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

Percentage Accurate: 95.6% → 98.0%

Time: 17.3s

Alternatives: 18

Speedup: 0.5×

• 42.7% 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: 95.6% 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: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. +-commutative 94.5%

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

   2. fma-def 96.1%

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

   3. +-commutative 96.1%

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

   4. associate-+r+ 96.1%

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

   5. +-commutative 96.1%

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

   6. fma-def 97.2%

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

   7. +-commutative 97.2%

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

   8. fma-def 97.6%

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

3. Simplified 97.6%

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

4. Final simplification 97.6%

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

Alternative 2: 97.9% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. +-commutative 94.5%

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

   2. fma-def 96.1%

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

   3. +-commutative 96.1%

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

   4. fma-def 96.5%

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

   5. fma-def 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 3: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 28.6%

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

      3. +-commutative 28.6%

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

      4. associate-+r+ 28.6%

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

      5. +-commutative 28.6%

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

      6. fma-def 50.0%

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

      7. +-commutative 50.0%

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

      8. fma-def 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in z around 0 57.1%

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

      1. fma-def 57.1%

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

   6. Simplified 57.1%

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

4. Final simplification 97.6%

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

Alternative 4: 97.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + \left(a \cdot b + \left(x \cdot y + z \cdot t\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \frac{1}{\frac{1}{a \cdot b + x \cdot y}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* a b) (+ (* x y) (* z t))))))
   (if (<= t_1 INFINITY) t_1 (fma c i (/ 1.0 (/ 1.0 (+ (* a b) (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((a * b) + ((x * y) + (z * t)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(c, i, (1.0 / (1.0 / ((a * b) + (x * y)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(c, i, Float64(1.0 / Float64(1.0 / Float64(Float64(a * b) + Float64(x * y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * i + N[(1.0 / N[(1.0 / N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 28.6%

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

      3. +-commutative 28.6%

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

      4. associate-+r+ 28.6%

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

      5. +-commutative 28.6%

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

      6. fma-def 50.0%

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

      7. +-commutative 50.0%

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

      8. fma-def 57.1%

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

   3. Simplified 57.1%

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

      1. fma-udef 35.7%

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

      2. fma-udef 28.6%

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

      3. associate-+r+ 28.6%

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

      4. +-commutative 28.6%

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

      5. fma-def 35.7%

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

      6. flip-+ 0.0%

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

      7. clear-num 0.0%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 0.0%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 35.7%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 35.7%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 57.1%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 57.1%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in z around 0 57.1%

      \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{a \cdot b + x \cdot y}}}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i + \left(a \cdot b + \left(x \cdot y + z \cdot t\right)\right) \leq \infty:\\ \;\;\;\;c \cdot i + \left(a \cdot b + \left(x \cdot y + z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \frac{1}{\frac{1}{a \cdot b + x \cdot y}}\right)\\ \end{array} \]

Alternative 5: 97.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 28.6%

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

      3. +-commutative 28.6%

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

      4. associate-+r+ 28.6%

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

      5. +-commutative 28.6%

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

      6. fma-def 50.0%

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

      7. +-commutative 50.0%

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

      8. fma-def 57.1%

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

   3. Simplified 57.1%

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

      1. fma-udef 35.7%

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

      2. fma-udef 28.6%

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

      3. associate-+r+ 28.6%

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

      4. +-commutative 28.6%

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

      5. fma-def 35.7%

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

      6. flip-+ 0.0%

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

      7. clear-num 0.0%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 0.0%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 35.7%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 35.7%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 57.1%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 57.1%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 28.6%

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

      1. +-commutative 28.6%

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

      2. *-commutative 28.6%

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

      3. associate-+r+ 28.6%

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

      4. fma-udef 35.7%

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

      5. *-commutative 35.7%

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

      6. fma-udef 57.1%

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

      7. fma-udef 50.0%

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

      8. +-commutative 50.0%

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

      9. fma-def 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in t around 0 44.5%

