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

Percentage Accurate: 96.0% → 97.8%

Time: 15.1s

Alternatives: 17

Speedup: 0.4×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% 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, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i \]
   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-define 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-define 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-define 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-undefine 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-undefine 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-define 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-undefine 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 a around 0 25.0%

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

   4. Taylor expanded in x around 0 25.1%

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

      1. +-commutative 25.1%

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

      2. fma-define 62.6%

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

   6. Simplified 62.6%

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

4. Final simplification 98.8%

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

Alternative 2: 98.0% 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 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 97.6%

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

   3. +-commutative 97.6%

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

   4. fma-define 98.4%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

      1. fma-undefine 100.0%

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

   8. Applied egg-rr 100.0%

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

   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 a around 0 25.0%

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

   4. Taylor expanded in x around 0 25.1%

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

      1. +-commutative 25.1%

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

      2. fma-define 62.6%

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

   6. Simplified 62.6%

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

4. Final simplification 98.8%

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

Alternative 4: 96.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. +-commutative 96.9%

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

   2. fma-define 97.6%

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

   3. +-commutative 97.6%

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

   4. fma-define 98.4%

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

   5. fma-define 98.4%

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

3. Simplified 98.4%

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

   1. fma-undefine 97.6%

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

   2. fma-define 97.6%

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

   3. associate-+r+ 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

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

Alternative 5: 64.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := z \cdot t + a \cdot b\\ t_3 := a \cdot b + x \cdot y\\ \mathbf{if}\;c \cdot i \leq -7.5 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -1.16 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -3.6 \cdot 10^{-167}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -4.3 \cdot 10^{-219}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 1.6 \cdot 10^{-161}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 1.8 \cdot 10^{+198}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i)))
        (t_2 (+ (* z t) (* a b)))
        (t_3 (+ (* a b) (* x y))))
   (if (<= (* c i) -7.5e+126)
     t_1
     (if (<= (* c i) -1.16e-141)
       t_2
       (if (<= (* c i) -3.6e-167)
         (* x y)
         (if (<= (* c i) -4.3e-219)
           t_2
           (if (<= (* c i) 1.6e-161)
             t_3
             (if (<= (* c i) 4.4e+62)
               t_2
               (if (<= (* c i) 1.8e+198) t_3 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (z * t) + (a * b);
	double t_3 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -7.5e+126) {
		tmp = t_1;
	} else if ((c * i) <= -1.16e-141) {
		tmp = t_2;
	} else if ((c * i) <= -3.6e-167) {
		tmp = x * y;
	} else if ((c * i) <= -4.3e-219) {
		tmp = t_2;
	} else if ((c * i) <= 1.6e-161) {
		tmp = t_3;
	} else if ((c * i) <= 4.4e+62) {
		tmp = t_2;
	} else if ((c * i) <= 1.8e+198) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = (z * t) + (a * b)
    t_3 = (a * b) + (x * y)
    if ((c * i) <= (-7.5d+126)) then
        tmp = t_1
    else if ((c * i) <= (-1.16d-141)) then
        tmp = t_2
    else if ((c * i) <= (-3.6d-167)) then
        tmp = x * y
    else if ((c * i) <= (-4.3d-219)) then
        tmp = t_2
    else if ((c * i) <= 1.6d-161) then
        tmp = t_3
    else if ((c * i) <= 4.4d+62) then
        tmp = t_2
    else if ((c * i) <= 1.8d+198) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (z * t) + (a * b);
	double t_3 = (a * b) + (x * y);
	double tmp;
	if ((c * i) <= -7.5e+126) {
		tmp = t_1;
	} else if ((c * i) <= -1.16e-141) {
		tmp = t_2;
	} else if ((c * i) <= -3.6e-167) {
		tmp = x * y;
	} else if ((c * i) <= -4.3e-219) {
		tmp = t_2;
	} else if ((c * i) <= 1.6e-161) {
		tmp = t_3;
	} else if ((c * i) <= 4.4e+62) {
		tmp = t_2;
	} else if ((c * i) <= 1.8e+198) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (z * t) + (a * b)
	t_3 = (a * b) + (x * y)
	tmp = 0
	if (c * i) <= -7.5e+126:
		tmp = t_1
	elif (c * i) <= -1.16e-141:
		tmp = t_2
	elif (c * i) <= -3.6e-167:
		tmp = x * y
	elif (c * i) <= -4.3e-219:
		tmp = t_2
	elif (c * i) <= 1.6e-161:
		tmp = t_3
	elif (c * i) <= 4.4e+62:
		tmp = t_2
	elif (c * i) <= 1.8e+198:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	t_2 = Float64(Float64(z * t) + Float64(a * b))
	t_3 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(c * i) <= -7.5e+126)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.16e-141)
		tmp = t_2;
	elseif (Float64(c * i) <= -3.6e-167)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -4.3e-219)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.6e-161)
		tmp = t_3;
	elseif (Float64(c * i) <= 4.4e+62)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.8e+198)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	t_2 = (z * t) + (a * b);
	t_3 = (a * b) + (x * y);
	tmp = 0.0;
	if ((c * i) <= -7.5e+126)
		tmp = t_1;
	elseif ((c * i) <= -1.16e-141)
		tmp = t_2;
	elseif ((c * i) <= -3.6e-167)
		tmp = x * y;
	elseif ((c * i) <= -4.3e-219)
		tmp = t_2;
	elseif ((c * i) <= 1.6e-161)
		tmp = t_3;
	elseif ((c * i) <= 4.4e+62)
		tmp = t_2;
	elseif ((c * i) <= 1.8e+198)
		tmp = t_3;
	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[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -7.5e+126], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.16e-141], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -3.6e-167], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -4.3e-219], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.6e-161], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], 4.4e+62], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.8e+198], t$95$3, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -7.5000000000000006e126 or 1.8000000000000001e198 < (*.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 82.7%

