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

Percentage Accurate: 95.9% → 97.8%

Time: 14.0s

Alternatives: 16

Speedup: 0.4×

• 41.4% 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: 95.9% 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: 97.8% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-def 96.8%

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

   3. +-commutative 96.8%

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

   4. fma-def 98.8%

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

   5. fma-def 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 2: 97.5% 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 96.1%

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

   1. +-commutative 96.1%

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

   2. fma-def 96.8%

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

   3. associate-+l+ 96.8%

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

   4. fma-def 97.3%

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

   5. fma-def 97.6%

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

3. Simplified 97.6%

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

   1. fma-udef 97.3%

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

6. Applied egg-rr 97.3%

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

7. Final simplification 97.3%

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

Alternative 3: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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. 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. fma-def 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + \left(a \cdot b + c \cdot i\right)} \]
   4. 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 a around 0 60.0%

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

      1. +-commutative 60.0%

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

      2. *-commutative 60.0%

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

      3. fma-def 60.0%

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

      4. *-commutative 60.0%

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

   5. Applied egg-rr 60.0%

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

   6. Taylor expanded in c around 0 60.1%

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

4. Final simplification 98.4%

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

Alternative 4: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. fma-def 99.6%

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

   3. Simplified 99.6%

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

      1. fma-udef 99.6%

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

      2. fma-def 99.6%

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

      3. associate-+r+ 99.6%

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

   6. Applied egg-rr 99.6%

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

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

   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 a around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. *-commutative 71.4%

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

      3. fma-def 71.4%

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

      4. *-commutative 71.4%

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

   5. Applied egg-rr 71.4%

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

   6. Taylor expanded in c around 0 71.4%

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

4. Final simplification 98.8%

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

Alternative 5: 42.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+126}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.4 \cdot 10^{-134}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.12 \cdot 10^{-299}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.6 \cdot 10^{-164}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+95}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.35e+126)
   (* x y)
   (if (<= (* x y) -1.05e+73)
     (* z t)
     (if (<= (* x y) -4.4e-134)
       (* a b)
       (if (<= (* x y) -1.12e-299)
         (* z t)
         (if (<= (* x y) 8.6e-164)
           (* c i)
           (if (<= (* x y) 3.4e+95) (* a b) (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.35e+126) {
		tmp = x * y;
	} else if ((x * y) <= -1.05e+73) {
		tmp = z * t;
	} else if ((x * y) <= -4.4e-134) {
		tmp = a * b;
	} else if ((x * y) <= -1.12e-299) {
		tmp = z * t;
	} else if ((x * y) <= 8.6e-164) {
		tmp = c * i;
	} else if ((x * y) <= 3.4e+95) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1.35d+126)) then
        tmp = x * y
    else if ((x * y) <= (-1.05d+73)) then
        tmp = z * t
    else if ((x * y) <= (-4.4d-134)) then
        tmp = a * b
    else if ((x * y) <= (-1.12d-299)) then
        tmp = z * t
    else if ((x * y) <= 8.6d-164) then
        tmp = c * i
    else if ((x * y) <= 3.4d+95) then
        tmp = a * b
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.35e+126) {
		tmp = x * y;
	} else if ((x * y) <= -1.05e+73) {
		tmp = z * t;
	} else if ((x * y) <= -4.4e-134) {
		tmp = a * b;
	} else if ((x * y) <= -1.12e-299) {
		tmp = z * t;
	} else if ((x * y) <= 8.6e-164) {
		tmp = c * i;
	} else if ((x * y) <= 3.4e+95) {
		tmp = a * b;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.35e+126:
		tmp = x * y
	elif (x * y) <= -1.05e+73:
		tmp = z * t
	elif (x * y) <= -4.4e-134:
		tmp = a * b
	elif (x * y) <= -1.12e-299:
		tmp = z * t
	elif (x * y) <= 8.6e-164:
		tmp = c * i
	elif (x * y) <= 3.4e+95:
		tmp = a * b
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.35e+126)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.05e+73)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -4.4e-134)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= -1.12e-299)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 8.6e-164)
		tmp = Float64(c * i);
	elseif (Float64(x * y) <= 3.4e+95)
		tmp = Float64(a * b);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1.35e+126)
		tmp = x * y;
	elseif ((x * y) <= -1.05e+73)
		tmp = z * t;
	elseif ((x * y) <= -4.4e-134)
		tmp = a * b;
	elseif ((x * y) <= -1.12e-299)
		tmp = z * t;
	elseif ((x * y) <= 8.6e-164)
		tmp = c * i;
	elseif ((x * y) <= 3.4e+95)
		tmp = a * b;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.35e+126], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.05e+73], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.4e-134], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.12e-299], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 8.6e-164], N[(c * i), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.4e+95], N[(a * b), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.35000000000000001e126 or 3.40000000000000022e95 < (*.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 z around 0 87.3%