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

       1. fma-def 44.5%

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

   11. Simplified 44.5%

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

4. Final simplification 96.9%

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

Alternative 6: 58.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+134}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{+72}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{-164}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+36} \lor \neg \left(x \cdot y \leq 10^{+84}\right) \land x \cdot y \leq 1.76 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* x y) -8.2e+134)
     (* x y)
     (if (<= (* x y) -2.9e+72)
       (* z t)
       (if (<= (* x y) -2.5e+72)
         (* x y)
         (if (<= (* x y) 0.0)
           t_1
           (if (<= (* x y) 1.2e-164)
             (* z t)
             (if (or (<= (* x y) 2.1e+36)
                     (and (not (<= (* x y) 1e+84)) (<= (* x y) 1.76e+161)))
               t_1
               (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -8.2e+134) {
		tmp = x * y;
	} else if ((x * y) <= -2.9e+72) {
		tmp = z * t;
	} else if ((x * y) <= -2.5e+72) {
		tmp = x * y;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.2e-164) {
		tmp = z * t;
	} else if (((x * y) <= 2.1e+36) || (!((x * y) <= 1e+84) && ((x * y) <= 1.76e+161))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((x * y) <= (-8.2d+134)) then
        tmp = x * y
    else if ((x * y) <= (-2.9d+72)) then
        tmp = z * t
    else if ((x * y) <= (-2.5d+72)) then
        tmp = x * y
    else if ((x * y) <= 0.0d0) then
        tmp = t_1
    else if ((x * y) <= 1.2d-164) then
        tmp = z * t
    else if (((x * y) <= 2.1d+36) .or. (.not. ((x * y) <= 1d+84)) .and. ((x * y) <= 1.76d+161)) then
        tmp = t_1
    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 t_1 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -8.2e+134) {
		tmp = x * y;
	} else if ((x * y) <= -2.9e+72) {
		tmp = z * t;
	} else if ((x * y) <= -2.5e+72) {
		tmp = x * y;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.2e-164) {
		tmp = z * t;
	} else if (((x * y) <= 2.1e+36) || (!((x * y) <= 1e+84) && ((x * y) <= 1.76e+161))) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -8.2e+134:
		tmp = x * y
	elif (x * y) <= -2.9e+72:
		tmp = z * t
	elif (x * y) <= -2.5e+72:
		tmp = x * y
	elif (x * y) <= 0.0:
		tmp = t_1
	elif (x * y) <= 1.2e-164:
		tmp = z * t
	elif ((x * y) <= 2.1e+36) or (not ((x * y) <= 1e+84) and ((x * y) <= 1.76e+161)):
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -8.2e+134)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.9e+72)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -2.5e+72)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 0.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.2e-164)
		tmp = Float64(z * t);
	elseif ((Float64(x * y) <= 2.1e+36) || (!(Float64(x * y) <= 1e+84) && (Float64(x * y) <= 1.76e+161)))
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -8.2e+134)
		tmp = x * y;
	elseif ((x * y) <= -2.9e+72)
		tmp = z * t;
	elseif ((x * y) <= -2.5e+72)
		tmp = x * y;
	elseif ((x * y) <= 0.0)
		tmp = t_1;
	elseif ((x * y) <= 1.2e-164)
		tmp = z * t;
	elseif (((x * y) <= 2.1e+36) || (~(((x * y) <= 1e+84)) && ((x * y) <= 1.76e+161)))
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8.2e+134], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.9e+72], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.5e+72], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.2e-164], N[(z * t), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 2.1e+36], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+84]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 1.76e+161]]], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.2000000000000007e134 or -2.90000000000000017e72 < (*.f64 x y) < -2.49999999999999996e72 or 2.10000000000000004e36 < (*.f64 x y) < 1.00000000000000006e84 or 1.75999999999999994e161 < (*.f64 x y)

   1. Initial program 93.9%

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

      1. +-commutative 93.9%

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

      2. fma-def 95.1%

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

      3. +-commutative 95.1%

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

      4. associate-+r+ 95.1%

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

      5. +-commutative 95.1%

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

      6. fma-def 96.3%

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

      7. +-commutative 96.3%

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

      8. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 76.1%

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

   if -8.2000000000000007e134 < (*.f64 x y) < -2.90000000000000017e72 or -0.0 < (*.f64 x y) < 1.19999999999999992e-164