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

   4. Taylor expanded in t around 0 84.2%

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

   if -7.5000000000000006e126 < (*.f64 c i) < -1.15999999999999996e-141 or -3.6000000000000001e-167 < (*.f64 c i) < -4.3000000000000003e-219 or 1.59999999999999993e-161 < (*.f64 c i) < 4.40000000000000029e62

   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 x around 0 84.6%

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

   4. Taylor expanded in c around 0 76.1%

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

   if -1.15999999999999996e-141 < (*.f64 c i) < -3.6000000000000001e-167

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if -4.3000000000000003e-219 < (*.f64 c i) < 1.59999999999999993e-161 or 4.40000000000000029e62 < (*.f64 c i) < 1.8000000000000001e198

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0 95.6%

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

      1. *-commutative 95.6%

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

      2. fma-define 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in z around 0 72.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.5 \cdot 10^{+126}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.16 \cdot 10^{-141}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -3.6 \cdot 10^{-167}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -4.3 \cdot 10^{-219}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.6 \cdot 10^{-161}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{+62}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.8 \cdot 10^{+198}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + a \cdot b\\ t_2 := z \cdot t + x \cdot y\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -1.35 \cdot 10^{+127}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \cdot i \leq -3.8 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{-236}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 1.85 \cdot 10^{-166}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.3 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 3.7 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq 3.2 \cdot 10^{+248}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* a b)))
        (t_2 (+ (* z t) (* x y)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* c i) -1.35e+127)
     t_3
     (if (<= (* c i) -3.8e-141)
       t_1
       (if (<= (* c i) -1.3e-236)
         t_2
         (if (<= (* c i) 1.85e-166)
           (+ (* a b) (* x y))
           (if (<= (* c i) 4.3e+24)
             t_1
             (if (<= (* c i) 3.7e+146)
               t_2
               (if (<= (* c i) 3.2e+248) t_3 (+ (* x y) (* c i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (a * b);
	double t_2 = (z * t) + (x * y);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.35e+127) {
		tmp = t_3;
	} else if ((c * i) <= -3.8e-141) {
		tmp = t_1;
	} else if ((c * i) <= -1.3e-236) {
		tmp = t_2;
	} else if ((c * i) <= 1.85e-166) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 4.3e+24) {
		tmp = t_1;
	} else if ((c * i) <= 3.7e+146) {
		tmp = t_2;
	} else if ((c * i) <= 3.2e+248) {
		tmp = t_3;
	} else {
		tmp = (x * y) + (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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) + (a * b)
    t_2 = (z * t) + (x * y)
    t_3 = (a * b) + (c * i)
    if ((c * i) <= (-1.35d+127)) then
        tmp = t_3
    else if ((c * i) <= (-3.8d-141)) then
        tmp = t_1
    else if ((c * i) <= (-1.3d-236)) then
        tmp = t_2
    else if ((c * i) <= 1.85d-166) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 4.3d+24) then
        tmp = t_1
    else if ((c * i) <= 3.7d+146) then
        tmp = t_2
    else if ((c * i) <= 3.2d+248) then
        tmp = t_3
    else
        tmp = (x * y) + (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 = (z * t) + (a * b);
	double t_2 = (z * t) + (x * y);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.35e+127) {
		tmp = t_3;
	} else if ((c * i) <= -3.8e-141) {
		tmp = t_1;
	} else if ((c * i) <= -1.3e-236) {
		tmp = t_2;
	} else if ((c * i) <= 1.85e-166) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 4.3e+24) {
		tmp = t_1;
	} else if ((c * i) <= 3.7e+146) {
		tmp = t_2;
	} else if ((c * i) <= 3.2e+248) {
		tmp = t_3;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (a * b)
	t_2 = (z * t) + (x * y)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -1.35e+127:
		tmp = t_3
	elif (c * i) <= -3.8e-141:
		tmp = t_1
	elif (c * i) <= -1.3e-236:
		tmp = t_2
	elif (c * i) <= 1.85e-166:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 4.3e+24:
		tmp = t_1
	elif (c * i) <= 3.7e+146:
		tmp = t_2
	elif (c * i) <= 3.2e+248:
		tmp = t_3
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(a * b))
	t_2 = Float64(Float64(z * t) + Float64(x * y))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -1.35e+127)
		tmp = t_3;
	elseif (Float64(c * i) <= -3.8e-141)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.3e-236)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.85e-166)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 4.3e+24)
		tmp = t_1;
	elseif (Float64(c * i) <= 3.7e+146)
		tmp = t_2;
	elseif (Float64(c * i) <= 3.2e+248)
		tmp = t_3;
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (a * b);
	t_2 = (z * t) + (x * y);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -1.35e+127)
		tmp = t_3;
	elseif ((c * i) <= -3.8e-141)
		tmp = t_1;
	elseif ((c * i) <= -1.3e-236)
		tmp = t_2;
	elseif ((c * i) <= 1.85e-166)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 4.3e+24)
		tmp = t_1;
	elseif ((c * i) <= 3.7e+146)
		tmp = t_2;
	elseif ((c * i) <= 3.2e+248)
		tmp = t_3;
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.35e+127], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], -3.8e-141], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.3e-236], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.85e-166], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.3e+24], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 3.7e+146], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 3.2e+248], t$95$3, N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 c i) < -1.3500000000000001e127 or 3.70000000000000004e146 < (*.f64 c i) < 3.19999999999999985e248

