5e+92], N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.6e+185], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.49999999999999999e92

   1. Initial program 88.6%

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

   2. Taylor expanded in a around inf 79.4%

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

   if -6.49999999999999999e92 < (*.f64 c i) < 3.60000000000000029e185

   1. Initial program 96.2%

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

      1. associate-+l+ 96.2%

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

      2. associate-+l+ 96.2%

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

      3. fma-def 97.8%

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

      4. fma-def 98.9%

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

      5. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 77.5%

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

   5. Taylor expanded in c around 0 67.3%

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

   if 3.60000000000000029e185 < (*.f64 c i)

   1. Initial program 80.8%

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

   2. Taylor expanded in c around inf 77.4%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+92}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.6 \cdot 10^{+185}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 13: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;y \leq -3850:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= y -3850.0)
     t_1
     (if (<= y 1.3e+94)
       (+ (* c i) (+ (* a b) (* z t)))
       (if (<= y 4.2e+224) t_1 (+ (* c i) (* 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) + (x * y);
	double tmp;
	if (y <= -3850.0) {
		tmp = t_1;
	} else if (y <= 1.3e+94) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if (y <= 4.2e+224) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    if (y <= (-3850.0d0)) then
        tmp = t_1
    else if (y <= 1.3d+94) then
        tmp = (c * i) + ((a * b) + (z * t))
    else if (y <= 4.2d+224) then
        tmp = t_1
    else
        tmp = (c * i) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if (y <= -3850.0) {
		tmp = t_1;
	} else if (y <= 1.3e+94) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if (y <= 4.2e+224) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if y <= -3850.0:
		tmp = t_1
	elif y <= 1.3e+94:
		tmp = (c * i) + ((a * b) + (z * t))
	elif y <= 4.2e+224:
		tmp = t_1
	else:
		tmp = (c * i) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (y <= -3850.0)
		tmp = t_1;
	elseif (y <= 1.3e+94)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	elseif (y <= 4.2e+224)
		tmp = t_1;
	else
		tmp = Float64(Float64(c * i) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	tmp = 0.0;
	if (y <= -3850.0)
		tmp = t_1;
	elseif (y <= 1.3e+94)
		tmp = (c * i) + ((a * b) + (z * t));
	elseif (y <= 4.2e+224)
		tmp = t_1;
	else
		tmp = (c * i) + (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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3850.0], t$95$1, If[LessEqual[y, 1.3e+94], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+224], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3850 or 1.3e94 < y < 4.2000000000000003e224

   1. Initial program 90.4%

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

      1. associate-+l+ 90.4%

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

      2. associate-+l+ 90.4%

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

      3. fma-def 91.6%

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

      4. fma-def 94.0%

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

      5. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 83.5%

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

   5. Taylor expanded in c around 0 75.4%

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

   if -3850 < y < 1.3e94

   1. Initial program 97.4%

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

   2. Taylor expanded in x around 0 83.3%

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

   if 4.2000000000000003e224 < y

   1. Initial program 72.2%

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

   2. Taylor expanded in x around inf 72.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3850:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+224}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]

Alternative 14: 38.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-279}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-265}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-104}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.25)
   (* x y)
   (if (<= y -2.2e-279)
     (* a b)
     (if (<= y 2.9e-265)
       (* c i)
       (if (<= y 4e-104) (* a b) (if (<= y 1.5e+94) (* c i) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.25) {
		tmp = x * y;
	} else if (y <= -2.2e-279) {
		tmp = a * b;
	} else if (y <= 2.9e-265) {
		tmp = c * i;
	} else if (y <= 4e-104) {
		tmp = a * b;
	} else if (y <= 1.5e+94) {
		tmp = c * i;
	} 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) :: tmp
    if (y <= (-1.25d0)) then
        tmp = x * y
    else if (y <= (-2.2d-279)) then
        tmp = a * b
    else if (y <= 2.9d-265) then
        tmp = c * i
    else if (y <= 4d-104) then
        tmp = a * b
    else if (y <= 1.5d+94) then
        tmp = c * i
    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 tmp;
	if (y <= -1.25) {
		tmp = x * y;
	} else if (y <= -2.2e-279) {
		tmp = a * b;
	} else if (y <= 2.9e-265) {
		tmp = c * i;
	} else if (y <= 4e-104) {
		tmp = a * b;
	} else if (y <= 1.5e+94) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.25:
		tmp = x * y
	elif y <= -2.2e-279:
		tmp = a * b
	elif y <= 2.9e-265:
		tmp = c * i
	elif y <= 4e-104:
		tmp = a * b
	elif y <= 1.5e+94:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.25)
		tmp = Float64(x * y);
	elseif (y <= -2.2e-279)
		tmp = Float64(a * b);
	elseif (y <= 2.9e-265)
		tmp = Float64(c * i);
	elseif (y <= 4e-104)
		tmp = Float64(a * b);
	elseif (y <= 1.5e+94)
		tmp = Float64(c * i);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.25)
		tmp = x * y;
	elseif (y <= -2.2e-279)
		tmp = a * b;
	elseif (y <= 2.9e-265)
		tmp = c * i;
	elseif (y <= 4e-104)
		tmp = a * b;
	elseif (y <= 1.5e+94)
		tmp = c * i;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.25], N[(x * y), $MachinePrecision], If[LessEqual[y, -2.2e-279], N[(a * b), $MachinePrecision], If[LessEqual[y, 2.9e-265], N[(c * i), $MachinePrecision], If[LessEqual[y, 4e-104], N[(a * b), $MachinePrecision], If[LessEqual[y, 1.5e+94], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25 or 1.5e94 < y