   1. Initial program 97.2%

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

      1. +-commutative 97.2%

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

      2. fma-def 97.2%

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

      3. +-commutative 97.2%

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

      4. associate-+r+ 97.2%

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

      5. +-commutative 97.2%

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

      6. fma-def 97.2%

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

      7. +-commutative 97.2%

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

      8. fma-def 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in z around inf 67.3%

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

   if -2.49999999999999996e72 < (*.f64 x y) < -0.0 or 1.19999999999999992e-164 < (*.f64 x y) < 2.10000000000000004e36 or 1.00000000000000006e84 < (*.f64 x y) < 1.75999999999999994e161

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. fma-def 96.3%

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

      3. +-commutative 96.3%

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

      4. associate-+r+ 96.3%

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

      5. +-commutative 96.3%

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

      6. fma-def 97.8%

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

      7. +-commutative 97.8%

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

      8. fma-def 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in x around 0 90.9%

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

   5. Taylor expanded in t around 0 64.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.2 \cdot 10^{+134}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{+72}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{-164}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+36} \lor \neg \left(x \cdot y \leq 10^{+84}\right) \land x \cdot y \leq 1.76 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 62.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -6.2 \cdot 10^{+224}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -3700000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{+36} \lor \neg \left(x \cdot y \leq 1.15 \cdot 10^{+84}\right) \land x \cdot y \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* x y) -6.2e+224)
     (* x y)
     (if (<= (* x y) -1.5e+73)
       t_1
       (if (<= (* x y) -3700000000000.0)
         t_2
         (if (<= (* x y) 8e-58)
           t_1
           (if (or (<= (* x y) 1.65e+36)
                   (and (not (<= (* x y) 1.15e+84)) (<= (* x y) 1.55e+161)))
             t_2
             (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -6.2e+224) {
		tmp = x * y;
	} else if ((x * y) <= -1.5e+73) {
		tmp = t_1;
	} else if ((x * y) <= -3700000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 8e-58) {
		tmp = t_1;
	} else if (((x * y) <= 1.65e+36) || (!((x * y) <= 1.15e+84) && ((x * y) <= 1.55e+161))) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((x * y) <= (-6.2d+224)) then
        tmp = x * y
    else if ((x * y) <= (-1.5d+73)) then
        tmp = t_1
    else if ((x * y) <= (-3700000000000.0d0)) then
        tmp = t_2
    else if ((x * y) <= 8d-58) then
        tmp = t_1
    else if (((x * y) <= 1.65d+36) .or. (.not. ((x * y) <= 1.15d+84)) .and. ((x * y) <= 1.55d+161)) then
        tmp = t_2
    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 t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -6.2e+224) {
		tmp = x * y;
	} else if ((x * y) <= -1.5e+73) {
		tmp = t_1;
	} else if ((x * y) <= -3700000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 8e-58) {
		tmp = t_1;
	} else if (((x * y) <= 1.65e+36) || (!((x * y) <= 1.15e+84) && ((x * y) <= 1.55e+161))) {
		tmp = t_2;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -6.2e+224:
		tmp = x * y
	elif (x * y) <= -1.5e+73:
		tmp = t_1
	elif (x * y) <= -3700000000000.0:
		tmp = t_2
	elif (x * y) <= 8e-58:
		tmp = t_1
	elif ((x * y) <= 1.65e+36) or (not ((x * y) <= 1.15e+84) and ((x * y) <= 1.55e+161)):
		tmp = t_2
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -6.2e+224)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.5e+73)
		tmp = t_1;
	elseif (Float64(x * y) <= -3700000000000.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 8e-58)
		tmp = t_1;
	elseif ((Float64(x * y) <= 1.65e+36) || (!(Float64(x * y) <= 1.15e+84) && (Float64(x * y) <= 1.55e+161)))
		tmp = t_2;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -6.2e+224)
		tmp = x * y;
	elseif ((x * y) <= -1.5e+73)
		tmp = t_1;
	elseif ((x * y) <= -3700000000000.0)
		tmp = t_2;
	elseif ((x * y) <= 8e-58)
		tmp = t_1;
	elseif (((x * y) <= 1.65e+36) || (~(((x * y) <= 1.15e+84)) && ((x * y) <= 1.55e+161)))
		tmp = t_2;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.2e+224], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.5e+73], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3700000000000.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 8e-58], t$95$1, If[Or[LessEqual[N[(x * y), $MachinePrecision], 1.65e+36], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.15e+84]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 1.55e+161]]], t$95$2, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.1999999999999999e224 or 1.6499999999999999e36 < (*.f64 x y) < 1.1499999999999999e84 or 1.55000000000000003e161 < (*.f64 x y)