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0 83.3%

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

   4. Taylor expanded in t around 0 81.7%

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

   if -1.3500000000000001e127 < (*.f64 c i) < -3.79999999999999987e-141 or 1.8500000000000001e-166 < (*.f64 c i) < 4.29999999999999987e24

   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 x around 0 84.2%

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

   4. Taylor expanded in c around 0 76.1%

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

   if -3.79999999999999987e-141 < (*.f64 c i) < -1.3e-236 or 4.29999999999999987e24 < (*.f64 c i) < 3.70000000000000004e146

   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 c around 0 91.1%

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

      1. *-commutative 91.1%

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

      2. fma-define 91.1%

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

   5. Applied egg-rr 91.1%

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

   6. Taylor expanded in a around 0 84.0%

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

   if -1.3e-236 < (*.f64 c i) < 1.8500000000000001e-166

   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 c around 0 98.3%

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

      1. *-commutative 98.3%

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

      2. fma-define 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in z around 0 75.0%

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

   if 3.19999999999999985e248 < (*.f64 c i)

   1. Initial program 87.0%

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

   3. Taylor expanded in a around 0 82.6%

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

   4. Taylor expanded in t around 0 91.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.35 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -3.8 \cdot 10^{-141}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -1.3 \cdot 10^{-236}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.85 \cdot 10^{-166}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 4.3 \cdot 10^{+24}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.7 \cdot 10^{+146}:\\ \;\;\;\;z \cdot t + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.2 \cdot 10^{+248}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 9.4 \cdot 10^{-251}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{-92}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4.5 \cdot 10^{+97} \lor \neg \left(a \cdot b \leq 4.8 \cdot 10^{+186}\right) \land a \cdot b \leq 4.4 \cdot 10^{+212}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -3.4e+27)
   (* a b)
   (if (<= (* a b) 9.4e-251)
     (* x y)
     (if (<= (* a b) 8.6e-92)
       (* c i)
       (if (<= (* a b) 9e-24)
         (* x y)
         (if (or (<= (* a b) 4.5e+97)
                 (and (not (<= (* a b) 4.8e+186)) (<= (* a b) 4.4e+212)))
           (* 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) <= -3.4e+27) {
		tmp = a * b;
	} else if ((a * b) <= 9.4e-251) {
		tmp = x * y;
	} else if ((a * b) <= 8.6e-92) {
		tmp = c * i;
	} else if ((a * b) <= 9e-24) {
		tmp = x * y;
	} else if (((a * b) <= 4.5e+97) || (!((a * b) <= 4.8e+186) && ((a * b) <= 4.4e+212))) {
		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) <= (-3.4d+27)) then
        tmp = a * b
    else if ((a * b) <= 9.4d-251) then
        tmp = x * y
    else if ((a * b) <= 8.6d-92) then
        tmp = c * i
    else if ((a * b) <= 9d-24) then
        tmp = x * y
    else if (((a * b) <= 4.5d+97) .or. (.not. ((a * b) <= 4.8d+186)) .and. ((a * b) <= 4.4d+212)) 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) <= -3.4e+27) {
		tmp = a * b;
	} else if ((a * b) <= 9.4e-251) {
		tmp = x * y;
	} else if ((a * b) <= 8.6e-92) {
		tmp = c * i;
	} else if ((a * b) <= 9e-24) {
		tmp = x * y;
	} else if (((a * b) <= 4.5e+97) || (!((a * b) <= 4.8e+186) && ((a * b) <= 4.4e+212))) {
		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) <= -3.4e+27:
		tmp = a * b
	elif (a * b) <= 9.4e-251:
		tmp = x * y
	elif (a * b) <= 8.6e-92:
		tmp = c * i
	elif (a * b) <= 9e-24:
		tmp = x * y
	elif ((a * b) <= 4.5e+97) or (not ((a * b) <= 4.8e+186) and ((a * b) <= 4.4e+212)):
		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) <= -3.4e+27)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 9.4e-251)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 8.6e-92)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 9e-24)
		tmp = Float64(x * y);
	elseif ((Float64(a * b) <= 4.5e+97) || (!(Float64(a * b) <= 4.8e+186) && (Float64(a * b) <= 4.4e+212)))
		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) <= -3.4e+27)
		tmp = a * b;
	elseif ((a * b) <= 9.4e-251)
		tmp = x * y;
	elseif ((a * b) <= 8.6e-92)
		tmp = c * i;
	elseif ((a * b) <= 9e-24)
		tmp = x * y;
	elseif (((a * b) <= 4.5e+97) || (~(((a * b) <= 4.8e+186)) && ((a * b) <= 4.4e+212)))
