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

Percentage Accurate: 95.5% → 97.5%

Time: 8.4s

Alternatives: 15

Speedup: 0.5×

• 41.6% 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: 95.5% 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: 97.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-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%

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

      2. fma-udef 100.0%

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

      3. associate-+l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

   5. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 20.0%

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

      3. associate-+l+ 20.0%

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

      4. fma-def 20.0%

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

      5. fma-def 30.0%

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

   3. Simplified 30.0%

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

      1. fma-udef 30.0%

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

      2. fma-udef 20.0%

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

      3. associate-+l+ 20.0%

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

      4. +-commutative 20.0%

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

      5. associate-+r+ 20.0%

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

   5. Applied egg-rr 20.0%

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

   6. Taylor expanded in z around inf 60.0%

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

4. Final simplification 98.4%

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

Alternative 2: 97.9% 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 96.1%

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

   1. associate-+l+ 96.1%

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

   2. associate-+l+ 96.1%

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

   3. fma-def 96.5%

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

   4. fma-def 96.8%

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

   5. fma-def 97.6%

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

3. Simplified 97.6%

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

4. Final simplification 97.6%

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

Alternative 3: 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 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-def 96.9%

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

   3. associate-+l+ 96.9%

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

   4. fma-def 96.9%

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

   5. fma-def 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 4: 97.5% accurate, 0.1× speedup

Math

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

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 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) + ((z * t) + (x * y)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(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(z * t) + Float64(x * y))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(c, i, Float64(z * t));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 20.0%