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. fma-def 94.3%

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

      3. +-commutative 94.3%

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

      4. associate-+r+ 94.3%

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

      5. +-commutative 94.3%

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

      6. fma-def 95.7%

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

      7. +-commutative 95.7%

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

      8. fma-def 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 82.7%

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

   if -6.1999999999999999e224 < (*.f64 x y) < -1.50000000000000005e73 or -3.7e12 < (*.f64 x y) < 8.0000000000000002e-58

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. fma-def 97.9%

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

      3. +-commutative 97.9%

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

      4. associate-+r+ 97.9%

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

      5. +-commutative 97.9%

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

      6. fma-def 99.3%

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

      7. +-commutative 99.3%

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

      8. fma-def 99.3%

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

   3. Simplified 99.3%

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

      1. fma-udef 97.9%

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

      2. fma-udef 97.9%

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

      3. associate-+r+ 97.9%

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

      4. +-commutative 97.9%

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

      5. fma-def 97.9%

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

      6. flip-+ 44.0%

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

      7. clear-num 43.9%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 43.9%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 97.6%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 97.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 97.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 97.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 97.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 99.0%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 99.0%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 83.0%

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

      1. +-commutative 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-+r+ 83.0%

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

      4. fma-udef 83.0%

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

      5. *-commutative 83.0%

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

      6. fma-udef 84.3%

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

      7. fma-udef 84.3%

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

      8. +-commutative 84.3%

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

      9. fma-def 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in x around 0 76.1%

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

   if -1.50000000000000005e73 < (*.f64 x y) < -3.7e12 or 8.0000000000000002e-58 < (*.f64 x y) < 1.6499999999999999e36 or 1.1499999999999999e84 < (*.f64 x y) < 1.55000000000000003e161