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

      1. +-commutative 87.3%

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

      2. *-commutative 87.3%

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

      3. fma-def 88.5%

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

   5. Applied egg-rr 88.5%

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

   6. Taylor expanded in y around inf 69.0%

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

   if -1.35000000000000001e126 < (*.f64 x y) < -1.0500000000000001e73 or -4.3999999999999999e-134 < (*.f64 x y) < -1.11999999999999998e-299

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 72.3%

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

      1. +-commutative 72.3%

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

      2. *-commutative 72.3%

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

      3. fma-def 72.3%

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

      4. *-commutative 72.3%

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

   5. Applied egg-rr 72.3%

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

   6. Taylor expanded in i around 0 49.4%

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

   if -1.0500000000000001e73 < (*.f64 x y) < -4.3999999999999999e-134 or 8.5999999999999996e-164 < (*.f64 x y) < 3.40000000000000022e95

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. *-commutative 77.6%

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

      3. fma-def 77.6%

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

   5. Applied egg-rr 77.6%

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

   6. Taylor expanded in a around inf 42.7%

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

   if -1.11999999999999998e-299 < (*.f64 x y) < 8.5999999999999996e-164

   1. Initial program 96.4%

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

   3. Taylor expanded in c around inf 50.2%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+126}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.4 \cdot 10^{-134}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -1.12 \cdot 10^{-299}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 8.6 \cdot 10^{-164}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+95}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1250:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -6 \cdot 10^{-66}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -3.4 \cdot 10^{-181}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -8e+112)
   (* a b)
   (if (<= (* a b) -1250.0)
     (* z t)
     (if (<= (* a b) -6e-66)
       (* c i)
       (if (<= (* a b) -3.4e-181)
         (* z t)
         (if (<= (* a b) 9.2e+46) (* c i) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -8e+112) {
		tmp = a * b;
	} else if ((a * b) <= -1250.0) {
		tmp = z * t;
	} else if ((a * b) <= -6e-66) {
		tmp = c * i;
	} else if ((a * b) <= -3.4e-181) {
		tmp = z * t;
	} else if ((a * b) <= 9.2e+46) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-8d+112)) then
        tmp = a * b
    else if ((a * b) <= (-1250.0d0)) then
        tmp = z * t
    else if ((a * b) <= (-6d-66)) then
        tmp = c * i
    else if ((a * b) <= (-3.4d-181)) then
        tmp = z * t
    else if ((a * b) <= 9.2d+46) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -8e+112) {
		tmp = a * b;
	} else if ((a * b) <= -1250.0) {
		tmp = z * t;
	} else if ((a * b) <= -6e-66) {
		tmp = c * i;
	} else if ((a * b) <= -3.4e-181) {
		tmp = z * t;
	} else if ((a * b) <= 9.2e+46) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -8e+112:
		tmp = a * b
	elif (a * b) <= -1250.0:
		tmp = z * t
	elif (a * b) <= -6e-66:
		tmp = c * i
	elif (a * b) <= -3.4e-181:
		tmp = z * t
	elif (a * b) <= 9.2e+46:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -8e+112)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1250.0)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= -6e-66)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= -3.4e-181)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 9.2e+46)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -8e+112)
		tmp = a * b;
	elseif ((a * b) <= -1250.0)
		tmp = z * t;
	elseif ((a * b) <= -6e-66)
		tmp = c * i;
	elseif ((a * b) <= -3.4e-181)
		tmp = z * t;
	elseif ((a * b) <= 9.2e+46)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -8e+112], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1250.0], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -6e-66], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -3.4e-181], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9.2e+46], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -7.9999999999999994e112 or 9.2000000000000002e46 < (*.f64 a b)