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

      3. associate-+l+ 20.0%

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

      4. fma-def 20.0%

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

      5. fma-def 30.0%

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

   3. Simplified 30.0%

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

      1. fma-udef 30.0%

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

      2. fma-udef 20.0%

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

      3. associate-+l+ 20.0%

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

      4. +-commutative 20.0%

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

      5. associate-+r+ 20.0%

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

   5. Applied egg-rr 20.0%

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

   6. Taylor expanded in z around inf 60.0%

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

4. Final simplification 98.4%

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

Alternative 5: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;c \cdot i \leq -8.2 \cdot 10^{+262}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -5.4 \cdot 10^{+124}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.15 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -1.05 \cdot 10^{-242}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.4 \cdot 10^{+62} \lor \neg \left(c \cdot i \leq 7.1 \cdot 10^{+115}\right) \land c \cdot i \leq 8.5 \cdot 10^{+261}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* c i) -8.2e+262)
     (* c i)
     (if (<= (* c i) -1.3e+206)
       t_1
       (if (<= (* c i) -5.4e+124)
         (* c i)
         (if (<= (* c i) -3.15e-137)
           t_1
           (if (<= (* c i) -1.05e-242)
             (* z t)
             (if (or (<= (* c i) 2.4e+62)
                     (and (not (<= (* c i) 7.1e+115)) (<= (* c i) 8.5e+261)))
               t_1
               (* c i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -8.2e+262) {
		tmp = c * i;
	} else if ((c * i) <= -1.3e+206) {
		tmp = t_1;
	} else if ((c * i) <= -5.4e+124) {
		tmp = c * i;
	} else if ((c * i) <= -3.15e-137) {
		tmp = t_1;
	} else if ((c * i) <= -1.05e-242) {
		tmp = z * t;
	} else if (((c * i) <= 2.4e+62) || (!((c * i) <= 7.1e+115) && ((c * i) <= 8.5e+261))) {
		tmp = t_1;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    if ((c * i) <= (-8.2d+262)) then
        tmp = c * i
    else if ((c * i) <= (-1.3d+206)) then
        tmp = t_1
    else if ((c * i) <= (-5.4d+124)) then
        tmp = c * i
    else if ((c * i) <= (-3.15d-137)) then
        tmp = t_1
    else if ((c * i) <= (-1.05d-242)) then
        tmp = z * t
    else if (((c * i) <= 2.4d+62) .or. (.not. ((c * i) <= 7.1d+115)) .and. ((c * i) <= 8.5d+261)) then
        tmp = t_1
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -8.2e+262) {
		tmp = c * i;
	} else if ((c * i) <= -1.3e+206) {
		tmp = t_1;
	} else if ((c * i) <= -5.4e+124) {
		tmp = c * i;
	} else if ((c * i) <= -3.15e-137) {
		tmp = t_1;
	} else if ((c * i) <= -1.05e-242) {
		tmp = z * t;
	} else if (((c * i) <= 2.4e+62) || (!((c * i) <= 7.1e+115) && ((c * i) <= 8.5e+261))) {
		tmp = t_1;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if (c * i) <= -8.2e+262:
		tmp = c * i
	elif (c * i) <= -1.3e+206:
		tmp = t_1
	elif (c * i) <= -5.4e+124:
		tmp = c * i
	elif (c * i) <= -3.15e-137:
		tmp = t_1
	elif (c * i) <= -1.05e-242:
		tmp = z * t
	elif ((c * i) <= 2.4e+62) or (not ((c * i) <= 7.1e+115) and ((c * i) <= 8.5e+261)):
		tmp = t_1
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(c * i) <= -8.2e+262)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.3e+206)
		tmp = t_1;
	elseif (Float64(c * i) <= -5.4e+124)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -3.15e-137)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.05e-242)
		tmp = Float64(z * t);
	elseif ((Float64(c * i) <= 2.4e+62) || (!(Float64(c * i) <= 7.1e+115) && (Float64(c * i) <= 8.5e+261)))
		tmp = t_1;
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	tmp = 0.0;
	if ((c * i) <= -8.2e+262)
		tmp = c * i;
	elseif ((c * i) <= -1.3e+206)
		tmp = t_1;
	elseif ((c * i) <= -5.4e+124)
		tmp = c * i;
	elseif ((c * i) <= -3.15e-137)
		tmp = t_1;
	elseif ((c * i) <= -1.05e-242)
		tmp = z * t;
	elseif (((c * i) <= 2.4e+62) || (~(((c * i) <= 7.1e+115)) && ((c * i) <= 8.5e+261)))
		tmp = t_1;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -8.2e+262], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.3e+206], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -5.4e+124], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -3.15e-137], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.05e-242], N[(z * t), $MachinePrecision], If[Or[LessEqual[N[(c * i), $MachinePrecision], 2.4e+62], And[N[Not[LessEqual[N[(c * i), $MachinePrecision], 7.1e+115]], $MachinePrecision], LessEqual[N[(c * i), $MachinePrecision], 8.5e+261]]], t$95$1, N[(c * i), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -8.20000000000000055e262 or -1.29999999999999994e206 < (*.f64 c i) < -5.39999999999999956e124 or 2.4e62 < (*.f64 c i) < 7.0999999999999997e115 or 8.5000000000000005e261 < (*.f64 c i)

   1. Initial program 92.8%

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

   2. Taylor expanded in c around inf 82.5%

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

   if -8.20000000000000055e262 < (*.f64 c i) < -1.29999999999999994e206 or -5.39999999999999956e124 < (*.f64 c i) < -3.15e-137 or -1.05000000000000009e-242 < (*.f64 c i) < 2.4e62 or 7.0999999999999997e115 < (*.f64 c i) < 8.5000000000000005e261

   1. Initial program 97.1%

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

      1. associate-+l+ 97.1%

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

      2. associate-+l+ 97.1%

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

      3. fma-def 97.1%

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

      4. fma-def 97.7%

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

      5. fma-def 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around 0 72.6%

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

   5. Taylor expanded in c around 0 64.3%

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

   if -3.15e-137 < (*.f64 c i) < -1.05000000000000009e-242

   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 70.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.2 \cdot 10^{+262}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{+206}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -5.4 \cdot 10^{+124}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.15 \cdot 10^{-137}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.05 \cdot 10^{-242}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.4 \cdot 10^{+62} \lor \neg \left(c \cdot i \leq 7.1 \cdot 10^{+115}\right) \land c \cdot i \leq 8.5 \cdot 10^{+261}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 6: 97.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* z t) (* x y))))))
   (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) + ((z * t) + (x * y)));
	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) + ((z * t) + (x * y)));
	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) + ((z * t) + (x * y)))
	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(z * t) + Float64(x * y))))
	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) + ((z * t) + (x * y)));
	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[(z * t), $MachinePrecision] + N[(x * y), $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 x around 0 10.0%