   1. Initial program 92.7%

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

      1. +-commutative 92.7%

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

      2. fma-def 92.7%

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

      3. +-commutative 92.7%

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

      4. associate-+r+ 92.7%

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

      5. +-commutative 92.7%

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

      6. fma-def 92.7%

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

      7. +-commutative 92.7%

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

      8. fma-def 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around 0 86.9%

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

   5. Taylor expanded in t around 0 77.3%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.2 \cdot 10^{+224}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{+73}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -3700000000000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{-58}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{+36} \lor \neg \left(x \cdot y \leq 1.15 \cdot 10^{+84}\right) \land x \cdot y \leq 1.55 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 43.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{+134}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -1.46 \cdot 10^{+66}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -17000000:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+32}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -6e+134)
   (* x y)
   (if (<= (* x y) -3.2e+74)
     (* z t)
     (if (<= (* x y) -1.46e+66)
       (* x y)
       (if (<= (* x y) -17000000.0)
         (* c i)
         (if (<= (* x y) 0.0)
           (* a b)
           (if (<= (* x y) 5.5e-49)
             (* z t)
             (if (<= (* x y) 1.55e+32) (* c i) (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -6e+134) {
		tmp = x * y;
	} else if ((x * y) <= -3.2e+74) {
		tmp = z * t;
	} else if ((x * y) <= -1.46e+66) {
		tmp = x * y;
	} else if ((x * y) <= -17000000.0) {
		tmp = c * i;
	} else if ((x * y) <= 0.0) {
		tmp = a * b;
	} else if ((x * y) <= 5.5e-49) {
		tmp = z * t;
	} else if ((x * y) <= 1.55e+32) {
		tmp = c * i;
	} 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) <= (-6d+134)) then
        tmp = x * y
    else if ((x * y) <= (-3.2d+74)) then
        tmp = z * t
    else if ((x * y) <= (-1.46d+66)) then
        tmp = x * y
    else if ((x * y) <= (-17000000.0d0)) then
        tmp = c * i
    else if ((x * y) <= 0.0d0) then
        tmp = a * b
    else if ((x * y) <= 5.5d-49) then
        tmp = z * t
    else if ((x * y) <= 1.55d+32) then
        tmp = c * i
    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) <= -6e+134) {
		tmp = x * y;
	} else if ((x * y) <= -3.2e+74) {
		tmp = z * t;
	} else if ((x * y) <= -1.46e+66) {
		tmp = x * y;
	} else if ((x * y) <= -17000000.0) {
		tmp = c * i;
	} else if ((x * y) <= 0.0) {
		tmp = a * b;
	} else if ((x * y) <= 5.5e-49) {
		tmp = z * t;
	} else if ((x * y) <= 1.55e+32) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -6e+134:
		tmp = x * y
	elif (x * y) <= -3.2e+74:
		tmp = z * t
	elif (x * y) <= -1.46e+66:
		tmp = x * y
	elif (x * y) <= -17000000.0:
		tmp = c * i
	elif (x * y) <= 0.0:
		tmp = a * b
	elif (x * y) <= 5.5e-49:
		tmp = z * t
	elif (x * y) <= 1.55e+32:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -6e+134)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.2e+74)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= -1.46e+66)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -17000000.0)
		tmp = Float64(c * i);
	elseif (Float64(x * y) <= 0.0)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 5.5e-49)
		tmp = Float64(z * t);
	elseif (Float64(x * y) <= 1.55e+32)
		tmp = Float64(c * i);
	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) <= -6e+134)
		tmp = x * y;
	elseif ((x * y) <= -3.2e+74)
		tmp = z * t;
	elseif ((x * y) <= -1.46e+66)
		tmp = x * y;
	elseif ((x * y) <= -17000000.0)
		tmp = c * i;
	elseif ((x * y) <= 0.0)
		tmp = a * b;
	elseif ((x * y) <= 5.5e-49)
		tmp = z * t;
	elseif ((x * y) <= 1.55e+32)
		tmp = c * i;
	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], -6e+134], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.2e+74], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.46e+66], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -17000000.0], N[(c * i), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.0], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.5e-49], N[(z * t), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.55e+32], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.99999999999999993e134 or -3.19999999999999995e74 < (*.f64 x y) < -1.45999999999999995e66 or 1.54999999999999997e32 < (*.f64 x y)

   1. Initial program 93.6%

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

      1. +-commutative 93.6%

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

      2. fma-def 94.6%

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

      3. +-commutative 94.6%

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

      4. associate-+r+ 94.6%

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

      5. +-commutative 94.6%

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

      6. fma-def 95.7%

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

      7. +-commutative 95.7%

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

      8. fma-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 68.6%

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

   if -5.99999999999999993e134 < (*.f64 x y) < -3.19999999999999995e74 or -0.0 < (*.f64 x y) < 5.50000000000000031e-49

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. fma-def 98.2%

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

      3. +-commutative 98.2%

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

      4. associate-+r+ 98.2%

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

      5. +-commutative 98.2%

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

      6. fma-def 98.2%

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

      7. +-commutative 98.2%

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

      8. fma-def 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around inf 58.9%

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

   if -1.45999999999999995e66 < (*.f64 x y) < -1.7e7 or 5.50000000000000031e-49 < (*.f64 x y) < 1.54999999999999997e32

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. fma-def 93.3%

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

      3. +-commutative 93.3%

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

      4. associate-+r+ 93.3%

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

      5. +-commutative 93.3%

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

      6. fma-def 93.3%

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

      7. +-commutative 93.3%

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

      8. fma-def 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in c around inf 66.4%

