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

Percentage Accurate: 95.7% → 97.7%

Time: 13.1s

Alternatives: 16

Speedup: 0.4×

• 40.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. associate-+l+ 100.0%

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

      6. fma-udef 100.0%

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

      7. associate-+r+ 100.0%

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

   6. Applied egg-rr 100.0%

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

   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. Add Preprocessing

   3. Taylor expanded in c around 0 23.1%

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

      1. +-commutative 23.1%

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

      2. +-commutative 23.1%

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

      3. associate-+r+ 23.1%

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

      4. *-commutative 23.1%

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

      5. *-commutative 23.1%

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

      6. fma-def 38.5%

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

      7. +-commutative 38.5%

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

      8. *-commutative 38.5%

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

      9. fma-def 53.8%

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

      10. *-commutative 53.8%

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

   5. Applied egg-rr 53.8%

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

4. Final simplification 97.6%

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

Alternative 2: 97.7% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 96.1%

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

   3. +-commutative 96.1%

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

   4. fma-def 97.2%

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

   5. fma-def 97.3%

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

3. Simplified 97.3%

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

5. Final simplification 97.3%

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

Alternative 3: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 96.1%

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

   3. associate-+l+ 96.1%

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

   4. fma-def 96.9%

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

   5. fma-def 96.9%

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

3. Simplified 96.9%

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

   1. fma-udef 96.9%

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

6. Applied egg-rr 96.9%

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

7. Final simplification 96.9%

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

Alternative 4: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. associate-+l+ 100.0%

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

      6. fma-udef 100.0%

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

      7. associate-+r+ 100.0%

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

   6. Applied egg-rr 100.0%

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

   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. Add Preprocessing

   3. Taylor expanded in c around 0 23.1%

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

      1. +-commutative 23.1%

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

      2. *-commutative 23.1%

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

      3. fma-def 23.1%

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

      4. *-commutative 23.1%

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

   5. Applied egg-rr 23.1%

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

   6. Taylor expanded in z around 0 31.2%

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

      1. +-commutative 31.2%

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

      2. *-commutative 31.2%

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

      3. fma-def 46.6%

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

   8. Applied egg-rr 46.6%

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

4. Final simplification 97.3%

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

Alternative 5: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + \left(a \cdot b + \left(x \cdot y + z \cdot t\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   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. Add Preprocessing