		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], -3.4e+27], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9.4e-251], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.6e-92], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9e-24], N[(x * y), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 4.5e+97], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 4.8e+186]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 4.4e+212]]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.4e27 or 4.49999999999999976e97 < (*.f64 a b) < 4.7999999999999999e186 or 4.3999999999999999e212 < (*.f64 a b)

   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 64.2%

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

   if -3.4e27 < (*.f64 a b) < 9.4000000000000003e-251 or 8.60000000000000027e-92 < (*.f64 a b) < 8.9999999999999995e-24

   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 inf 42.9%

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

   if 9.4000000000000003e-251 < (*.f64 a b) < 8.60000000000000027e-92 or 8.9999999999999995e-24 < (*.f64 a b) < 4.49999999999999976e97 or 4.7999999999999999e186 < (*.f64 a b) < 4.3999999999999999e212

   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 c around inf 56.2%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 9.4 \cdot 10^{-251}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 8.6 \cdot 10^{-92}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4.5 \cdot 10^{+97} \lor \neg \left(a \cdot b \leq 4.8 \cdot 10^{+186}\right) \land a \cdot b \leq 4.4 \cdot 10^{+212}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -9.2 \cdot 10^{+126}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -9.6 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -3.6 \cdot 10^{-167}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.1 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq 10^{-161}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.76 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* a b))))
   (if (<= (* c i) -9.2e+126)
     (+ (* a b) (* c i))
     (if (<= (* c i) -9.6e-142)
       t_1
       (if (<= (* c i) -3.6e-167)
         (* x y)
         (if (<= (* c i) -1.1e-217)
           t_1
           (if (<= (* c i) 1e-161)
             (+ (* a b) (* x y))
             (if (<= (* c i) 1.76e+46) t_1 (+ (* x y) (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (a * b);
	double tmp;
	if ((c * i) <= -9.2e+126) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -9.6e-142) {
		tmp = t_1;
	} else if ((c * i) <= -3.6e-167) {
		tmp = x * y;
	} else if ((c * i) <= -1.1e-217) {
		tmp = t_1;
	} else if ((c * i) <= 1e-161) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 1.76e+46) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (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 = (z * t) + (a * b)
    if ((c * i) <= (-9.2d+126)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= (-9.6d-142)) then
        tmp = t_1
    else if ((c * i) <= (-3.6d-167)) then
        tmp = x * y
    else if ((c * i) <= (-1.1d-217)) then
        tmp = t_1
    else if ((c * i) <= 1d-161) then
        tmp = (a * b) + (x * y)
    else if ((c * i) <= 1.76d+46) then
        tmp = t_1
    else
        tmp = (x * y) + (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 = (z * t) + (a * b);
	double tmp;
	if ((c * i) <= -9.2e+126) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -9.6e-142) {
		tmp = t_1;
	} else if ((c * i) <= -3.6e-167) {
		tmp = x * y;
	} else if ((c * i) <= -1.1e-217) {
		tmp = t_1;
	} else if ((c * i) <= 1e-161) {
		tmp = (a * b) + (x * y);
	} else if ((c * i) <= 1.76e+46) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (a * b)
	tmp = 0
	if (c * i) <= -9.2e+126:
		tmp = (a * b) + (c * i)
	elif (c * i) <= -9.6e-142:
		tmp = t_1
	elif (c * i) <= -3.6e-167:
		tmp = x * y
	elif (c * i) <= -1.1e-217:
		tmp = t_1
	elif (c * i) <= 1e-161:
		tmp = (a * b) + (x * y)
	elif (c * i) <= 1.76e+46:
		tmp = t_1
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(a * b))
	tmp = 0.0
	if (Float64(c * i) <= -9.2e+126)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= -9.6e-142)
		tmp = t_1;
	elseif (Float64(c * i) <= -3.6e-167)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -1.1e-217)
		tmp = t_1;
	elseif (Float64(c * i) <= 1e-161)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(c * i) <= 1.76e+46)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (a * b);
	tmp = 0.0;
	if ((c * i) <= -9.2e+126)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= -9.6e-142)
		tmp = t_1;
	elseif ((c * i) <= -3.6e-167)
		tmp = x * y;
	elseif ((c * i) <= -1.1e-217)
		tmp = t_1;
	elseif ((c * i) <= 1e-161)
		tmp = (a * b) + (x * y);
	elseif ((c * i) <= 1.76e+46)
		tmp = t_1;
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -9.2e+126], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -9.6e-142], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -3.6e-167], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.1e-217], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1e-161], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.76e+46], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 c i) < -9.2000000000000002e126