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

   if -1.7e7 < (*.f64 x y) < -0.0

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. fma-def 97.3%

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

      3. +-commutative 97.3%

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

      4. associate-+r+ 97.3%

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

      5. +-commutative 97.3%

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

      6. fma-def 100.0%

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

      7. +-commutative 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 46.6%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{+134}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.2 \cdot 10^{+74}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -1.46 \cdot 10^{+66}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -17000000:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{+32}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;x \cdot y \leq -3.05 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -5.2 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -9500000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 9.4 \cdot 10^{+32}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t)))
        (t_2 (+ (* a b) (* x y)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* x y) -3.05e+134)
     t_2
     (if (<= (* x y) -5.2e+106)
       t_1
       (if (<= (* x y) -4.5e+70)
         t_2
         (if (<= (* x y) -9500000000000.0)
           t_3
           (if (<= (* x y) 1.3e-38)
             t_1
             (if (<= (* x y) 9.4e+32) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -3.05e+134) {
		tmp = t_2;
	} else if ((x * y) <= -5.2e+106) {
		tmp = t_1;
	} else if ((x * y) <= -4.5e+70) {
		tmp = t_2;
	} else if ((x * y) <= -9500000000000.0) {
		tmp = t_3;
	} else if ((x * y) <= 1.3e-38) {
		tmp = t_1;
	} else if ((x * y) <= 9.4e+32) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (a * b) + (x * y)
    t_3 = (a * b) + (c * i)
    if ((x * y) <= (-3.05d+134)) then
        tmp = t_2
    else if ((x * y) <= (-5.2d+106)) then
        tmp = t_1
    else if ((x * y) <= (-4.5d+70)) then
        tmp = t_2
    else if ((x * y) <= (-9500000000000.0d0)) then
        tmp = t_3
    else if ((x * y) <= 1.3d-38) then
        tmp = t_1
    else if ((x * y) <= 9.4d+32) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (a * b) + (x * y);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((x * y) <= -3.05e+134) {
		tmp = t_2;
	} else if ((x * y) <= -5.2e+106) {
		tmp = t_1;
	} else if ((x * y) <= -4.5e+70) {
		tmp = t_2;
	} else if ((x * y) <= -9500000000000.0) {
		tmp = t_3;
	} else if ((x * y) <= 1.3e-38) {
		tmp = t_1;
	} else if ((x * y) <= 9.4e+32) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (a * b) + (x * y)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (x * y) <= -3.05e+134:
		tmp = t_2
	elif (x * y) <= -5.2e+106:
		tmp = t_1
	elif (x * y) <= -4.5e+70:
		tmp = t_2
	elif (x * y) <= -9500000000000.0:
		tmp = t_3
	elif (x * y) <= 1.3e-38:
		tmp = t_1
	elif (x * y) <= 9.4e+32:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(x * y) <= -3.05e+134)
		tmp = t_2;
	elseif (Float64(x * y) <= -5.2e+106)
		tmp = t_1;
	elseif (Float64(x * y) <= -4.5e+70)
		tmp = t_2;
	elseif (Float64(x * y) <= -9500000000000.0)
		tmp = t_3;
	elseif (Float64(x * y) <= 1.3e-38)
		tmp = t_1;
	elseif (Float64(x * y) <= 9.4e+32)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (a * b) + (x * y);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((x * y) <= -3.05e+134)
		tmp = t_2;
	elseif ((x * y) <= -5.2e+106)
		tmp = t_1;
	elseif ((x * y) <= -4.5e+70)
		tmp = t_2;
	elseif ((x * y) <= -9500000000000.0)
		tmp = t_3;
	elseif ((x * y) <= 1.3e-38)
		tmp = t_1;
	elseif ((x * y) <= 9.4e+32)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.05e+134], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -5.2e+106], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4.5e+70], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -9500000000000.0], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 1.3e-38], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 9.4e+32], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.04999999999999989e134 or -5.20000000000000039e106 < (*.f64 x y) < -4.4999999999999999e70 or 9.40000000000000047e32 < (*.f64 x y)