   3. Taylor expanded in c around 0 23.1%

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

      1. +-commutative 23.1%

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

      2. *-commutative 23.1%

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

      3. fma-def 23.1%

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

      4. *-commutative 23.1%

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

   5. Applied egg-rr 23.1%

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

   6. Taylor expanded in z around 0 31.2%

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

      1. +-commutative 31.2%

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

      2. *-commutative 31.2%

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

      3. fma-def 46.6%

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

   8. Applied egg-rr 46.6%

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

4. Final simplification 97.3%

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

Alternative 6: 66.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + z \cdot t\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -3.05 \cdot 10^{+103}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \cdot i \leq -7.5 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -4.2 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 1.55 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 15500000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y)))
        (t_2 (+ (* a b) (* z t)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* c i) -3.05e+103)
     t_3
     (if (<= (* c i) -7.5e-78)
       t_1
       (if (<= (* c i) -4.2e-291)
         t_2
         (if (<= (* c i) 1.55e-209)
           t_1
           (if (<= (* c i) 15500000000.0) 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) + (x * y);
	double t_2 = (a * b) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -3.05e+103) {
		tmp = t_3;
	} else if ((c * i) <= -7.5e-78) {
		tmp = t_1;
	} else if ((c * i) <= -4.2e-291) {
		tmp = t_2;
	} else if ((c * i) <= 1.55e-209) {
		tmp = t_1;
	} else if ((c * i) <= 15500000000.0) {
		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) + (x * y)
    t_2 = (a * b) + (z * t)
    t_3 = (a * b) + (c * i)
    if ((c * i) <= (-3.05d+103)) then
        tmp = t_3
    else if ((c * i) <= (-7.5d-78)) then
        tmp = t_1
    else if ((c * i) <= (-4.2d-291)) then
        tmp = t_2
    else if ((c * i) <= 1.55d-209) then
        tmp = t_1
    else if ((c * i) <= 15500000000.0d0) 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) + (x * y);
	double t_2 = (a * b) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -3.05e+103) {
		tmp = t_3;
	} else if ((c * i) <= -7.5e-78) {
		tmp = t_1;
	} else if ((c * i) <= -4.2e-291) {
		tmp = t_2;
	} else if ((c * i) <= 1.55e-209) {
		tmp = t_1;
	} else if ((c * i) <= 15500000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (a * b) + (z * t)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -3.05e+103:
		tmp = t_3
	elif (c * i) <= -7.5e-78:
		tmp = t_1
	elif (c * i) <= -4.2e-291:
		tmp = t_2
	elif (c * i) <= 1.55e-209:
		tmp = t_1
	elif (c * i) <= 15500000000.0:
		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(x * y))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -3.05e+103)
		tmp = t_3;
	elseif (Float64(c * i) <= -7.5e-78)
		tmp = t_1;
	elseif (Float64(c * i) <= -4.2e-291)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.55e-209)
		tmp = t_1;
	elseif (Float64(c * i) <= 15500000000.0)
		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) + (x * y);
	t_2 = (a * b) + (z * t);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -3.05e+103)
		tmp = t_3;
	elseif ((c * i) <= -7.5e-78)
		tmp = t_1;
	elseif ((c * i) <= -4.2e-291)
		tmp = t_2;
	elseif ((c * i) <= 1.55e-209)
		tmp = t_1;
	elseif ((c * i) <= 15500000000.0)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.05e+103], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], -7.5e-78], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -4.2e-291], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.55e-209], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 15500000000.0], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.0500000000000001e103 or 1.55e10 < (*.f64 c i)

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 82.8%

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

   4. Taylor expanded in t around 0 73.1%

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

   if -3.0500000000000001e103 < (*.f64 c i) < -7.50000000000000041e-78 or -4.1999999999999999e-291 < (*.f64 c i) < 1.55e-209

   1. Initial program 98.7%

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

   3. Taylor expanded in c around 0 93.7%

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

      1. +-commutative 93.7%

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

      2. *-commutative 93.7%

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

      3. fma-def 93.7%

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

      4. *-commutative 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in z around 0 82.1%

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

   if -7.50000000000000041e-78 < (*.f64 c i) < -4.1999999999999999e-291 or 1.55e-209 < (*.f64 c i) < 1.55e10

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0 81.0%

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

   4. Taylor expanded in c around 0 77.7%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.05 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.5 \cdot 10^{-78}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -4.2 \cdot 10^{-291}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.55 \cdot 10^{-209}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 15500000000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -2.45 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.8 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -3.8 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 2.4 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* c i) -2.45e+103)
     (+ (* a b) (* c i))
     (if (<= (* c i) -2.8e-78)
       t_1
       (if (<= (* c i) -3.8e-291)
         t_2
         (if (<= (* c i) 4.5e-210)
           t_1
           (if (<= (* c i) 2.4e+68) t_2 (+ (* 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) + (x * y);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -2.45e+103) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -2.8e-78) {
		tmp = t_1;
	} else if ((c * i) <= -3.8e-291) {
		tmp = t_2;
	} else if ((c * i) <= 4.5e-210) {
		tmp = t_1;
	} else if ((c * i) <= 2.4e+68) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    t_2 = (a * b) + (z * t)
    if ((c * i) <= (-2.45d+103)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= (-2.8d-78)) then
        tmp = t_1
    else if ((c * i) <= (-3.8d-291)) then
        tmp = t_2
    else if ((c * i) <= 4.5d-210) then
        tmp = t_1
    else if ((c * i) <= 2.4d+68) then
        tmp = t_2
    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) + (x * y);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -2.45e+103) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -2.8e-78) {
		tmp = t_1;
	} else if ((c * i) <= -3.8e-291) {
		tmp = t_2;
	} else if ((c * i) <= 4.5e-210) {
		tmp = t_1;
	} else if ((c * i) <= 2.4e+68) {
		tmp = t_2;
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -2.45e+103:
		tmp = (a * b) + (c * i)
	elif (c * i) <= -2.8e-78:
		tmp = t_1
	elif (c * i) <= -3.8e-291:
		tmp = t_2
	elif (c * i) <= 4.5e-210:
		tmp = t_1
	elif (c * i) <= 2.4e+68:
		tmp = t_2
	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(x * y))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -2.45e+103)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= -2.8e-78)
		tmp = t_1;
	elseif (Float64(c * i) <= -3.8e-291)
		tmp = t_2;
	elseif (Float64(c * i) <= 4.5e-210)
		tmp = t_1;
	elseif (Float64(c * i) <= 2.4e+68)
		tmp = t_2;
	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) + (x * y);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -2.45e+103)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= -2.8e-78)
		tmp = t_1;
	elseif ((c * i) <= -3.8e-291)
		tmp = t_2;
	elseif ((c * i) <= 4.5e-210)
		tmp = t_1;
	elseif ((c * i) <= 2.4e+68)
		tmp = t_2;
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -2.45e+103], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.8e-78], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -3.8e-291], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 4.5e-210], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 2.4e+68], t$95$2, N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -2.4499999999999999e103

