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

Percentage Accurate: 95.8% → 97.9%

Time: 11.9s

Alternatives: 18

Speedup: 0.5×

• 41.8% 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: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l+ 96.5%

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

   2. +-commutative 96.5%

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

   3. associate-+l+ 96.5%

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

   4. fma-def 97.6%

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

   5. associate-+r+ 97.6%

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

   6. +-commutative 97.6%

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

   7. fma-def 98.8%

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

   8. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l+ 96.5%

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

   2. +-commutative 96.5%

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

   3. associate-+l+ 96.5%

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

   4. fma-def 97.6%

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

   5. associate-+r+ 97.6%

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

   6. +-commutative 97.6%

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

   7. fma-def 98.8%

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

   8. fma-def 98.8%

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

3. Simplified 98.8%

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

   1. fma-udef 97.6%

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

   2. +-commutative 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 3: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. fma-udef 100.0%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. *-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. 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. +-commutative 0.0%

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

      3. associate-+l+ 0.0%

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

      4. fma-def 33.3%

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

      5. associate-+r+ 33.3%

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

      6. +-commutative 33.3%

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

      7. fma-def 66.7%

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

      8. fma-def 66.7%

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

   3. Simplified 66.7%

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

      1. fma-udef 33.3%

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

      2. +-commutative 33.3%

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

   5. Applied egg-rr 33.3%

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

   6. Taylor expanded in x around inf 55.9%

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

4. Final simplification 98.4%

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

Alternative 4: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. 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. +-commutative 0.0%

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

      3. associate-+l+ 0.0%

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

      4. fma-def 33.3%

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

      5. associate-+r+ 33.3%

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

      6. +-commutative 33.3%

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

      7. fma-def 66.7%

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

      8. fma-def 66.7%

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

   3. Simplified 66.7%

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

      1. fma-udef 33.3%

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

      2. +-commutative 33.3%

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

   5. Applied egg-rr 33.3%

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

   6. Taylor expanded in x around inf 55.9%

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

4. Final simplification 98.4%

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

Alternative 5: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ t_3 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1.06 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{+223}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t)))
        (t_2 (+ (* a b) (* c i)))
        (t_3 (+ (* a b) (* x y))))
   (if (<= (* x y) -2.1e+98)
     t_3
     (if (<= (* x y) -2.6e+52)
       t_1
       (if (<= (* x y) -1.06e-242)
         t_2
         (if (<= (* x y) 4e+26)
           t_1
           (if (<= (* x y) 1.1e+74)
             t_2
             (if (<= (* x y) 3.8e+151)
               t_1
               (if (<= (* x y) 3.1e+223) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double t_3 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -2.1e+98) {
		tmp = t_3;
	} else if ((x * y) <= -2.6e+52) {
		tmp = t_1;
	} else if ((x * y) <= -1.06e-242) {
		tmp = t_2;
	} else if ((x * y) <= 4e+26) {
		tmp = t_1;
	} else if ((x * y) <= 1.1e+74) {
		tmp = t_2;
	} else if ((x * y) <= 3.8e+151) {
		tmp = t_1;
	} else if ((x * y) <= 3.1e+223) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (c * i)
    t_3 = (a * b) + (x * y)
    if ((x * y) <= (-2.1d+98)) then
        tmp = t_3
    else if ((x * y) <= (-2.6d+52)) then
        tmp = t_1
    else if ((x * y) <= (-1.06d-242)) then
        tmp = t_2
    else if ((x * y) <= 4d+26) then
        tmp = t_1
    else if ((x * y) <= 1.1d+74) then
        tmp = t_2
    else if ((x * y) <= 3.8d+151) then
        tmp = t_1
    else if ((x * y) <= 3.1d+223) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double t_3 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -2.1e+98) {
		tmp = t_3;
	} else if ((x * y) <= -2.6e+52) {
		tmp = t_1;
	} else if ((x * y) <= -1.06e-242) {
		tmp = t_2;
	} else if ((x * y) <= 4e+26) {
		tmp = t_1;
	} else if ((x * y) <= 1.1e+74) {
		tmp = t_2;
	} else if ((x * y) <= 3.8e+151) {
		tmp = t_1;
	} else if ((x * y) <= 3.1e+223) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (c * i)
	t_3 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -2.1e+98:
		tmp = t_3
	elif (x * y) <= -2.6e+52:
		tmp = t_1
	elif (x * y) <= -1.06e-242:
		tmp = t_2
	elif (x * y) <= 4e+26:
		tmp = t_1
	elif (x * y) <= 1.1e+74:
		tmp = t_2
	elif (x * y) <= 3.8e+151:
		tmp = t_1
	elif (x * y) <= 3.1e+223:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	t_3 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.1e+98)
		tmp = t_3;
	elseif (Float64(x * y) <= -2.6e+52)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.06e-242)
		tmp = t_2;
	elseif (Float64(x * y) <= 4e+26)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.1e+74)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.8e+151)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.1e+223)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (c * i);
	t_3 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.1e+98)
		tmp = t_3;
	elseif ((x * y) <= -2.6e+52)
		tmp = t_1;
	elseif ((x * y) <= -1.06e-242)
		tmp = t_2;
	elseif ((x * y) <= 4e+26)
		tmp = t_1;
	elseif ((x * y) <= 1.1e+74)
		tmp = t_2;
	elseif ((x * y) <= 3.8e+151)
		tmp = t_1;
	elseif ((x * y) <= 3.1e+223)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e+98], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2.6e+52], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.06e-242], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4e+26], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.1e+74], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+151], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.1e+223], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.10000000000000004e98 or 3.09999999999999982e223 < (*.f64 x y)