   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 85.5%

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

   4. Taylor expanded in t around 0 83.4%

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

   if -9.2000000000000002e126 < (*.f64 c i) < -9.59999999999999952e-142 or -3.6000000000000001e-167 < (*.f64 c i) < -1.09999999999999991e-217 or 1.00000000000000003e-161 < (*.f64 c i) < 1.76e46

   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 x around 0 84.3%

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

   4. Taylor expanded in c around 0 77.4%

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

   if -9.59999999999999952e-142 < (*.f64 c i) < -3.6000000000000001e-167

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if -1.09999999999999991e-217 < (*.f64 c i) < 1.00000000000000003e-161

   1. Initial program 98.5%

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

   3. Taylor expanded in c around 0 98.5%

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

      1. *-commutative 98.5%

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

      2. fma-define 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in z around 0 74.4%

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

   if 1.76e46 < (*.f64 c i)

   1. Initial program 94.1%

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

   3. Taylor expanded in a around 0 84.1%

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

   4. Taylor expanded in t around 0 77.5%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9.2 \cdot 10^{+126}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -9.6 \cdot 10^{-142}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -3.6 \cdot 10^{-167}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.1 \cdot 10^{-217}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 10^{-161}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.76 \cdot 10^{+46}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.1 \cdot 10^{+28}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.15 \cdot 10^{-302}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{+99} \lor \neg \left(a \cdot b \leq 1.2 \cdot 10^{+189}\right) \land a \cdot b \leq 2.5 \cdot 10^{+212}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -3.1e+28)
   (* a b)
   (if (<= (* a b) 1.15e-302)
     (* z t)
     (if (or (<= (* a b) 6.2e+99)
             (and (not (<= (* a b) 1.2e+189)) (<= (* a b) 2.5e+212)))
       (* 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) <= -3.1e+28) {
		tmp = a * b;
	} else if ((a * b) <= 1.15e-302) {
		tmp = z * t;
	} else if (((a * b) <= 6.2e+99) || (!((a * b) <= 1.2e+189) && ((a * b) <= 2.5e+212))) {
		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) <= (-3.1d+28)) then
        tmp = a * b
    else if ((a * b) <= 1.15d-302) then
        tmp = z * t
    else if (((a * b) <= 6.2d+99) .or. (.not. ((a * b) <= 1.2d+189)) .and. ((a * b) <= 2.5d+212)) 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) <= -3.1e+28) {
		tmp = a * b;
	} else if ((a * b) <= 1.15e-302) {
		tmp = z * t;
	} else if (((a * b) <= 6.2e+99) || (!((a * b) <= 1.2e+189) && ((a * b) <= 2.5e+212))) {
		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) <= -3.1e+28:
		tmp = a * b
	elif (a * b) <= 1.15e-302:
		tmp = z * t
	elif ((a * b) <= 6.2e+99) or (not ((a * b) <= 1.2e+189) and ((a * b) <= 2.5e+212)):
		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) <= -3.1e+28)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 1.15e-302)
		tmp = Float64(z * t);
	elseif ((Float64(a * b) <= 6.2e+99) || (!(Float64(a * b) <= 1.2e+189) && (Float64(a * b) <= 2.5e+212)))
		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) <= -3.1e+28)
		tmp = a * b;
	elseif ((a * b) <= 1.15e-302)
		tmp = z * t;
	elseif (((a * b) <= 6.2e+99) || (~(((a * b) <= 1.2e+189)) && ((a * b) <= 2.5e+212)))
		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], -3.1e+28], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.15e-302], N[(z * t), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 6.2e+99], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.2e+189]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 2.5e+212]]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.1000000000000001e28 or 6.2000000000000001e99 < (*.f64 a b) < 1.2e189 or 2.49999999999999996e212 < (*.f64 a b)