   1. Initial program 93.3%

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

   3. Taylor expanded in x around 0 86.9%

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

   4. Taylor expanded in t around 0 82.6%

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

   if -2.4499999999999999e103 < (*.f64 c i) < -2.80000000000000024e-78 or -3.7999999999999998e-291 < (*.f64 c i) < 4.5000000000000002e-210

   1. Initial program 98.7%

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

   3. Taylor expanded in c around 0 93.7%

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

      1. +-commutative 93.7%

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

      2. *-commutative 93.7%

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

      3. fma-def 93.7%

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

      4. *-commutative 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in z around 0 82.1%

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

   if -2.80000000000000024e-78 < (*.f64 c i) < -3.7999999999999998e-291 or 4.5000000000000002e-210 < (*.f64 c i) < 2.40000000000000008e68

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 78.7%

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

   4. Taylor expanded in c around 0 74.2%

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

   if 2.40000000000000008e68 < (*.f64 c i)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 82.5%

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

   4. Taylor expanded in a around 0 74.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.45 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.8 \cdot 10^{-78}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -3.8 \cdot 10^{-291}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.5 \cdot 10^{-210}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.4 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;c \cdot i \leq -7.6 \cdot 10^{+102}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.4 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -5.7 \cdot 10^{-291}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* c i) -7.6e+102)
     (+ (* a b) (* c i))
     (if (<= (* c i) -3.4e-78)
       t_1
       (if (<= (* c i) -5.7e-291)
         (+ (* a b) (* z t))
         (if (<= (* c i) 5e-237)
           t_1
           (if (<= (* c i) 3.2e+68)
             (+ (* x y) (* z t))
             (+ (* 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) + (x * y);
	double tmp;
	if ((c * i) <= -7.6e+102) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -3.4e-78) {
		tmp = t_1;
	} else if ((c * i) <= -5.7e-291) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 5e-237) {
		tmp = t_1;
	} else if ((c * i) <= 3.2e+68) {
		tmp = (x * y) + (z * t);
	} 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) + (x * y)
    if ((c * i) <= (-7.6d+102)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= (-3.4d-78)) then
        tmp = t_1
    else if ((c * i) <= (-5.7d-291)) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 5d-237) then
        tmp = t_1
    else if ((c * i) <= 3.2d+68) then
        tmp = (x * y) + (z * t)
    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) + (x * y);
	double tmp;
	if ((c * i) <= -7.6e+102) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -3.4e-78) {
		tmp = t_1;
	} else if ((c * i) <= -5.7e-291) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 5e-237) {
		tmp = t_1;
	} else if ((c * i) <= 3.2e+68) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (c * i) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	tmp = 0
	if (c * i) <= -7.6e+102:
		tmp = (a * b) + (c * i)
	elif (c * i) <= -3.4e-78:
		tmp = t_1
	elif (c * i) <= -5.7e-291:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 5e-237:
		tmp = t_1
	elif (c * i) <= 3.2e+68:
		tmp = (x * y) + (z * t)
	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(x * y))
	tmp = 0.0
	if (Float64(c * i) <= -7.6e+102)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= -3.4e-78)
		tmp = t_1;
	elseif (Float64(c * i) <= -5.7e-291)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 5e-237)
		tmp = t_1;
	elseif (Float64(c * i) <= 3.2e+68)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	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) + (x * y);
	tmp = 0.0;
	if ((c * i) <= -7.6e+102)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= -3.4e-78)
		tmp = t_1;
	elseif ((c * i) <= -5.7e-291)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 5e-237)
		tmp = t_1;
	elseif ((c * i) <= 3.2e+68)
		tmp = (x * y) + (z * t);
	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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -7.6e+102], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -3.4e-78], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -5.7e-291], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5e-237], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 3.2e+68], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 c i) < -7.59999999999999958e102