   1. Initial program 92.8%

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

      1. associate-+l+ 92.8%

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

      2. +-commutative 92.8%

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

      3. associate-+l+ 92.8%

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

      4. fma-def 95.7%

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

      5. associate-+r+ 95.7%

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

      6. +-commutative 95.7%

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

      7. fma-def 98.5%

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

      8. fma-def 98.5%

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

   3. Simplified 98.5%

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

      1. fma-udef 95.7%

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

      2. +-commutative 95.7%

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

   5. Applied egg-rr 95.7%

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

      1. fma-udef 92.8%

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

      2. *-commutative 92.8%

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

      3. +-commutative 92.8%

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

      4. associate-+r+ 92.8%

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

      5. *-commutative 92.8%

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

   7. Applied egg-rr 92.8%

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

   8. Taylor expanded in z around 0 85.6%

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

   9. Taylor expanded in c around 0 80.1%

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

   if -2.10000000000000004e98 < (*.f64 x y) < -2.6e52 or -1.06000000000000008e-242 < (*.f64 x y) < 4.00000000000000019e26 or 1.1000000000000001e74 < (*.f64 x y) < 3.8e151

   1. Initial program 99.1%

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

   2. Taylor expanded in c around 0 80.6%

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

   3. Taylor expanded in x around 0 74.7%

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

   if -2.6e52 < (*.f64 x y) < -1.06000000000000008e-242 or 4.00000000000000019e26 < (*.f64 x y) < 1.1000000000000001e74 or 3.8e151 < (*.f64 x y) < 3.09999999999999982e223

   1. Initial program 96.1%

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

      1. associate-+l+ 96.1%

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

      2. +-commutative 96.1%

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

      3. associate-+l+ 96.1%

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

      4. fma-def 97.4%

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

      5. associate-+r+ 97.4%

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

      6. +-commutative 97.4%

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

      7. fma-def 97.4%

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

      8. fma-def 97.4%

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

   3. Simplified 97.4%

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

      1. fma-udef 97.4%

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

      2. +-commutative 97.4%

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

   5. Applied egg-rr 97.4%

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

      1. fma-udef 96.1%

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

      2. *-commutative 96.1%

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

      3. +-commutative 96.1%

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

      4. associate-+r+ 96.1%

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

      5. *-commutative 96.1%

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

   7. Applied egg-rr 96.1%

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

   8. Taylor expanded in z around 0 79.2%

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

   9. Taylor expanded in c around inf 74.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+98}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -1.06 \cdot 10^{-242}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+26}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.1 \cdot 10^{+74}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+151}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{+223}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 6: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{+100}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 0.38:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.75 \cdot 10^{+84} \lor \neg \left(x \cdot y \leq 1.1 \cdot 10^{+174}\right) \land x \cdot y \leq 5.5 \cdot 10^{+211}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))))
   (if (<= (* x y) -1.85e+100)
     (+ (* c i) (* x y))
     (if (<= (* x y) -4.5e-190)
       t_1
       (if (<= (* x y) 0.38)
         (+ (* a b) (* z t))
         (if (or (<= (* x y) 2.75e+84)
                 (and (not (<= (* x y) 1.1e+174)) (<= (* x y) 5.5e+211)))
           t_1
           (+ (* a b) (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double tmp;
	if ((x * y) <= -1.85e+100) {
		tmp = (c * i) + (x * y);
	} else if ((x * y) <= -4.5e-190) {
		tmp = t_1;
	} else if ((x * y) <= 0.38) {
		tmp = (a * b) + (z * t);
	} else if (((x * y) <= 2.75e+84) || (!((x * y) <= 1.1e+174) && ((x * y) <= 5.5e+211))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    if ((x * y) <= (-1.85d+100)) then
        tmp = (c * i) + (x * y)
    else if ((x * y) <= (-4.5d-190)) then
        tmp = t_1
    else if ((x * y) <= 0.38d0) then
        tmp = (a * b) + (z * t)
    else if (((x * y) <= 2.75d+84) .or. (.not. ((x * y) <= 1.1d+174)) .and. ((x * y) <= 5.5d+211)) then
        tmp = t_1
    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 t_1 = (c * i) + (z * t);
	double tmp;
	if ((x * y) <= -1.85e+100) {
		tmp = (c * i) + (x * y);
	} else if ((x * y) <= -4.5e-190) {
		tmp = t_1;
	} else if ((x * y) <= 0.38) {
		tmp = (a * b) + (z * t);
	} else if (((x * y) <= 2.75e+84) || (!((x * y) <= 1.1e+174) && ((x * y) <= 5.5e+211))) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	tmp = 0
	if (x * y) <= -1.85e+100:
		tmp = (c * i) + (x * y)
	elif (x * y) <= -4.5e-190:
		tmp = t_1
	elif (x * y) <= 0.38:
		tmp = (a * b) + (z * t)
	elif ((x * y) <= 2.75e+84) or (not ((x * y) <= 1.1e+174) and ((x * y) <= 5.5e+211)):
		tmp = t_1
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -1.85e+100)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(x * y) <= -4.5e-190)
		tmp = t_1;
	elseif (Float64(x * y) <= 0.38)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif ((Float64(x * y) <= 2.75e+84) || (!(Float64(x * y) <= 1.1e+174) && (Float64(x * y) <= 5.5e+211)))
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -1.85e+100)
		tmp = (c * i) + (x * y);
	elseif ((x * y) <= -4.5e-190)
		tmp = t_1;
	elseif ((x * y) <= 0.38)
		tmp = (a * b) + (z * t);
	elseif (((x * y) <= 2.75e+84) || (~(((x * y) <= 1.1e+174)) && ((x * y) <= 5.5e+211)))
		tmp = t_1;
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.85e+100], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.5e-190], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 0.38], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 2.75e+84], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.1e+174]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 5.5e+211]]], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.8500000000000001e100