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

   3. Taylor expanded in a around 0 50.0%

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

4. Final simplification 98.0%

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

Alternative 7: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -5000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-317}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{-307}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* a b) -5000000.0)
     t_2
     (if (<= (* a b) -1e-317)
       t_1
       (if (<= (* a b) 4.8e-307)
         (+ (* c i) (* x y))
         (if (<= (* a b) 1.05e+125) 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 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -5000000.0) {
		tmp = t_2;
	} else if ((a * b) <= -1e-317) {
		tmp = t_1;
	} else if ((a * b) <= 4.8e-307) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 1.05e+125) {
		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 = (c * i) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((a * b) <= (-5000000.0d0)) then
        tmp = t_2
    else if ((a * b) <= (-1d-317)) then
        tmp = t_1
    else if ((a * b) <= 4.8d-307) then
        tmp = (c * i) + (x * y)
    else if ((a * b) <= 1.05d+125) 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 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((a * b) <= -5000000.0) {
		tmp = t_2;
	} else if ((a * b) <= -1e-317) {
		tmp = t_1;
	} else if ((a * b) <= 4.8e-307) {
		tmp = (c * i) + (x * y);
	} else if ((a * b) <= 1.05e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (a * b) <= -5000000.0:
		tmp = t_2
	elif (a * b) <= -1e-317:
		tmp = t_1
	elif (a * b) <= 4.8e-307:
		tmp = (c * i) + (x * y)
	elif (a * b) <= 1.05e+125:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -5000000.0)
		tmp = t_2;
	elseif (Float64(a * b) <= -1e-317)
		tmp = t_1;
	elseif (Float64(a * b) <= 4.8e-307)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(a * b) <= 1.05e+125)
		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 = (c * i) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((a * b) <= -5000000.0)
		tmp = t_2;
	elseif ((a * b) <= -1e-317)
		tmp = t_1;
	elseif ((a * b) <= 4.8e-307)
		tmp = (c * i) + (x * y);
	elseif ((a * b) <= 1.05e+125)
		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[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5000000.0], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1e-317], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4.8e-307], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.05e+125], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5e6 or 1.05e125 < (*.f64 a b)

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-+l+ 91.5%

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

      3. fma-def 92.4%

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

      4. fma-def 93.4%

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

      5. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 84.5%

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

   5. Taylor expanded in c around 0 75.7%

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

   if -5e6 < (*.f64 a b) < -1.00000023e-317 or 4.80000000000000036e-307 < (*.f64 a b) < 1.05e125

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 81.4%

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

   3. Taylor expanded in a around 0 72.5%

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

   if -1.00000023e-317 < (*.f64 a b) < 4.80000000000000036e-307

   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 a around 0 99.9%

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

   3. Taylor expanded in t around 0 82.8%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5000000:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-317}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4.8 \cdot 10^{-307}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.05 \cdot 10^{+125}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 8: 82.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+224}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+74} \lor \neg \left(x \leq 1.25 \cdot 10^{-79}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.1e+224)
   (+ (* c i) (+ (* z t) (* x y)))
   (if (or (<= x -8.2e+74) (not (<= x 1.25e-79)))
     (+ (* c i) (+ (* a b) (* x y)))
     (+ (* c i) (+ (* a b) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.1e+224) {
		tmp = (c * i) + ((z * t) + (x * y));
	} else if ((x <= -8.2e+74) || !(x <= 1.25e-79)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-2.1d+224)) then
        tmp = (c * i) + ((z * t) + (x * y))
    else if ((x <= (-8.2d+74)) .or. (.not. (x <= 1.25d-79))) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.1e+224) {
		tmp = (c * i) + ((z * t) + (x * y));
	} else if ((x <= -8.2e+74) || !(x <= 1.25e-79)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -2.1e+224:
		tmp = (c * i) + ((z * t) + (x * y))
	elif (x <= -8.2e+74) or not (x <= 1.25e-79):
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.1e+224)
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(x * y)));
	elseif ((x <= -8.2e+74) || !(x <= 1.25e-79))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -2.1e+224)
		tmp = (c * i) + ((z * t) + (x * y));
	elseif ((x <= -8.2e+74) || ~((x <= 1.25e-79)))
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.1e+224], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -8.2e+74], N[Not[LessEqual[x, 1.25e-79]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1000000000000002e224