   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 64.2%

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

   if -3.1000000000000001e28 < (*.f64 a b) < 1.15000000000000001e-302

   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 inf 36.0%

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

   if 1.15000000000000001e-302 < (*.f64 a b) < 6.2000000000000001e99 or 1.2e189 < (*.f64 a b) < 2.49999999999999996e212

   1. Initial program 98.4%

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

   3. Taylor expanded in c around inf 47.4%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.1 \cdot 10^{+28}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 1.15 \cdot 10^{-302}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.2 \cdot 10^{+99} \lor \neg \left(a \cdot b \leq 1.2 \cdot 10^{+189}\right) \land a \cdot b \leq 2.5 \cdot 10^{+212}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + a \cdot b\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -1.15 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \cdot i \leq -9.6 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \cdot i \leq -3.35 \cdot 10^{-167}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.85 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* a b))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* c i) -1.15e+127)
     t_2
     (if (<= (* c i) -9.6e-142)
       t_1
       (if (<= (* c i) -3.35e-167)
         (* x y)
         (if (<= (* c i) 1.85e+146) 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 = (z * t) + (a * b);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.15e+127) {
		tmp = t_2;
	} else if ((c * i) <= -9.6e-142) {
		tmp = t_1;
	} else if ((c * i) <= -3.35e-167) {
		tmp = x * y;
	} else if ((c * i) <= 1.85e+146) {
		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 = (z * t) + (a * b)
    t_2 = (a * b) + (c * i)
    if ((c * i) <= (-1.15d+127)) then
        tmp = t_2
    else if ((c * i) <= (-9.6d-142)) then
        tmp = t_1
    else if ((c * i) <= (-3.35d-167)) then
        tmp = x * y
    else if ((c * i) <= 1.85d+146) 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 = (z * t) + (a * b);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -1.15e+127) {
		tmp = t_2;
	} else if ((c * i) <= -9.6e-142) {
		tmp = t_1;
	} else if ((c * i) <= -3.35e-167) {
		tmp = x * y;
	} else if ((c * i) <= 1.85e+146) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (a * b)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -1.15e+127:
		tmp = t_2
	elif (c * i) <= -9.6e-142:
		tmp = t_1
	elif (c * i) <= -3.35e-167:
		tmp = x * y
	elif (c * i) <= 1.85e+146:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(a * b))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -1.15e+127)
		tmp = t_2;
	elseif (Float64(c * i) <= -9.6e-142)
		tmp = t_1;
	elseif (Float64(c * i) <= -3.35e-167)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 1.85e+146)
		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 = (z * t) + (a * b);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -1.15e+127)
		tmp = t_2;
	elseif ((c * i) <= -9.6e-142)
		tmp = t_1;
	elseif ((c * i) <= -3.35e-167)
		tmp = x * y;
	elseif ((c * i) <= 1.85e+146)
		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[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.15e+127], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -9.6e-142], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -3.35e-167], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.85e+146], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.1500000000000001e127 or 1.85000000000000002e146 < (*.f64 c i)

   1. Initial program 92.5%

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

   3. Taylor expanded in x around 0 80.7%

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

   4. Taylor expanded in t around 0 82.1%

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

   if -1.1500000000000001e127 < (*.f64 c i) < -9.59999999999999952e-142 or -3.35000000000000004e-167 < (*.f64 c i) < 1.85000000000000002e146

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 71.6%

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

   4. Taylor expanded in c around 0 66.5%

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

   if -9.59999999999999952e-142 < (*.f64 c i) < -3.35000000000000004e-167

   1. Initial program 80.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.15 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -9.6 \cdot 10^{-142}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -3.35 \cdot 10^{-167}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.85 \cdot 10^{+146}:\\ \;\;\;\;z \cdot t + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.1% accurate, 0.4× speedup

Math

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

FPCore

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

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) + ((a * b) + ((z * t) + (x * y)))) <= Double.POSITIVE_INFINITY) {
		tmp = ((x * y) + (c * i)) + ((z * t) + (a * b));
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