   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. +-commutative 95.6%

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

      3. associate-+l+ 95.6%

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

      4. fma-def 97.8%

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

      5. associate-+r+ 97.8%

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

      6. +-commutative 97.8%

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

      7. fma-def 99.9%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 97.8%

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

      2. +-commutative 97.8%

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

   5. Applied egg-rr 97.8%

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

      1. fma-udef 95.6%

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

      2. *-commutative 95.6%

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

      3. +-commutative 95.6%

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

      4. associate-+r+ 95.6%

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

      5. *-commutative 95.6%

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

   7. Applied egg-rr 95.6%

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

   8. Taylor expanded in z around 0 88.9%

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

   9. Taylor expanded in a around 0 79.0%

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

   if -1.8500000000000001e100 < (*.f64 x y) < -4.50000000000000021e-190 or 0.38 < (*.f64 x y) < 2.7500000000000002e84 or 1.1000000000000001e174 < (*.f64 x y) < 5.49999999999999988e211

   1. Initial program 97.5%

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

   2. Taylor expanded in a around 0 82.1%

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

   3. Taylor expanded in x around 0 77.2%

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

   if -4.50000000000000021e-190 < (*.f64 x y) < 0.38

   1. Initial program 98.8%

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

   2. Taylor expanded in c around 0 78.0%

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

   3. Taylor expanded in x around 0 75.8%

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

   if 2.7500000000000002e84 < (*.f64 x y) < 1.1000000000000001e174 or 5.49999999999999988e211 < (*.f64 x y)

   1. Initial program 90.2%

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

      1. associate-+l+ 90.2%

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

      2. +-commutative 90.2%

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

      3. associate-+l+ 90.2%

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

      4. fma-def 95.1%

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

      5. associate-+r+ 95.1%

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

      6. +-commutative 95.1%

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

      7. fma-def 97.6%

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

      8. fma-def 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 95.1%

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

      2. +-commutative 95.1%

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

   5. Applied egg-rr 95.1%

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

      1. fma-udef 90.2%

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

      2. *-commutative 90.2%

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

      3. +-commutative 90.2%

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

      4. associate-+r+ 90.2%

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

      5. *-commutative 90.2%

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

   7. Applied egg-rr 90.2%

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

   8. Taylor expanded in z around 0 81.1%

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

   9. Taylor expanded in c around 0 75.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{+100}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{-190}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 0.38:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.75 \cdot 10^{+84} \lor \neg \left(x \cdot y \leq 1.1 \cdot 10^{+174}\right) \land x \cdot y \leq 5.5 \cdot 10^{+211}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 7: 97.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   2. 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. +-commutative 0.0%

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

      3. associate-+l+ 0.0%

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

      4. fma-def 33.3%

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

      5. associate-+r+ 33.3%

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

      6. +-commutative 33.3%

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

      7. fma-def 66.7%

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

      8. fma-def 66.7%

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

   3. Simplified 66.7%

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

      1. fma-udef 33.3%

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

      2. +-commutative 33.3%

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

   5. Applied egg-rr 33.3%

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

      1. fma-udef 0.0%

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

      2. *-commutative 0.0%

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

      3. +-commutative 0.0%

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

      4. associate-+r+ 0.0%

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

      5. *-commutative 0.0%

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

   7. Applied egg-rr 0.0%

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

   8. Taylor expanded in z around 0 33.3%

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

   9. Taylor expanded in c around 0 45.0%

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

4. Final simplification 98.0%

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

Alternative 8: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+105} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+133}\right) \land z \cdot t \leq 2 \cdot 10^{+164}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+160)
   (+ (* x y) (* z t))
   (if (or (<= (* z t) 5e+105)
           (and (not (<= (* z t) 5e+133)) (<= (* z t) 2e+164)))
     (+ (* a b) (+ (* c i) (* x y)))
     (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -5e+160) {
		tmp = (x * y) + (z * t);
	} else if (((z * t) <= 5e+105) || (!((z * t) <= 5e+133) && ((z * t) <= 2e+164))) {
		tmp = (a * b) + ((c * i) + (x * y));
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-5d+160)) then
        tmp = (x * y) + (z * t)
    else if (((z * t) <= 5d+105) .or. (.not. ((z * t) <= 5d+133)) .and. ((z * t) <= 2d+164)) then
        tmp = (a * b) + ((c * i) + (x * y))
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -5e+160) {
		tmp = (x * y) + (z * t);
	} else if (((z * t) <= 5e+105) || (!((z * t) <= 5e+133) && ((z * t) <= 2e+164))) {
		tmp = (a * b) + ((c * i) + (x * y));
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -5e+160:
		tmp = (x * y) + (z * t)
	elif ((z * t) <= 5e+105) or (not ((z * t) <= 5e+133) and ((z * t) <= 2e+164)):
		tmp = (a * b) + ((c * i) + (x * y))
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+160)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif ((Float64(z * t) <= 5e+105) || (!(Float64(z * t) <= 5e+133) && (Float64(z * t) <= 2e+164)))
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(x * y)));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -5e+160)
		tmp = (x * y) + (z * t);
	elseif (((z * t) <= 5e+105) || (~(((z * t) <= 5e+133)) && ((z * t) <= 2e+164)))
		tmp = (a * b) + ((c * i) + (x * y));
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+160], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(z * t), $MachinePrecision], 5e+105], And[N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+133]], $MachinePrecision], LessEqual[N[(z * t), $MachinePrecision], 2e+164]]], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -5.0000000000000002e160