   1. Initial program 74.9%

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

   2. Taylor expanded in a around 0 68.1%

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

   if -2.1000000000000002e224 < x < -8.2000000000000001e74 or 1.25e-79 < x

   1. Initial program 98.0%

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

   2. Taylor expanded in z around 0 81.3%

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

   if -8.2000000000000001e74 < x < 1.25e-79

   1. Initial program 96.4%

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

   2. Taylor expanded in x around 0 91.0%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+224}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+74} \lor \neg \left(x \leq 1.25 \cdot 10^{-79}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 9: 37.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-40}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-219}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-200}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.95e+30)
   (* c i)
   (if (<= c -8.2e-40)
     (* a b)
     (if (<= c -2.1e-219)
       (* z t)
       (if (<= c 1.3e-230)
         (* a b)
         (if (<= c 4.2e-200) (* z t) (if (<= c 1.8e-112) (* 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 <= -1.95e+30) {
		tmp = c * i;
	} else if (c <= -8.2e-40) {
		tmp = a * b;
	} else if (c <= -2.1e-219) {
		tmp = z * t;
	} else if (c <= 1.3e-230) {
		tmp = a * b;
	} else if (c <= 4.2e-200) {
		tmp = z * t;
	} else if (c <= 1.8e-112) {
		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 <= (-1.95d+30)) then
        tmp = c * i
    else if (c <= (-8.2d-40)) then
        tmp = a * b
    else if (c <= (-2.1d-219)) then
        tmp = z * t
    else if (c <= 1.3d-230) then
        tmp = a * b
    else if (c <= 4.2d-200) then
        tmp = z * t
    else if (c <= 1.8d-112) 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 <= -1.95e+30) {
		tmp = c * i;
	} else if (c <= -8.2e-40) {
		tmp = a * b;
	} else if (c <= -2.1e-219) {
		tmp = z * t;
	} else if (c <= 1.3e-230) {
		tmp = a * b;
	} else if (c <= 4.2e-200) {
		tmp = z * t;
	} else if (c <= 1.8e-112) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.95e+30:
		tmp = c * i
	elif c <= -8.2e-40:
		tmp = a * b
	elif c <= -2.1e-219:
		tmp = z * t
	elif c <= 1.3e-230:
		tmp = a * b
	elif c <= 4.2e-200:
		tmp = z * t
	elif c <= 1.8e-112:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.95e+30)
		tmp = Float64(c * i);
	elseif (c <= -8.2e-40)
		tmp = Float64(a * b);
	elseif (c <= -2.1e-219)
		tmp = Float64(z * t);
	elseif (c <= 1.3e-230)
		tmp = Float64(a * b);
	elseif (c <= 4.2e-200)
		tmp = Float64(z * t);
	elseif (c <= 1.8e-112)
		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 <= -1.95e+30)
		tmp = c * i;
	elseif (c <= -8.2e-40)
		tmp = a * b;
	elseif (c <= -2.1e-219)
		tmp = z * t;
	elseif (c <= 1.3e-230)
		tmp = a * b;
	elseif (c <= 4.2e-200)
		tmp = z * t;
	elseif (c <= 1.8e-112)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.95e+30], N[(c * i), $MachinePrecision], If[LessEqual[c, -8.2e-40], N[(a * b), $MachinePrecision], If[LessEqual[c, -2.1e-219], N[(z * t), $MachinePrecision], If[LessEqual[c, 1.3e-230], N[(a * b), $MachinePrecision], If[LessEqual[c, 4.2e-200], N[(z * t), $MachinePrecision], If[LessEqual[c, 1.8e-112], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.95000000000000005e30 or 1.8e-112 < c

   1. Initial program 95.8%

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

   2. Taylor expanded in c around inf 44.7%

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

   if -1.95000000000000005e30 < c < -8.19999999999999926e-40 or -2.1e-219 < c < 1.3000000000000001e-230 or 4.1999999999999998e-200 < c < 1.8e-112

   1. Initial program 95.8%

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

   2. Taylor expanded in a around inf 45.8%

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

   if -8.19999999999999926e-40 < c < -2.1e-219 or 1.3000000000000001e-230 < c < 4.1999999999999998e-200