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. *-commutative 80.2%

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

      3. fma-def 81.2%

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

   5. Applied egg-rr 81.2%

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

   6. Taylor expanded in a around inf 64.7%

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

   if -7.9999999999999994e112 < (*.f64 a b) < -1250 or -6.0000000000000004e-66 < (*.f64 a b) < -3.4e-181

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 47.2%

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

      1. +-commutative 47.2%

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

      2. *-commutative 47.2%

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

      3. fma-def 47.2%

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

      4. *-commutative 47.2%

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

   5. Applied egg-rr 47.2%

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

   6. Taylor expanded in i around 0 37.1%

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

   if -1250 < (*.f64 a b) < -6.0000000000000004e-66 or -3.4e-181 < (*.f64 a b) < 9.2000000000000002e46

   1. Initial program 99.9%

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

   3. Taylor expanded in c around inf 44.5%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -8 \cdot 10^{+112}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1250:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq -6 \cdot 10^{-66}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -3.4 \cdot 10^{-181}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ \mathbf{if}\;c \cdot i \leq -1.6 \cdot 10^{+27}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.6 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{-148}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.6 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))))
   (if (<= (* c i) -1.6e+27)
     (+ (* z t) (* c i))
     (if (<= (* c i) -2.6e-195)
       t_1
       (if (<= (* c i) 1.05e-148)
         (+ (* x y) (* z t))
         (if (<= (* c i) 1.6e+160) 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) + (x * y);
	double tmp;
	if ((c * i) <= -1.6e+27) {
		tmp = (z * t) + (c * i);
	} else if ((c * i) <= -2.6e-195) {
		tmp = t_1;
	} else if ((c * i) <= 1.05e-148) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 1.6e+160) {
		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) + (x * y)
    if ((c * i) <= (-1.6d+27)) then
        tmp = (z * t) + (c * i)
    else if ((c * i) <= (-2.6d-195)) then
        tmp = t_1
    else if ((c * i) <= 1.05d-148) then
        tmp = (x * y) + (z * t)
    else if ((c * i) <= 1.6d+160) 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) + (x * y);
	double tmp;
	if ((c * i) <= -1.6e+27) {
		tmp = (z * t) + (c * i);
	} else if ((c * i) <= -2.6e-195) {
		tmp = t_1;
	} else if ((c * i) <= 1.05e-148) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 1.6e+160) {
		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) + (x * y)
	tmp = 0
	if (c * i) <= -1.6e+27:
		tmp = (z * t) + (c * i)
	elif (c * i) <= -2.6e-195:
		tmp = t_1
	elif (c * i) <= 1.05e-148:
		tmp = (x * y) + (z * t)
	elif (c * i) <= 1.6e+160:
		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(x * y))
	tmp = 0.0
	if (Float64(c * i) <= -1.6e+27)
		tmp = Float64(Float64(z * t) + Float64(c * i));
	elseif (Float64(c * i) <= -2.6e-195)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.05e-148)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(c * i) <= 1.6e+160)
		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) + (x * y);
	tmp = 0.0;
	if ((c * i) <= -1.6e+27)
		tmp = (z * t) + (c * i);
	elseif ((c * i) <= -2.6e-195)
		tmp = t_1;
	elseif ((c * i) <= 1.05e-148)
		tmp = (x * y) + (z * t);
	elseif ((c * i) <= 1.6e+160)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.6e+27], N[(N[(z * t), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.6e-195], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.05e-148], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.6e+160], 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) < -1.60000000000000008e27

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 76.2%

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

   if -1.60000000000000008e27 < (*.f64 c i) < -2.6000000000000002e-195 or 1.05e-148 < (*.f64 c i) < 1.5999999999999999e160