   1. Initial program 91.1%

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

   2. Taylor expanded in c around 0 86.8%

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

   3. Taylor expanded in a around 0 80.5%

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

   if -5.0000000000000002e160 < (*.f64 z t) < 5.00000000000000046e105 or 4.99999999999999961e133 < (*.f64 z t) < 2e164

   1. Initial program 98.3%

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

      1. associate-+l+ 98.3%

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

      2. +-commutative 98.3%

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

      3. associate-+l+ 98.3%

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

      4. fma-def 98.3%

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

      5. associate-+r+ 98.3%

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

      6. +-commutative 98.3%

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

      7. fma-def 99.4%

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

      8. fma-def 99.4%

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

   3. Simplified 99.4%

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

      1. fma-udef 98.3%

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

      2. +-commutative 98.3%

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

   5. Applied egg-rr 98.3%

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

      1. fma-udef 98.3%

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

      2. *-commutative 98.3%

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

      3. +-commutative 98.3%

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

      4. associate-+r+ 98.3%

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

      5. *-commutative 98.3%

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

   7. Applied egg-rr 98.3%

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

   8. Taylor expanded in z around 0 87.3%

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

   if 5.00000000000000046e105 < (*.f64 z t) < 4.99999999999999961e133 or 2e164 < (*.f64 z t)

   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 0 96.6%

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

   3. Taylor expanded in x around 0 93.3%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+160}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+105} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+133}\right) \land z \cdot t \leq 2 \cdot 10^{+164}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 9: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -8.2 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.55 \cdot 10^{-38}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.32 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))))
   (if (<= (* c i) -8.2e+150)
     (+ (* c i) (* z t))
     (if (<= (* c i) 0.0)
       t_1
       (if (<= (* c i) 1.55e-38)
         (+ (* a b) (* x y))
         (if (<= (* c i) 1.32e+70) t_1 (+ (* 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 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -8.2e+150) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 0.0) {
		tmp = t_1;
	} else if ((c * i) <= 1.55e-38) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 1.32e+70) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    if ((c * i) <= (-8.2d+150)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 0.0d0) then
        tmp = t_1
    else if ((c * i) <= 1.55d-38) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 1.32d+70) then
        tmp = t_1
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -8.2e+150) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 0.0) {
		tmp = t_1;
	} else if ((c * i) <= 1.55e-38) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 1.32e+70) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -8.2e+150:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 0.0:
		tmp = t_1
	elif (c * i) <= 1.55e-38:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 1.32e+70:
		tmp = t_1
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -8.2e+150)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 0.0)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.55e-38)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 1.32e+70)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -8.2e+150)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 0.0)
		tmp = t_1;
	elseif ((c * i) <= 1.55e-38)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 1.32e+70)
		tmp = t_1;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -8.2e+150], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.55e-38], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.32e+70], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -8.19999999999999988e150

   1. Initial program 86.1%

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

   2. Taylor expanded in a around 0 82.4%

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

   3. Taylor expanded in x around 0 79.8%

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

   if -8.19999999999999988e150 < (*.f64 c i) < 0.0 or 1.54999999999999991e-38 < (*.f64 c i) < 1.3199999999999999e70

   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 c around 0 94.8%

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

   3. Taylor expanded in x around 0 75.0%

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

   if 0.0 < (*.f64 c i) < 1.54999999999999991e-38

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. fma-def 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. fma-def 99.9%

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

      8. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. fma-udef 99.9%

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

      2. *-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. *-commutative 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in z around 0 70.4%

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

   9. Taylor expanded in c around 0 67.1%

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

   if 1.3199999999999999e70 < (*.f64 c i)