   1. Initial program 93.3%

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

   3. Taylor expanded in x around 0 86.9%

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

   4. Taylor expanded in t around 0 82.6%

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

   if -7.59999999999999958e102 < (*.f64 c i) < -3.40000000000000012e-78 or -5.70000000000000034e-291 < (*.f64 c i) < 5.0000000000000002e-237

   1. Initial program 98.6%

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

   3. Taylor expanded in c around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. *-commutative 93.4%

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

      3. fma-def 93.4%

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

      4. *-commutative 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in z around 0 82.5%

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

   if -3.40000000000000012e-78 < (*.f64 c i) < -5.70000000000000034e-291

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 84.1%

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

   4. Taylor expanded in c around 0 84.0%

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

   if 5.0000000000000002e-237 < (*.f64 c i) < 3.19999999999999994e68

   1. Initial program 97.4%

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

   3. Taylor expanded in c around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. *-commutative 90.1%

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

      3. fma-def 90.1%

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

      4. *-commutative 90.1%

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

   5. Applied egg-rr 90.1%

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

   6. Taylor expanded in a around 0 69.6%

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

   if 3.19999999999999994e68 < (*.f64 c i)

   1. Initial program 89.6%

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

   3. Taylor expanded in x around 0 82.5%

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

   4. Taylor expanded in a around 0 74.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.6 \cdot 10^{+102}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.4 \cdot 10^{-78}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -5.7 \cdot 10^{-291}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5 \cdot 10^{-237}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.2 \cdot 10^{+68}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + \left(x \cdot y + z \cdot t\right)\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -1.5 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 10^{+182}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.5 \cdot 10^{+226}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (+ (* x y) (* z t)))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -1.5e+122)
     t_2
     (if (<= (* c i) 2.8e+68)
       t_1
       (if (<= (* c i) 1e+182)
         (+ (* c i) (* z t))
         (if (<= (* c i) 3.5e+226) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.5e+122) {
		tmp = t_2;
	} else if ((c * i) <= 2.8e+68) {
		tmp = t_1;
	} else if ((c * i) <= 1e+182) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 3.5e+226) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + ((x * y) + (z * t))
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-1.5d+122)) then
        tmp = t_2
    else if ((c * i) <= 2.8d+68) then
        tmp = t_1
    else if ((c * i) <= 1d+182) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 3.5d+226) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + ((x * y) + (z * t));
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.5e+122) {
		tmp = t_2;
	} else if ((c * i) <= 2.8e+68) {
		tmp = t_1;
	} else if ((c * i) <= 1e+182) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 3.5e+226) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + ((x * y) + (z * t))
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -1.5e+122:
		tmp = t_2
	elif (c * i) <= 2.8e+68:
		tmp = t_1
	elif (c * i) <= 1e+182:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 3.5e+226:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -1.5e+122)
		tmp = t_2;
	elseif (Float64(c * i) <= 2.8e+68)
		tmp = t_1;
	elseif (Float64(c * i) <= 1e+182)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 3.5e+226)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + ((x * y) + (z * t));
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -1.5e+122)
		tmp = t_2;
	elseif ((c * i) <= 2.8e+68)
		tmp = t_1;
	elseif ((c * i) <= 1e+182)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 3.5e+226)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.5e+122], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 2.8e+68], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1e+182], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.5e+226], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.49999999999999993e122 or 3.4999999999999998e226 < (*.f64 c i)

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 86.0%

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

   4. Taylor expanded in t around 0 84.8%

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

   if -1.49999999999999993e122 < (*.f64 c i) < 2.8e68 or 1.0000000000000001e182 < (*.f64 c i) < 3.4999999999999998e226