   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 z around inf 44.4%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \leq -8.2 \cdot 10^{-40}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-219}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-230}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{-200}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 10: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+197} \lor \neg \left(x \leq -3 \cdot 10^{+147}\right) \land \left(x \leq -1.25 \cdot 10^{+119} \lor \neg \left(x \leq 2.05 \cdot 10^{-64}\right)\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.9e+197)
         (and (not (<= x -3e+147))
              (or (<= x -1.25e+119) (not (<= x 2.05e-64)))))
   (+ (* a b) (* x y))
   (+ (* 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 ((x <= -2.9e+197) || (!(x <= -3e+147) && ((x <= -1.25e+119) || !(x <= 2.05e-64)))) {
		tmp = (a * b) + (x * y);
	} 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) :: tmp
    if ((x <= (-2.9d+197)) .or. (.not. (x <= (-3d+147))) .and. (x <= (-1.25d+119)) .or. (.not. (x <= 2.05d-64))) then
        tmp = (a * b) + (x * y)
    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 tmp;
	if ((x <= -2.9e+197) || (!(x <= -3e+147) && ((x <= -1.25e+119) || !(x <= 2.05e-64)))) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (c * i) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.9e+197) or (not (x <= -3e+147) and ((x <= -1.25e+119) or not (x <= 2.05e-64))):
		tmp = (a * b) + (x * y)
	else:
		tmp = (c * i) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.9e+197) || (!(x <= -3e+147) && ((x <= -1.25e+119) || !(x <= 2.05e-64))))
		tmp = Float64(Float64(a * b) + Float64(x * y));
	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)
	tmp = 0.0;
	if ((x <= -2.9e+197) || (~((x <= -3e+147)) && ((x <= -1.25e+119) || ~((x <= 2.05e-64)))))
		tmp = (a * b) + (x * y);
	else
		tmp = (c * i) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.9e+197], And[N[Not[LessEqual[x, -3e+147]], $MachinePrecision], Or[LessEqual[x, -1.25e+119], N[Not[LessEqual[x, 2.05e-64]], $MachinePrecision]]]], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.90000000000000002e197 or -2.99999999999999993e147 < x < -1.25e119 or 2.05e-64 < x

   1. Initial program 95.5%

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

      1. associate-+l+ 95.5%

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

      2. associate-+l+ 95.5%

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

      3. fma-def 96.6%

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

      4. fma-def 96.6%

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

      5. fma-def 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 82.8%

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

   5. Taylor expanded in c around 0 64.7%

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

   if -2.90000000000000002e197 < x < -2.99999999999999993e147 or -1.25e119 < x < 2.05e-64

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 89.3%

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

   3. Taylor expanded in t around 0 62.8%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+197} \lor \neg \left(x \leq -3 \cdot 10^{+147}\right) \land \left(x \leq -1.25 \cdot 10^{+119} \lor \neg \left(x \leq 2.05 \cdot 10^{-64}\right)\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + a \cdot b\\ \end{array} \]

Alternative 11: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4700000 \lor \neg \left(a \cdot b \leq 3.7 \cdot 10^{+127}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -4700000.0) (not (<= (* a b) 3.7e+127)))
   (+ (* 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 (((a * b) <= -4700000.0) || !((a * b) <= 3.7e+127)) {
		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 (((a * b) <= (-4700000.0d0)) .or. (.not. ((a * b) <= 3.7d+127))) 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 (((a * b) <= -4700000.0) || !((a * b) <= 3.7e+127)) {
		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 ((a * b) <= -4700000.0) or not ((a * b) <= 3.7e+127):
		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(a * b) <= -4700000.0) || !(Float64(a * b) <= 3.7e+127))
		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 (((a * b) <= -4700000.0) || ~(((a * b) <= 3.7e+127)))
		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[Or[LessEqual[N[(a * b), $MachinePrecision], -4700000.0], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3.7e+127]], $MachinePrecision]], 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 2 regimes

2. if (*.f64 a b) < -4.7e6 or 3.6999999999999998e127 < (*.f64 a b)