   1. Initial program 92.4%

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

      1. associate-+l+ 92.4%

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

      2. +-commutative 92.4%

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

      3. associate-+l+ 92.4%

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

      4. fma-def 96.2%

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

      5. associate-+r+ 96.2%

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

      6. +-commutative 96.2%

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

      7. fma-def 98.1%

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

      8. fma-def 98.1%

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

   3. Simplified 98.1%

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

      1. fma-udef 96.2%

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

      2. +-commutative 96.2%

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

   5. Applied egg-rr 96.2%

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

      1. fma-udef 92.5%

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

      2. *-commutative 92.5%

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

      3. +-commutative 92.5%

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

      4. associate-+r+ 92.5%

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

      5. *-commutative 92.5%

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

   7. Applied egg-rr 92.5%

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

   8. Taylor expanded in z around 0 88.5%

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

   9. Taylor expanded in c around inf 72.2%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.2 \cdot 10^{+150}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.55 \cdot 10^{-38}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.32 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 10: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.7 \cdot 10^{+149} \lor \neg \left(c \cdot i \leq 3.4 \cdot 10^{+66}\right):\\ \;\;\;\;a \cdot b + \left(c \cdot i + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -5.7e+149) (not (<= (* c i) 3.4e+66)))
   (+ (* a b) (+ (* c i) (* x y)))
   (+ (* a b) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -5.7e+149) || !((c * i) <= 3.4e+66)) {
		tmp = (a * b) + ((c * i) + (x * y));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-5.7d+149)) .or. (.not. ((c * i) <= 3.4d+66))) then
        tmp = (a * b) + ((c * i) + (x * y))
    else
        tmp = (a * b) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -5.7e+149) || !((c * i) <= 3.4e+66)) {
		tmp = (a * b) + ((c * i) + (x * y));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -5.7e+149) or not ((c * i) <= 3.4e+66):
		tmp = (a * b) + ((c * i) + (x * y))
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -5.7e+149) || !(Float64(c * i) <= 3.4e+66))
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(x * y)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -5.7e+149) || ~(((c * i) <= 3.4e+66)))
		tmp = (a * b) + ((c * i) + (x * y));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -5.7e+149], N[Not[LessEqual[N[(c * i), $MachinePrecision], 3.4e+66]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5.69999999999999965e149 or 3.4000000000000003e66 < (*.f64 c i)

   1. Initial program 89.9%

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

      1. associate-+l+ 89.9%

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

      2. +-commutative 89.9%

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

      3. associate-+l+ 89.9%

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

      4. fma-def 93.2%

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

      5. associate-+r+ 93.2%

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

      6. +-commutative 93.2%

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

      7. fma-def 96.6%

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

      8. fma-def 96.6%

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

   3. Simplified 96.6%

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

      1. fma-udef 93.3%

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

      2. +-commutative 93.3%

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

   5. Applied egg-rr 93.3%

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

      1. fma-udef 89.9%

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

      2. *-commutative 89.9%

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

      3. +-commutative 89.9%

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

      4. associate-+r+ 89.9%

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

      5. *-commutative 89.9%

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

   7. Applied egg-rr 89.9%

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

   8. Taylor expanded in z around 0 85.4%

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

   if -5.69999999999999965e149 < (*.f64 c i) < 3.4000000000000003e66

   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 c around 0 95.1%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.7 \cdot 10^{+149} \lor \neg \left(c \cdot i \leq 3.4 \cdot 10^{+66}\right):\\ \;\;\;\;a \cdot b + \left(c \cdot i + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 11: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{+65}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.8e+29)
   (+ (* c i) (+ (* a b) (* z t)))
   (if (<= (* c i) 7e+65)
     (+ (* a b) (+ (* x y) (* z t)))
     (+ (* a b) (+ (* c i) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.8e+29) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((c * i) <= 7e+65) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + ((c * i) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.8d+29)) then
        tmp = (c * i) + ((a * b) + (z * t))
    else if ((c * i) <= 7d+65) then
        tmp = (a * b) + ((x * y) + (z * t))
    else
        tmp = (a * b) + ((c * i) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.8e+29) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else if ((c * i) <= 7e+65) {
		tmp = (a * b) + ((x * y) + (z * t));
	} else {
		tmp = (a * b) + ((c * i) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.8e+29:
		tmp = (c * i) + ((a * b) + (z * t))
	elif (c * i) <= 7e+65:
		tmp = (a * b) + ((x * y) + (z * t))
	else:
		tmp = (a * b) + ((c * i) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.8e+29)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	elseif (Float64(c * i) <= 7e+65)
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.8e+29)
		tmp = (c * i) + ((a * b) + (z * t));
	elseif ((c * i) <= 7e+65)
		tmp = (a * b) + ((x * y) + (z * t));
	else
		tmp = (a * b) + ((c * i) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.8e+29], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7e+65], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.79999999999999971e29

   1. Initial program 90.6%

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

   2. Taylor expanded in x around 0 86.9%

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

   if -3.79999999999999971e29 < (*.f64 c i) < 7.0000000000000002e65

   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 c around 0 97.0%

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

   if 7.0000000000000002e65 < (*.f64 c i)

   1. Initial program 92.4%

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

      1. associate-+l+ 92.4%

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

      2. +-commutative 92.4%

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

      3. associate-+l+ 92.4%

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

      4. fma-def 96.2%

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

      5. associate-+r+ 96.2%

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

      6. +-commutative 96.2%

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

      7. fma-def 98.1%

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

      8. fma-def 98.1%

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

   3. Simplified 98.1%

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

      1. fma-udef 96.2%

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

      2. +-commutative 96.2%

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

   5. Applied egg-rr 96.2%

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

      1. fma-udef 92.5%

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

      2. *-commutative 92.5%

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

      3. +-commutative 92.5%

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

      4. associate-+r+ 92.5%

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

      5. *-commutative 92.5%

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

   7. Applied egg-rr 92.5%

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

   8. Taylor expanded in z around 0 88.5%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{+65}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + x \cdot y\right)\\ \end{array} \]