   1. Initial program 87.1%

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

      1. associate-+l+ 87.1%

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

      2. associate-+l+ 87.1%

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

      3. fma-def 91.1%

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

      4. fma-def 93.1%

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

      5. fma-def 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 83.5%

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

   5. Taylor expanded in x around inf 52.0%

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

   if -1.25 < y < -2.2e-279 or 2.89999999999999975e-265 < y < 3.99999999999999971e-104

   1. Initial program 99.1%

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

      1. associate-+l+ 99.1%

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

      2. associate-+l+ 99.1%

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

      3. fma-def 99.1%

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

      4. fma-def 99.1%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 76.0%

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

   5. Taylor expanded in a around inf 36.6%

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

   if -2.2e-279 < y < 2.89999999999999975e-265 or 3.99999999999999971e-104 < y < 1.5e94

   1. Initial program 93.1%

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

   2. Taylor expanded in c around inf 44.0%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-279}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-265}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-104}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+94}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 15: 43.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+144}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -4.6e+89) (* c i) (if (<= (* c i) 3e+144) (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4.6e+89) {
		tmp = c * i;
	} else if ((c * i) <= 3e+144) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-4.6d+89)) then
        tmp = c * i
    else if ((c * i) <= 3d+144) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -4.6e+89) {
		tmp = c * i;
	} else if ((c * i) <= 3e+144) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -4.6e+89:
		tmp = c * i
	elif (c * i) <= 3e+144:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -4.6e+89)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 3e+144)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -4.6e+89)
		tmp = c * i;
	elseif ((c * i) <= 3e+144)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -4.6e+89], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3e+144], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -4.5999999999999998e89 or 2.9999999999999999e144 < (*.f64 c i)

   1. Initial program 87.3%

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

   2. Taylor expanded in c around inf 69.7%

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

   if -4.5999999999999998e89 < (*.f64 c i) < 2.9999999999999999e144

   1. Initial program 96.0%

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

      1. associate-+l+ 96.0%

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

      2. associate-+l+ 96.0%

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

      3. fma-def 97.7%

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

      4. fma-def 98.8%

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

      5. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 77.5%

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

   5. Taylor expanded in a around inf 37.5%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -4.6 \cdot 10^{+89}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+144}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 16: 54.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3900:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+122}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3900.0) (* x y) (if (<= y 6.6e+122) (+ (* c i) (* a b)) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3900.0) {
		tmp = x * y;
	} else if (y <= 6.6e+122) {
		tmp = (c * i) + (a * b);
	} 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) :: tmp
    if (y <= (-3900.0d0)) then
        tmp = x * y
    else if (y <= 6.6d+122) then
        tmp = (c * i) + (a * b)
    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 tmp;
	if (y <= -3900.0) {
		tmp = x * y;
	} else if (y <= 6.6e+122) {
		tmp = (c * i) + (a * b);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3900.0:
		tmp = x * y
	elif y <= 6.6e+122:
		tmp = (c * i) + (a * b)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3900.0)
		tmp = Float64(x * y);
	elseif (y <= 6.6e+122)
		tmp = Float64(Float64(c * i) + Float64(a * b));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3900.0)
		tmp = x * y;
	elseif (y <= 6.6e+122)
		tmp = (c * i) + (a * b);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3900.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 6.6e+122], N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3900 or 6.5999999999999998e122 < y

   1. Initial program 87.5%

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

      1. associate-+l+ 87.5%

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

      2. associate-+l+ 87.5%

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

      3. fma-def 91.7%

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

      4. fma-def 92.7%

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

      5. fma-def 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 82.6%

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

   5. Taylor expanded in x around inf 52.5%

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

   if -3900 < y < 6.5999999999999998e122

   1. Initial program 96.8%

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

   2. Taylor expanded in a around inf 63.6%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3900:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+122}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 17: 27.4% 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 93.3%

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

   1. associate-+l+ 93.3%

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

   2. associate-+l+ 93.3%

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

   3. fma-def 94.9%

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

   4. fma-def 96.1%

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

   5. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in z around 0 80.1%

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

5. Taylor expanded in a around inf 30.4%

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

6. Final simplification 30.4%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023200 
(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)))