   1. Initial program 91.5%

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

      1. associate-+l+ 91.5%

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

      2. associate-+l+ 91.5%

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

      3. fma-def 92.4%

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

      4. fma-def 93.4%

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

      5. fma-def 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 84.5%

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

   5. Taylor expanded in c around 0 75.7%

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

   if -4.7e6 < (*.f64 a b) < 3.6999999999999998e127

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 78.9%

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

   3. Taylor expanded in a around 0 71.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4700000 \lor \neg \left(a \cdot b \leq 3.7 \cdot 10^{+127}\right):\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 12: 82.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+74} \lor \neg \left(x \leq 2.4 \cdot 10^{-79}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.2e+74) (not (<= x 2.4e-79)))
   (+ (* c i) (+ (* a b) (* x y)))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.2e+74) || !(x <= 2.4e-79)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-4.2d+74)) .or. (.not. (x <= 2.4d-79))) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.2e+74) || !(x <= 2.4e-79)) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.2e+74) or not (x <= 2.4e-79):
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.2e+74) || !(x <= 2.4e-79))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4.2e+74) || ~((x <= 2.4e-79)))
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.2e+74], N[Not[LessEqual[x, 2.4e-79]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999998e74 or 2.40000000000000006e-79 < x

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 80.7%

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

   if -4.1999999999999998e74 < x < 2.40000000000000006e-79

   1. Initial program 96.4%

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

   2. Taylor expanded in x around 0 91.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+74} \lor \neg \left(x \leq 2.4 \cdot 10^{-79}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 13: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+237}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-64}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -5e+237)
   (+ (* c i) (* x y))
   (if (<= x 2.05e-64) (+ (* c i) (+ (* a b) (* 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 (x <= -5e+237) {
		tmp = (c * i) + (x * y);
	} else if (x <= 2.05e-64) {
		tmp = (c * i) + ((a * b) + (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 (x <= (-5d+237)) then
        tmp = (c * i) + (x * y)
    else if (x <= 2.05d-64) then
        tmp = (c * i) + ((a * b) + (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 (x <= -5e+237) {
		tmp = (c * i) + (x * y);
	} else if (x <= 2.05e-64) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -5e+237:
		tmp = (c * i) + (x * y)
	elif x <= 2.05e-64:
		tmp = (c * i) + ((a * b) + (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 (x <= -5e+237)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (x <= 2.05e-64)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + 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 (x <= -5e+237)
		tmp = (c * i) + (x * y);
	elseif (x <= 2.05e-64)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -5e+237], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e-64], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.0000000000000002e237

   1. Initial program 89.8%

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

   2. Taylor expanded in a around 0 81.7%

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

   3. Taylor expanded in t around 0 72.2%

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

   if -5.0000000000000002e237 < x < 2.05e-64

   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 0 84.7%

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

   if 2.05e-64 < x

   1. Initial program 98.5%

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

      1. associate-+l+ 98.5%

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

      2. associate-+l+ 98.5%

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

      3. fma-def 98.5%

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

      4. fma-def 98.5%

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

      5. fma-def 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in z around 0 80.8%

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

   5. Taylor expanded in c around 0 59.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+237}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-64}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 14: 36.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+30}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= c -1.7e+30) (* c i) (if (<= c 1.8e-112) (* 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 <= -1.7e+30) {
		tmp = c * i;
	} else if (c <= 1.8e-112) {
		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 <= (-1.7d+30)) then
        tmp = c * i
    else if (c <= 1.8d-112) 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 <= -1.7e+30) {
		tmp = c * i;
	} else if (c <= 1.8e-112) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if c <= -1.7e+30:
		tmp = c * i
	elif c <= 1.8e-112:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (c <= -1.7e+30)
		tmp = Float64(c * i);
	elseif (c <= 1.8e-112)
		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 <= -1.7e+30)
		tmp = c * i;
	elseif (c <= 1.8e-112)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[c, -1.7e+30], N[(c * i), $MachinePrecision], If[LessEqual[c, 1.8e-112], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c < -1.7000000000000001e30 or 1.8e-112 < c

   1. Initial program 95.8%

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

   2. Taylor expanded in c around inf 44.7%

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

   if -1.7000000000000001e30 < c < 1.8e-112

   1. Initial program 96.4%

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

   2. Taylor expanded in a around inf 39.5%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+30}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-112}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 15: 27.1% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

2. Taylor expanded in a around inf 30.1%

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

3. Final simplification 30.1%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023208 
(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)))