Alternative 12: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;i \leq -1.1 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-224}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= i -1.1e-110)
     t_1
     (if (<= i 3.6e-224)
       (+ (* x y) (* z t))
       (if (<= i 1.6e-15)
         (+ (* a b) (* z t))
         (if (<= i 2.1e+112)
           (+ (* a b) (* x y))
           (if (<= i 3.6e+178) 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 = (a * b) + (c * i);
	double tmp;
	if (i <= -1.1e-110) {
		tmp = t_1;
	} else if (i <= 3.6e-224) {
		tmp = (x * y) + (z * t);
	} else if (i <= 1.6e-15) {
		tmp = (a * b) + (z * t);
	} else if (i <= 2.1e+112) {
		tmp = (a * b) + (x * y);
	} else if (i <= 3.6e+178) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if (i <= (-1.1d-110)) then
        tmp = t_1
    else if (i <= 3.6d-224) then
        tmp = (x * y) + (z * t)
    else if (i <= 1.6d-15) then
        tmp = (a * b) + (z * t)
    else if (i <= 2.1d+112) then
        tmp = (a * b) + (x * y)
    else if (i <= 3.6d+178) then
        tmp = t_1
    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 t_1 = (a * b) + (c * i);
	double tmp;
	if (i <= -1.1e-110) {
		tmp = t_1;
	} else if (i <= 3.6e-224) {
		tmp = (x * y) + (z * t);
	} else if (i <= 1.6e-15) {
		tmp = (a * b) + (z * t);
	} else if (i <= 2.1e+112) {
		tmp = (a * b) + (x * y);
	} else if (i <= 3.6e+178) {
		tmp = t_1;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if i <= -1.1e-110:
		tmp = t_1
	elif i <= 3.6e-224:
		tmp = (x * y) + (z * t)
	elif i <= 1.6e-15:
		tmp = (a * b) + (z * t)
	elif i <= 2.1e+112:
		tmp = (a * b) + (x * y)
	elif i <= 3.6e+178:
		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(a * b) + Float64(c * i))
	tmp = 0.0
	if (i <= -1.1e-110)
		tmp = t_1;
	elseif (i <= 3.6e-224)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (i <= 1.6e-15)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (i <= 2.1e+112)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (i <= 3.6e+178)
		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 = (a * b) + (c * i);
	tmp = 0.0;
	if (i <= -1.1e-110)
		tmp = t_1;
	elseif (i <= 3.6e-224)
		tmp = (x * y) + (z * t);
	elseif (i <= 1.6e-15)
		tmp = (a * b) + (z * t);
	elseif (i <= 2.1e+112)
		tmp = (a * b) + (x * y);
	elseif (i <= 3.6e+178)
		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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.1e-110], t$95$1, If[LessEqual[i, 3.6e-224], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e-15], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.1e+112], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.6e+178], t$95$1, N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.1e-110 or 2.0999999999999999e112 < i < 3.5999999999999998e178

   1. Initial program 96.1%

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

      1. associate-+l+ 96.1%

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

      2. +-commutative 96.1%

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

      3. associate-+l+ 96.1%

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

      4. fma-def 97.1%

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

      5. associate-+r+ 97.1%

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

      6. +-commutative 97.1%

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

      7. fma-def 98.1%

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

      8. fma-def 98.1%

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

   3. Simplified 98.1%

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

      1. fma-udef 97.1%

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

      2. +-commutative 97.1%

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

   5. Applied egg-rr 97.1%

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

      1. fma-udef 96.1%

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

      2. *-commutative 96.1%

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

      3. +-commutative 96.1%

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

      4. associate-+r+ 96.1%

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

      5. *-commutative 96.1%

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

   7. Applied egg-rr 96.1%

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

   8. Taylor expanded in z around 0 75.6%

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

   9. Taylor expanded in c around inf 62.3%

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

   if -1.1e-110 < i < 3.6e-224

   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 c around 0 97.1%

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

   3. Taylor expanded in a around 0 67.2%

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

   if 3.6e-224 < i < 1.6e-15

   1. Initial program 97.2%

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

   2. Taylor expanded in c around 0 89.5%

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

   3. Taylor expanded in x around 0 76.0%

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

   if 1.6e-15 < i < 2.0999999999999999e112

   1. Initial program 96.1%

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

      1. associate-+l+ 96.1%

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

      2. +-commutative 96.1%

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

      3. associate-+l+ 96.1%

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

      4. fma-def 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. fma-def 99.9%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. fma-udef 96.2%