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 82.9%

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

      1. +-commutative 82.9%

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

      2. *-commutative 82.9%

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

      3. fma-def 83.0%

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

   5. Applied egg-rr 83.0%

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

   6. Taylor expanded in c around 0 72.4%

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

   if -2.6000000000000002e-195 < (*.f64 c i) < 1.05e-148

   1. Initial program 95.6%

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

   3. Taylor expanded in a around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. *-commutative 79.1%

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

      3. fma-def 79.1%

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

      4. *-commutative 79.1%

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

   5. Applied egg-rr 79.1%

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

   6. Taylor expanded in c around 0 79.1%

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

   if 1.5999999999999999e160 < (*.f64 c i)

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 81.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.6 \cdot 10^{+27}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.6 \cdot 10^{-195}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{-148}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.6 \cdot 10^{+160}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.1% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (+ (* a b) t_1) (* c i))))
   (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 = ((a * b) + t_1) + (c * i);
	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 = ((a * b) + t_1) + (c * i);
	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 = ((a * b) + t_1) + (c * i)
	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(Float64(a * b) + t_1) + Float64(c * i))
	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 = ((a * b) + t_1) + (c * i);
	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[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(c * i), $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 a around 0 60.0%

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

      1. +-commutative 60.0%

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

      2. *-commutative 60.0%

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

      3. fma-def 60.0%

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

      4. *-commutative 60.0%

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

   5. Applied egg-rr 60.0%

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

   6. Taylor expanded in c around 0 60.1%

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

4. Final simplification 98.4%

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

Alternative 9: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+129}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{+101}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2e+129)
   (+ (* a b) (* x y))
   (if (<= (* x y) 4.4e+101)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* 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) <= -2e+129) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 4.4e+101) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (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) <= (-2d+129)) then
        tmp = (a * b) + (x * y)
    else if ((x * y) <= 4.4d+101) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (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) <= -2e+129) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 4.4e+101) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2e+129:
		tmp = (a * b) + (x * y)
	elif (x * y) <= 4.4e+101:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -2e+129)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(x * y) <= 4.4e+101)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = 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) <= -2e+129)
		tmp = (a * b) + (x * y);
	elseif ((x * y) <= 4.4e+101)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (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], -2e+129], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.4e+101], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e129

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 92.5%

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

      1. +-commutative 92.5%

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

      2. *-commutative 92.5%

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

      3. fma-def 92.5%

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

   5. Applied egg-rr 92.5%

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

   6. Taylor expanded in c around 0 81.0%

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

   if -2e129 < (*.f64 x y) < 4.4000000000000001e101

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 90.1%

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

   if 4.4000000000000001e101 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in a around 0 89.3%

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

      1. +-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. fma-def 89.3%

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

      4. *-commutative 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in c around 0 85.9%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+129}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.4 \cdot 10^{+101}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;\left(a \cdot b + x \cdot y\right) + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+101}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.6e+122)
   (+ (+ (* a b) (* x y)) (* c i))
   (if (<= (* x y) 2.15e+101)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* 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) <= -1.6e+122) {
		tmp = ((a * b) + (x * y)) + (c * i);
	} else if ((x * y) <= 2.15e+101) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (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) <= (-1.6d+122)) then
        tmp = ((a * b) + (x * y)) + (c * i)
    else if ((x * y) <= 2.15d+101) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (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) <= -1.6e+122) {
		tmp = ((a * b) + (x * y)) + (c * i);
	} else if ((x * y) <= 2.15e+101) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.6e+122:
		tmp = ((a * b) + (x * y)) + (c * i)
	elif (x * y) <= 2.15e+101:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (z * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.6e+122)
		tmp = Float64(Float64(Float64(a * b) + Float64(x * y)) + Float64(c * i));
	elseif (Float64(x * y) <= 2.15e+101)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = 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) <= -1.6e+122)
		tmp = ((a * b) + (x * y)) + (c * i);
	elseif ((x * y) <= 2.15e+101)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (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], -1.6e+122], N[(N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.15e+101], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.60000000000000006e122

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 92.5%

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

   if -1.60000000000000006e122 < (*.f64 x y) < 2.15e101

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 90.1%

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

   if 2.15e101 < (*.f64 x y)