      1. fma-undefine 100.0%

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

   8. Applied egg-rr 100.0%

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

   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 inf 50.5%

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

4. Final simplification 98.4%

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

Alternative 12: 41.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{-25} \lor \neg \left(a \cdot b \leq 2.1 \cdot 10^{+100}\right) \land \left(a \cdot b \leq 1.06 \cdot 10^{+189} \lor \neg \left(a \cdot b \leq 2.7 \cdot 10^{+212}\right)\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -2.05e-25)
         (and (not (<= (* a b) 2.1e+100))
              (or (<= (* a b) 1.06e+189) (not (<= (* a b) 2.7e+212)))))
   (* 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) <= -2.05e-25) || (!((a * b) <= 2.1e+100) && (((a * b) <= 1.06e+189) || !((a * b) <= 2.7e+212)))) {
		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) <= (-2.05d-25)) .or. (.not. ((a * b) <= 2.1d+100)) .and. ((a * b) <= 1.06d+189) .or. (.not. ((a * b) <= 2.7d+212))) 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) <= -2.05e-25) || (!((a * b) <= 2.1e+100) && (((a * b) <= 1.06e+189) || !((a * b) <= 2.7e+212)))) {
		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) <= -2.05e-25) or (not ((a * b) <= 2.1e+100) and (((a * b) <= 1.06e+189) or not ((a * b) <= 2.7e+212))):
		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) <= -2.05e-25) || (!(Float64(a * b) <= 2.1e+100) && ((Float64(a * b) <= 1.06e+189) || !(Float64(a * b) <= 2.7e+212))))
		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) <= -2.05e-25) || (~(((a * b) <= 2.1e+100)) && (((a * b) <= 1.06e+189) || ~(((a * b) <= 2.7e+212)))))
		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], -2.05e-25], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.1e+100]], $MachinePrecision], Or[LessEqual[N[(a * b), $MachinePrecision], 1.06e+189], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.7e+212]], $MachinePrecision]]]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.04999999999999994e-25 or 2.0999999999999999e100 < (*.f64 a b) < 1.05999999999999998e189 or 2.7e212 < (*.f64 a b)

   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 inf 59.2%

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

   if -2.04999999999999994e-25 < (*.f64 a b) < 2.0999999999999999e100 or 1.05999999999999998e189 < (*.f64 a b) < 2.7e212

   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 c around inf 38.1%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.05 \cdot 10^{-25} \lor \neg \left(a \cdot b \leq 2.1 \cdot 10^{+100}\right) \land \left(a \cdot b \leq 1.06 \cdot 10^{+189} \lor \neg \left(a \cdot b \leq 2.7 \cdot 10^{+212}\right)\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.7 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.8 \cdot 10^{+166}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.7e+127)
   (+ (* a b) (* c i))
   (if (<= (* c i) 2.8e+166)
     (+ (* a b) (+ (* z t) (* x y)))
     (+ (* x y) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.7e+127) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 2.8e+166) {
		tmp = (a * b) + ((z * t) + (x * y));
	} else {
		tmp = (x * y) + (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) <= (-1.7d+127)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= 2.8d+166) then
        tmp = (a * b) + ((z * t) + (x * y))
    else
        tmp = (x * y) + (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) <= -1.7e+127) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 2.8e+166) {
		tmp = (a * b) + ((z * t) + (x * y));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.7e+127:
		tmp = (a * b) + (c * i)
	elif (c * i) <= 2.8e+166:
		tmp = (a * b) + ((z * t) + (x * y))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.7e+127)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= 2.8e+166)
		tmp = Float64(Float64(a * b) + Float64(Float64(z * t) + Float64(x * y)));
	else
		tmp = Float64(Float64(x * y) + 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) <= -1.7e+127)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= 2.8e+166)
		tmp = (a * b) + ((z * t) + (x * y));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.7e+127], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.8e+166], N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.69999999999999989e127

   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 85.5%

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

   4. Taylor expanded in t around 0 83.4%

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

   if -1.69999999999999989e127 < (*.f64 c i) < 2.79999999999999996e166

   1. Initial program 98.9%

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

   3. Taylor expanded in c around 0 93.1%

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

   if 2.79999999999999996e166 < (*.f64 c i)

   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 81.6%

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

   4. Taylor expanded in t around 0 87.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.7 \cdot 10^{+127}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.8 \cdot 10^{+166}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{+168}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.9e+61)
   (+ (* c i) (+ (* z t) (* a b)))
   (if (<= (* c i) 8.5e+168)
     (+ (* a b) (+ (* z t) (* x y)))
     (+ (* x y) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.9e+61) {
		tmp = (c * i) + ((z * t) + (a * b));
	} else if ((c * i) <= 8.5e+168) {
		tmp = (a * b) + ((z * t) + (x * y));
	} else {
		tmp = (x * y) + (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) <= (-1.9d+61)) then
        tmp = (c * i) + ((z * t) + (a * b))
    else if ((c * i) <= 8.5d+168) then
        tmp = (a * b) + ((z * t) + (x * y))
    else
        tmp = (x * y) + (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) <= -1.9e+61) {
		tmp = (c * i) + ((z * t) + (a * b));
	} else if ((c * i) <= 8.5e+168) {
		tmp = (a * b) + ((z * t) + (x * y));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.9e+61:
		tmp = (c * i) + ((z * t) + (a * b))
	elif (c * i) <= 8.5e+168:
		tmp = (a * b) + ((z * t) + (x * y))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.9e+61)
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(a * b)));
	elseif (Float64(c * i) <= 8.5e+168)
		tmp = Float64(Float64(a * b) + Float64(Float64(z * t) + Float64(x * y)));
	else
		tmp = Float64(Float64(x * y) + 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) <= -1.9e+61)
		tmp = (c * i) + ((z * t) + (a * b));
	elseif ((c * i) <= 8.5e+168)
		tmp = (a * b) + ((z * t) + (x * y));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.9e+61], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.5e+168], N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.89999999999999998e61