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

      2. *-commutative 96.2%

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

      3. +-commutative 96.2%

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

      4. associate-+r+ 96.2%

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

      5. *-commutative 96.2%

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

   7. Applied egg-rr 96.2%

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

   8. Taylor expanded in z around 0 76.9%

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

   9. Taylor expanded in c around 0 57.9%

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

   if 3.5999999999999998e178 < i

   1. Initial program 88.0%

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

   2. Taylor expanded in a around 0 84.0%

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

   3. Taylor expanded in x around 0 80.0%

      \[\leadsto \color{blue}{c \cdot i + t \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{-110}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-224}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-15}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+178}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 13: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+107}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-179}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-198}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-25}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+116}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -2.55e+107)
   (* a b)
   (if (<= b -8e-179)
     (* z t)
     (if (<= b 2.7e-198)
       (* c i)
       (if (<= b 1.15e-25)
         (* z t)
         (if (<= b 3.6e-5) (* x y) (if (<= b 2.8e+116) (* z t) (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -2.55e+107) {
		tmp = a * b;
	} else if (b <= -8e-179) {
		tmp = z * t;
	} else if (b <= 2.7e-198) {
		tmp = c * i;
	} else if (b <= 1.15e-25) {
		tmp = z * t;
	} else if (b <= 3.6e-5) {
		tmp = x * y;
	} else if (b <= 2.8e+116) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (b <= (-2.55d+107)) then
        tmp = a * b
    else if (b <= (-8d-179)) then
        tmp = z * t
    else if (b <= 2.7d-198) then
        tmp = c * i
    else if (b <= 1.15d-25) then
        tmp = z * t
    else if (b <= 3.6d-5) then
        tmp = x * y
    else if (b <= 2.8d+116) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -2.55e+107) {
		tmp = a * b;
	} else if (b <= -8e-179) {
		tmp = z * t;
	} else if (b <= 2.7e-198) {
		tmp = c * i;
	} else if (b <= 1.15e-25) {
		tmp = z * t;
	} else if (b <= 3.6e-5) {
		tmp = x * y;
	} else if (b <= 2.8e+116) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -2.55e+107:
		tmp = a * b
	elif b <= -8e-179:
		tmp = z * t
	elif b <= 2.7e-198:
		tmp = c * i
	elif b <= 1.15e-25:
		tmp = z * t
	elif b <= 3.6e-5:
		tmp = x * y
	elif b <= 2.8e+116:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -2.55e+107)
		tmp = Float64(a * b);
	elseif (b <= -8e-179)
		tmp = Float64(z * t);
	elseif (b <= 2.7e-198)
		tmp = Float64(c * i);
	elseif (b <= 1.15e-25)
		tmp = Float64(z * t);
	elseif (b <= 3.6e-5)
		tmp = Float64(x * y);
	elseif (b <= 2.8e+116)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -2.55e+107)
		tmp = a * b;
	elseif (b <= -8e-179)
		tmp = z * t;
	elseif (b <= 2.7e-198)
		tmp = c * i;
	elseif (b <= 1.15e-25)
		tmp = z * t;
	elseif (b <= 3.6e-5)
		tmp = x * y;
	elseif (b <= 2.8e+116)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -2.55e+107], N[(a * b), $MachinePrecision], If[LessEqual[b, -8e-179], N[(z * t), $MachinePrecision], If[LessEqual[b, 2.7e-198], N[(c * i), $MachinePrecision], If[LessEqual[b, 1.15e-25], N[(z * t), $MachinePrecision], If[LessEqual[b, 3.6e-5], N[(x * y), $MachinePrecision], If[LessEqual[b, 2.8e+116], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.5500000000000001e107 or 2.80000000000000004e116 < b

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 57.1%

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

   if -2.5500000000000001e107 < b < -8.0000000000000002e-179 or 2.7000000000000002e-198 < b < 1.15e-25 or 3.60000000000000009e-5 < b < 2.80000000000000004e116

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf 39.4%

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

   if -8.0000000000000002e-179 < b < 2.7000000000000002e-198

   1. Initial program 92.2%

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

   2. Taylor expanded in c around inf 34.8%

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

   if 1.15e-25 < b < 3.60000000000000009e-5

   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 x around inf 63.7%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.55 \cdot 10^{+107}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-179}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-198}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-25}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+116}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 14: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+150} \lor \neg \left(x \cdot y \leq 1.15 \cdot 10^{+227}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.35e+150) (not (<= (* x y) 1.15e+227)))
   (* x y)
   (+ (* 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 (((x * y) <= -1.35e+150) || !((x * y) <= 1.15e+227)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-1.35d+150)) .or. (.not. ((x * y) <= 1.15d+227))) then
        tmp = x * y
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -1.35e+150) || !((x * y) <= 1.15e+227)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -1.35e+150) or not ((x * y) <= 1.15e+227):
		tmp = x * y
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -1.35e+150) || !(Float64(x * y) <= 1.15e+227))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -1.35e+150) || ~(((x * y) <= 1.15e+227)))
		tmp = x * y;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.35e+150], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.15e+227]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.35000000000000004e150 or 1.1499999999999999e227 < (*.f64 x y)