   1. Initial program 90.6%

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

   3. Taylor expanded in a around 0 89.3%

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

      1. +-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. fma-def 89.3%

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

      4. *-commutative 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in c around 0 85.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;\left(a \cdot b + x \cdot y\right) + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+101}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 88.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+123}:\\ \;\;\;\;\left(a \cdot b + x \cdot y\right) + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{+91}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -5.5e+123)
   (+ (+ (* a b) (* x y)) (* c i))
   (if (<= (* x y) 6.4e+91)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (+ (* x y) (* 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 ((x * y) <= -5.5e+123) {
		tmp = ((a * b) + (x * y)) + (c * i);
	} else if ((x * y) <= 6.4e+91) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = ((x * y) + (z * t)) + (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) <= (-5.5d+123)) then
        tmp = ((a * b) + (x * y)) + (c * i)
    else if ((x * y) <= 6.4d+91) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = ((x * y) + (z * t)) + (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) <= -5.5e+123) {
		tmp = ((a * b) + (x * y)) + (c * i);
	} else if ((x * y) <= 6.4e+91) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = ((x * y) + (z * t)) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -5.5e+123:
		tmp = ((a * b) + (x * y)) + (c * i)
	elif (x * y) <= 6.4e+91:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = ((x * y) + (z * t)) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -5.5e+123)
		tmp = Float64(Float64(Float64(a * b) + Float64(x * y)) + Float64(c * i));
	elseif (Float64(x * y) <= 6.4e+91)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) + 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) <= -5.5e+123)
		tmp = ((a * b) + (x * y)) + (c * i);
	elseif ((x * y) <= 6.4e+91)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = ((x * y) + (z * t)) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -5.5e+123], N[(N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.4e+91], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.5000000000000002e123

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 92.5%

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

   if -5.5000000000000002e123 < (*.f64 x y) < 6.39999999999999979e91

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 90.5%

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

   if 6.39999999999999979e91 < (*.f64 x y)

   1. Initial program 91.2%

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

   3. Taylor expanded in a around 0 90.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+123}:\\ \;\;\;\;\left(a \cdot b + x \cdot y\right) + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.4 \cdot 10^{+91}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot t\right) + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+182} \lor \neg \left(x \cdot y \leq 3.8 \cdot 10^{+139}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -4e+182) (not (<= (* x y) 3.8e+139)))
   (* 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) <= -4e+182) || !((x * y) <= 3.8e+139)) {
		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) <= (-4d+182)) .or. (.not. ((x * y) <= 3.8d+139))) 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) <= -4e+182) || !((x * y) <= 3.8e+139)) {
		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) <= -4e+182) or not ((x * y) <= 3.8e+139):
		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) <= -4e+182) || !(Float64(x * y) <= 3.8e+139))
		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) <= -4e+182) || ~(((x * y) <= 3.8e+139)))
		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], -4e+182], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.8e+139]], $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) < -4.0000000000000003e182 or 3.79999999999999999e139 < (*.f64 x y)

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. *-commutative 86.4%

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

      3. fma-def 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in y around inf 74.0%

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

   if -4.0000000000000003e182 < (*.f64 x y) < 3.79999999999999999e139

   1. Initial program 97.2%

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

   3. Taylor expanded in a around inf 66.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+182} \lor \neg \left(x \cdot y \leq 3.8 \cdot 10^{+139}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.2 \cdot 10^{+31} \lor \neg \left(c \cdot i \leq 1.5 \cdot 10^{+159}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -7.2e+31) (not (<= (* c i) 1.5e+159)))
   (+ (* a b) (* c i))
   (+ (* a b) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -7.2e+31) || !((c * i) <= 1.5e+159)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-7.2d+31)) .or. (.not. ((c * i) <= 1.5d+159))) then
        tmp = (a * b) + (c * i)
    else
        tmp = (a * b) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -7.2e+31) || !((c * i) <= 1.5e+159)) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -7.2e+31) or not ((c * i) <= 1.5e+159):
		tmp = (a * b) + (c * i)
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -7.2e+31) || !(Float64(c * i) <= 1.5e+159))
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -7.2e+31) || ~(((c * i) <= 1.5e+159)))
		tmp = (a * b) + (c * i);
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -7.2e+31], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.5e+159]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -7.19999999999999992e31 or 1.5000000000000001e159 < (*.f64 c i)