   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 x around 0 87.4%

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

   if -1.89999999999999998e61 < (*.f64 c i) < 8.50000000000000069e168

   1. Initial program 98.8%

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

   3. Taylor expanded in c around 0 93.7%

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

   if 8.50000000000000069e168 < (*.f64 c i)

   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 81.6%

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

   4. Taylor expanded in t around 0 87.9%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{+168}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -1.25 \cdot 10^{-12}:\\ \;\;\;\;a \cdot b + t\_1\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{+95}:\\ \;\;\;\;c \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* z t) (* x y))))
   (if (<= (* a b) -1.25e-12)
     (+ (* a b) t_1)
     (if (<= (* a b) 2.9e+95)
       (+ (* c i) t_1)
       (+ (* c i) (+ (* z t) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (x * y);
	double tmp;
	if ((a * b) <= -1.25e-12) {
		tmp = (a * b) + t_1;
	} else if ((a * b) <= 2.9e+95) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (c * i) + ((z * t) + (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) + (x * y)
    if ((a * b) <= (-1.25d-12)) then
        tmp = (a * b) + t_1
    else if ((a * b) <= 2.9d+95) then
        tmp = (c * i) + t_1
    else
        tmp = (c * i) + ((z * t) + (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (z * t) + (x * y);
	double tmp;
	if ((a * b) <= -1.25e-12) {
		tmp = (a * b) + t_1;
	} else if ((a * b) <= 2.9e+95) {
		tmp = (c * i) + t_1;
	} else {
		tmp = (c * i) + ((z * t) + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (z * t) + (x * y)
	tmp = 0
	if (a * b) <= -1.25e-12:
		tmp = (a * b) + t_1
	elif (a * b) <= 2.9e+95:
		tmp = (c * i) + t_1
	else:
		tmp = (c * i) + ((z * t) + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(z * t) + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -1.25e-12)
		tmp = Float64(Float64(a * b) + t_1);
	elseif (Float64(a * b) <= 2.9e+95)
		tmp = Float64(Float64(c * i) + t_1);
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (z * t) + (x * y);
	tmp = 0.0;
	if ((a * b) <= -1.25e-12)
		tmp = (a * b) + t_1;
	elseif ((a * b) <= 2.9e+95)
		tmp = (c * i) + t_1;
	else
		tmp = (c * i) + ((z * t) + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.25e-12], N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2.9e+95], N[(N[(c * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.24999999999999992e-12

   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 c around 0 88.9%

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

   if -1.24999999999999992e-12 < (*.f64 a b) < 2.90000000000000013e95

   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 a around 0 94.9%

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

   if 2.90000000000000013e95 < (*.f64 a b)

   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 x around 0 88.7%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.25 \cdot 10^{-12}:\\ \;\;\;\;a \cdot b + \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;a \cdot b \leq 2.9 \cdot 10^{+95}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+121} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.65e+121) (not (<= (* x y) 2.9e+101)))
   (* 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) <= -1.65e+121) || !((x * y) <= 2.9e+101)) {
		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) <= (-1.65d+121)) .or. (.not. ((x * y) <= 2.9d+101))) 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) <= -1.65e+121) || !((x * y) <= 2.9e+101)) {
		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) <= -1.65e+121) or not ((x * y) <= 2.9e+101):
		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) <= -1.65e+121) || !(Float64(x * y) <= 2.9e+101))
		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) <= -1.65e+121) || ~(((x * y) <= 2.9e+101)))
		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], -1.65e+121], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.9e+101]], $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) < -1.6499999999999999e121 or 2.89999999999999987e101 < (*.f64 x y)

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 69.8%

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

   if -1.6499999999999999e121 < (*.f64 x y) < 2.89999999999999987e101

   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 89.5%

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

   4. Taylor expanded in t around 0 64.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+121} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+101}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 27.9% 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 96.9%

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

3. Taylor expanded in a around inf 28.2%

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

4. Final simplification 28.2%

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

Reproduce

herbie shell --seed 2024039 
(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)))