   1. Initial program 98.0%

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

   3. Taylor expanded in c around 0 92.7%

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

   if 2.8e68 < (*.f64 c i) < 1.0000000000000001e182

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 87.0%

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

   4. Taylor expanded in a around 0 74.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.5 \cdot 10^{+122}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;c \cdot i \leq 10^{+182}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.5 \cdot 10^{+226}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := c \cdot i + \left(a \cdot b + t\_1\right)\\ \mathbf{if}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* c i) (+ (* a b) t_1))))
   (if (<= t_2 INFINITY) t_2 t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 = (x * y) + (z * t);
	double t_2 = (c * i) + ((a * b) + t_1);
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (c * i) + ((a * b) + t_1)
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(Float64(a * b) + t_1))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = (c * i) + ((a * b) + t_1);
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

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. Add Preprocessing

   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. Add Preprocessing

   3. Taylor expanded in c around 0 23.1%

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

      1. +-commutative 23.1%

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

      2. *-commutative 23.1%

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

      3. fma-def 23.1%

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

      4. *-commutative 23.1%

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

   5. Applied egg-rr 23.1%

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

   6. Taylor expanded in a around 0 46.2%

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

4. Final simplification 97.2%

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

Alternative 11: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.1 \cdot 10^{+221}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{+74}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -6.1e+221)
   (+ (* a b) (* x y))
   (if (<= (* x y) 1.3e+74)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* 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 ((x * y) <= -6.1e+221) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 1.3e+74) {
		tmp = (c * i) + ((a * b) + (z * t));
	} 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 ((x * y) <= (-6.1d+221)) then
        tmp = (a * b) + (x * y)
    else if ((x * y) <= 1.3d+74) then
        tmp = (c * i) + ((a * b) + (z * t))
    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 ((x * y) <= -6.1e+221) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 1.3e+74) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -6.1e+221:
		tmp = (a * b) + (x * y)
	elif (x * y) <= 1.3e+74:
		tmp = (c * i) + ((a * b) + (z * t))
	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(x * y) <= -6.1e+221)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(x * y) <= 1.3e+74)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	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 ((x * y) <= -6.1e+221)
		tmp = (a * b) + (x * y);
	elseif ((x * y) <= 1.3e+74)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -6.1e+221], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.3e+74], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.0999999999999998e221

   1. Initial program 70.8%

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

   3. Taylor expanded in c around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. *-commutative 71.1%

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

      3. fma-def 71.1%

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

      4. *-commutative 71.1%

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

   5. Applied egg-rr 71.1%

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

   6. Taylor expanded in z around 0 79.5%

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

   if -6.0999999999999998e221 < (*.f64 x y) < 1.3e74

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 92.6%

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

   if 1.3e74 < (*.f64 x y)

   1. Initial program 94.2%

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

   3. Taylor expanded in c around 0 83.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.1 \cdot 10^{+221}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{+74}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.6 \cdot 10^{+67}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.7 \cdot 10^{-237}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+89}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -8.6e+67)
   (* c i)
   (if (<= (* c i) 1.7e-237)
     (* a b)
     (if (<= (* c i) 1.05e+89) (* z t) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -8.6e+67) {
		tmp = c * i;
	} else if ((c * i) <= 1.7e-237) {
		tmp = a * b;
	} else if ((c * i) <= 1.05e+89) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-8.6d+67)) then
        tmp = c * i
    else if ((c * i) <= 1.7d-237) then
        tmp = a * b
    else if ((c * i) <= 1.05d+89) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -8.6e+67) {
		tmp = c * i;
	} else if ((c * i) <= 1.7e-237) {
		tmp = a * b;
	} else if ((c * i) <= 1.05e+89) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -8.6e+67:
		tmp = c * i
	elif (c * i) <= 1.7e-237:
		tmp = a * b
	elif (c * i) <= 1.05e+89:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -8.6e+67)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 1.7e-237)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 1.05e+89)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -8.6e+67)
		tmp = c * i;
	elseif ((c * i) <= 1.7e-237)
		tmp = a * b;
	elseif ((c * i) <= 1.05e+89)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -8.6e+67], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.7e-237], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.05e+89], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -8.6000000000000002e67 or 1.04999999999999993e89 < (*.f64 c i)