   1. Initial program 94.5%

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

   3. Taylor expanded in a around inf 77.2%

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

   if -7.19999999999999992e31 < (*.f64 c i) < 1.5000000000000001e159

   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 z around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. *-commutative 75.5%

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

      3. fma-def 75.5%

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

   5. Applied egg-rr 75.5%

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

   6. Taylor expanded in c around 0 69.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.2 \cdot 10^{+31} \lor \neg \left(c \cdot i \leq 1.5 \cdot 10^{+159}\right):\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 7.6 \cdot 10^{+158}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.35e+27)
   (+ (* z t) (* c i))
   (if (<= (* c i) 7.6e+158) (+ (* a b) (* 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 ((c * i) <= -1.35e+27) {
		tmp = (z * t) + (c * i);
	} else if ((c * i) <= 7.6e+158) {
		tmp = (a * b) + (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 ((c * i) <= (-1.35d+27)) then
        tmp = (z * t) + (c * i)
    else if ((c * i) <= 7.6d+158) then
        tmp = (a * b) + (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 ((c * i) <= -1.35e+27) {
		tmp = (z * t) + (c * i);
	} else if ((c * i) <= 7.6e+158) {
		tmp = (a * b) + (x * y);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.35e+27:
		tmp = (z * t) + (c * i)
	elif (c * i) <= 7.6e+158:
		tmp = (a * b) + (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(c * i) <= -1.35e+27)
		tmp = Float64(Float64(z * t) + Float64(c * i));
	elseif (Float64(c * i) <= 7.6e+158)
		tmp = Float64(Float64(a * b) + 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 ((c * i) <= -1.35e+27)
		tmp = (z * t) + (c * i);
	elseif ((c * i) <= 7.6e+158)
		tmp = (a * b) + (x * y);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.35e+27], N[(N[(z * t), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7.6e+158], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.3499999999999999e27

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 76.2%

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

   if -1.3499999999999999e27 < (*.f64 c i) < 7.5999999999999997e158

   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 z around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. *-commutative 75.9%

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

      3. fma-def 76.0%

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

   5. Applied egg-rr 76.0%

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

   6. Taylor expanded in c around 0 69.8%

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

   if 7.5999999999999997e158 < (*.f64 c i)

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 81.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 7.6 \cdot 10^{+158}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.1 \cdot 10^{+110} \lor \neg \left(a \cdot b \leq 9 \cdot 10^{+46}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.1e+110) (not (<= (* a b) 9e+46))) (* a b) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -1.1e+110) || !((a * b) <= 9e+46)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((a * b) <= (-1.1d+110)) .or. (.not. ((a * b) <= 9d+46))) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -1.1e+110) || !((a * b) <= 9e+46)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -1.1e+110) or not ((a * b) <= 9e+46):
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -1.1e+110) || !(Float64(a * b) <= 9e+46))
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -1.1e+110) || ~(((a * b) <= 9e+46)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.1e+110], N[Not[LessEqual[N[(a * b), $MachinePrecision], 9e+46]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.09999999999999996e110 or 9.00000000000000019e46 < (*.f64 a b)

   1. Initial program 90.4%

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

   3. Taylor expanded in z around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. *-commutative 79.4%

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

      3. fma-def 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in a around inf 64.1%

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

   if -1.09999999999999996e110 < (*.f64 a b) < 9.00000000000000019e46

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 37.5%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.1 \cdot 10^{+110} \lor \neg \left(a \cdot b \leq 9 \cdot 10^{+46}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.3% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in z around 0 77.9%

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

   1. +-commutative 77.9%

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

   2. *-commutative 77.9%

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

   3. fma-def 78.3%

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

5. Applied egg-rr 78.3%

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

6. Taylor expanded in a around inf 29.9%

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

7. Final simplification 29.9%

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

Reproduce

herbie shell --seed 2024020 
(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)))