   1. Initial program 91.8%

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

   2. Taylor expanded in x around inf 74.9%

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

   if -1.35000000000000004e150 < (*.f64 x y) < 1.1499999999999999e227

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. +-commutative 97.9%

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

      3. associate-+l+ 97.9%

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

      4. fma-def 98.5%

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

      5. associate-+r+ 98.5%

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

      6. +-commutative 98.5%

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

      7. fma-def 99.0%

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

      8. fma-def 99.0%

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

   3. Simplified 99.0%

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

      1. fma-udef 98.5%

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

      2. +-commutative 98.5%

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

   5. Applied egg-rr 98.5%

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

      1. fma-udef 97.9%

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

      2. *-commutative 97.9%

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

      3. +-commutative 97.9%

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

      4. associate-+r+ 97.9%

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

      5. *-commutative 97.9%

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

   7. Applied egg-rr 97.9%

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

   8. Taylor expanded in z around 0 68.3%

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

   9. Taylor expanded in c around inf 61.3%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+150} \lor \neg \left(x \cdot y \leq 1.15 \cdot 10^{+227}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 15: 37.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+111}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq -1.56 \cdot 10^{-177}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-198}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+116}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -1.8e+111)
   (* a b)
   (if (<= b -1.56e-177)
     (* z t)
     (if (<= b 2.55e-198) (* c i) (if (<= b 2.85e+116) (* z t) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -1.8e+111) {
		tmp = a * b;
	} else if (b <= -1.56e-177) {
		tmp = z * t;
	} else if (b <= 2.55e-198) {
		tmp = c * i;
	} else if (b <= 2.85e+116) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (b <= (-1.8d+111)) then
        tmp = a * b
    else if (b <= (-1.56d-177)) then
        tmp = z * t
    else if (b <= 2.55d-198) then
        tmp = c * i
    else if (b <= 2.85d+116) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -1.8e+111) {
		tmp = a * b;
	} else if (b <= -1.56e-177) {
		tmp = z * t;
	} else if (b <= 2.55e-198) {
		tmp = c * i;
	} else if (b <= 2.85e+116) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -1.8e+111:
		tmp = a * b
	elif b <= -1.56e-177:
		tmp = z * t
	elif b <= 2.55e-198:
		tmp = c * i
	elif b <= 2.85e+116:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -1.8e+111)
		tmp = Float64(a * b);
	elseif (b <= -1.56e-177)
		tmp = Float64(z * t);
	elseif (b <= 2.55e-198)
		tmp = Float64(c * i);
	elseif (b <= 2.85e+116)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -1.8e+111)
		tmp = a * b;
	elseif (b <= -1.56e-177)
		tmp = z * t;
	elseif (b <= 2.55e-198)
		tmp = c * i;
	elseif (b <= 2.85e+116)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -1.8e+111], N[(a * b), $MachinePrecision], If[LessEqual[b, -1.56e-177], N[(z * t), $MachinePrecision], If[LessEqual[b, 2.55e-198], N[(c * i), $MachinePrecision], If[LessEqual[b, 2.85e+116], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8000000000000001e111 or 2.84999999999999991e116 < b

   1. Initial program 98.6%

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

   2. Taylor expanded in a around inf 57.9%

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

   if -1.8000000000000001e111 < b < -1.5600000000000001e-177 or 2.5499999999999998e-198 < b < 2.84999999999999991e116

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 37.0%

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

   if -1.5600000000000001e-177 < b < 2.5499999999999998e-198

   1. Initial program 92.2%

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

   2. Taylor expanded in c around inf 34.8%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+111}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;b \leq -1.56 \cdot 10^{-177}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-198}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+116}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 16: 42.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+39} \lor \neg \left(a \cdot b \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -5.2e+39) (not (<= (* a b) 7.5e+122))) (* a b) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -5.2e+39) || !((a * b) <= 7.5e+122)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((a * b) <= (-5.2d+39)) .or. (.not. ((a * b) <= 7.5d+122))) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -5.2e+39) || !((a * b) <= 7.5e+122)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -5.2e+39) or not ((a * b) <= 7.5e+122):
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -5.2e+39) || !(Float64(a * b) <= 7.5e+122))
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -5.2e+39) || ~(((a * b) <= 7.5e+122)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5.2e+39], N[Not[LessEqual[N[(a * b), $MachinePrecision], 7.5e+122]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.2e39 or 7.5000000000000002e122 < (*.f64 a b)

   1. Initial program 95.9%

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

   2. Taylor expanded in a around inf 57.4%

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

   if -5.2e39 < (*.f64 a b) < 7.5000000000000002e122

   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 c around inf 36.7%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+39} \lor \neg \left(a \cdot b \leq 7.5 \cdot 10^{+122}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 17: 60.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{-110} \lor \neg \left(i \leq 6 \cdot 10^{+113}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.1e-110) (not (<= i 6e+113)))
   (+ (* a b) (* 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 ((i <= -1.1e-110) || !(i <= 6e+113)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1.1d-110)) .or. (.not. (i <= 6d+113))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.1e-110) || !(i <= 6e+113)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.1e-110) or not (i <= 6e+113):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.1e-110) || !(i <= 6e+113))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1.1e-110) || ~((i <= 6e+113)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.1e-110], N[Not[LessEqual[i, 6e+113]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.1e-110 or 6e113 < i

   1. Initial program 94.5%

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

      1. associate-+l+ 94.5%

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

      2. +-commutative 94.5%

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

      3. associate-+l+ 94.5%

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

      4. fma-def 96.1%

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

      5. associate-+r+ 96.1%

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

      6. +-commutative 96.1%

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

      7. fma-def 98.4%

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

      8. fma-def 98.4%

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

   3. Simplified 98.4%

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

      1. fma-udef 96.1%

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

      2. +-commutative 96.1%

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

   5. Applied egg-rr 96.1%

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

      1. fma-udef 94.5%

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

      2. *-commutative 94.5%

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

      3. +-commutative 94.5%

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

      4. associate-+r+ 94.5%

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

      5. *-commutative 94.5%

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

   7. Applied egg-rr 94.5%

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

   8. Taylor expanded in z around 0 75.5%

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

   9. Taylor expanded in c around inf 63.3%

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

   if -1.1e-110 < i < 6e113

   1. Initial program 98.4%

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

   2. Taylor expanded in c around 0 91.8%

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

   3. Taylor expanded in x around 0 62.7%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.1 \cdot 10^{-110} \lor \neg \left(i \leq 6 \cdot 10^{+113}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 18: 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 96.5%

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

2. Taylor expanded in a around inf 26.3%

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

3. Final simplification 26.3%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023299 
(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)))