   1. Initial program 92.3%

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

   3. Taylor expanded in c around inf 60.7%

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

   if -8.6000000000000002e67 < (*.f64 c i) < 1.7000000000000001e-237

   1. Initial program 97.9%

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

   3. Taylor expanded in a around inf 48.5%

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

   if 1.7000000000000001e-237 < (*.f64 c i) < 1.04999999999999993e89

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 44.8%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.6 \cdot 10^{+67}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.7 \cdot 10^{-237}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{+89}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+219} \lor \neg \left(x \cdot y \leq 3.5 \cdot 10^{+242}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.75e+219) (not (<= (* x y) 3.5e+242)))
   (* 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) <= -1.75e+219) || !((x * y) <= 3.5e+242)) {
		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) <= (-1.75d+219)) .or. (.not. ((x * y) <= 3.5d+242))) 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) <= -1.75e+219) || !((x * y) <= 3.5e+242)) {
		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) <= -1.75e+219) or not ((x * y) <= 3.5e+242):
		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) <= -1.75e+219) || !(Float64(x * y) <= 3.5e+242))
		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) <= -1.75e+219) || ~(((x * y) <= 3.5e+242)))
		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], -1.75e+219], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.5e+242]], $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) < -1.7500000000000001e219 or 3.4999999999999999e242 < (*.f64 x y)

   1. Initial program 81.2%

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

   3. Taylor expanded in x around inf 83.4%

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

   if -1.7500000000000001e219 < (*.f64 x y) < 3.4999999999999999e242

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 87.9%

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

   4. Taylor expanded in t around 0 66.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+219} \lor \neg \left(x \cdot y \leq 3.5 \cdot 10^{+242}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+74} \lor \neg \left(c \cdot i \leq 13500000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -3.8e+74) (not (<= (* c i) 13500000000.0)))
   (+ (* 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 (((c * i) <= -3.8e+74) || !((c * i) <= 13500000000.0)) {
		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 (((c * i) <= (-3.8d+74)) .or. (.not. ((c * i) <= 13500000000.0d0))) 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 (((c * i) <= -3.8e+74) || !((c * i) <= 13500000000.0)) {
		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 ((c * i) <= -3.8e+74) or not ((c * i) <= 13500000000.0):
		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 ((Float64(c * i) <= -3.8e+74) || !(Float64(c * i) <= 13500000000.0))
		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 (((c * i) <= -3.8e+74) || ~(((c * i) <= 13500000000.0)))
		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[N[(c * i), $MachinePrecision], -3.8e+74], N[Not[LessEqual[N[(c * i), $MachinePrecision], 13500000000.0]], $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 (*.f64 c i) < -3.7999999999999998e74 or 1.35e10 < (*.f64 c i)

   1. Initial program 92.2%

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

   3. Taylor expanded in x around 0 81.1%

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

   4. Taylor expanded in t around 0 70.7%

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

   if -3.7999999999999998e74 < (*.f64 c i) < 1.35e10

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0 70.0%

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

   4. Taylor expanded in c around 0 67.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.8 \cdot 10^{+74} \lor \neg \left(c \cdot i \leq 13500000000\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+81} \lor \neg \left(a \cdot b \leq 1.7 \cdot 10^{+43}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -5.8e+81) (not (<= (* a b) 1.7e+43))) (* 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) <= -5.8e+81) || !((a * b) <= 1.7e+43)) {
		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) <= (-5.8d+81)) .or. (.not. ((a * b) <= 1.7d+43))) 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) <= -5.8e+81) || !((a * b) <= 1.7e+43)) {
		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) <= -5.8e+81) or not ((a * b) <= 1.7e+43):
		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) <= -5.8e+81) || !(Float64(a * b) <= 1.7e+43))
		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) <= -5.8e+81) || ~(((a * b) <= 1.7e+43)))
		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], -5.8e+81], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.7e+43]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.7999999999999999e81 or 1.70000000000000006e43 < (*.f64 a b)

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf 60.1%

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

   if -5.7999999999999999e81 < (*.f64 a b) < 1.70000000000000006e43

   1. Initial program 97.3%

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

   3. Taylor expanded in c around inf 43.8%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.8 \cdot 10^{+81} \lor \neg \left(a \cdot b \leq 1.7 \cdot 10^{+43}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.7% 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 94.9%

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

3. Taylor expanded in a around inf 29.7%

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

4. Final simplification 29.7%

   \[\leadsto a \cdot b \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024041 
(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)))