   1. Initial program 93.9%

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

      1. +-commutative 93.9%

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

      2. fma-def 94.9%

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

      3. +-commutative 94.9%

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

      4. associate-+r+ 94.9%

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

      5. +-commutative 94.9%

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

      6. fma-def 95.9%

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

      7. +-commutative 95.9%

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

      8. fma-def 97.0%

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

   3. Simplified 97.0%

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

      1. fma-udef 95.9%

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

      2. fma-udef 94.9%

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

      3. associate-+r+ 94.9%

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

      4. +-commutative 94.9%

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

      5. fma-def 95.9%

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

      6. flip-+ 18.4%

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

      7. clear-num 18.3%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 18.3%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 95.8%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 94.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 94.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 94.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 95.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 96.8%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-+r+ 89.1%

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

      4. fma-udef 90.1%

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

      5. *-commutative 90.1%

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

      6. fma-udef 91.1%

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

      7. fma-udef 90.1%

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

      8. +-commutative 90.1%

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

      9. fma-def 90.1%

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

   8. Simplified 90.1%

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

   9. Taylor expanded in t around 0 78.1%

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

   if -3.04999999999999989e134 < (*.f64 x y) < -5.20000000000000039e106 or -9.5e12 < (*.f64 x y) < 1.30000000000000005e-38

   1. Initial program 95.3%

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

      1. +-commutative 95.3%

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

      2. fma-def 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. associate-+r+ 97.6%

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

      5. +-commutative 97.6%

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

      6. fma-def 99.2%

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

      7. +-commutative 99.2%

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

      8. fma-def 99.2%

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

   3. Simplified 99.2%

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

      1. fma-udef 97.6%

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

      2. fma-udef 97.6%

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

      3. associate-+r+ 97.6%

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

      4. +-commutative 97.6%

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

      5. fma-def 97.6%

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

      6. flip-+ 45.0%

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

      7. clear-num 44.9%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 44.9%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 97.3%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 97.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 97.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 97.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 97.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 98.9%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-+r+ 82.2%

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

      4. fma-udef 82.2%

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

      5. *-commutative 82.2%

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

      6. fma-udef 83.8%

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

      7. fma-udef 83.8%

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

      8. +-commutative 83.8%

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

      9. fma-def 83.8%

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

   8. Simplified 83.8%

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

   9. Taylor expanded in x around 0 79.2%

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

   if -4.4999999999999999e70 < (*.f64 x y) < -9.5e12 or 1.30000000000000005e-38 < (*.f64 x y) < 9.40000000000000047e32

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. fma-def 93.1%

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

      3. +-commutative 93.1%

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

      4. associate-+r+ 93.1%

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

      5. +-commutative 93.1%

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

      6. fma-def 93.1%

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

      7. +-commutative 93.1%

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

      8. fma-def 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around 0 91.2%

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

   5. Taylor expanded in t around 0 81.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.05 \cdot 10^{+134}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.2 \cdot 10^{+106}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -9500000000000:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 9.4 \cdot 10^{+32}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 10: 66.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -4.35 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{-134}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.7 \cdot 10^{+32}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+84}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))) (t_2 (+ (* x y) (* z t))))
   (if (<= (* x y) -3.2e+64)
     t_2
     (if (<= (* x y) -4.35e+18)
       t_1
       (if (<= (* x y) 6.8e-134)
         (+ (* a b) (* z t))
         (if (<= (* x y) 4.7e+32)
           (+ (* c i) (* z t))
           (if (<= (* x y) 1.6e+84)
             (+ (* a b) (* x y))
             (if (<= (* x y) 1.9e+161) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -3.2e+64) {
		tmp = t_2;
	} else if ((x * y) <= -4.35e+18) {
		tmp = t_1;
	} else if ((x * y) <= 6.8e-134) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 4.7e+32) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 1.6e+84) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 1.9e+161) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = (x * y) + (z * t)
    if ((x * y) <= (-3.2d+64)) then
        tmp = t_2
    else if ((x * y) <= (-4.35d+18)) then
        tmp = t_1
    else if ((x * y) <= 6.8d-134) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 4.7d+32) then
        tmp = (c * i) + (z * t)
    else if ((x * y) <= 1.6d+84) then
        tmp = (a * b) + (x * y)
    else if ((x * y) <= 1.9d+161) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((x * y) <= -3.2e+64) {
		tmp = t_2;
	} else if ((x * y) <= -4.35e+18) {
		tmp = t_1;
	} else if ((x * y) <= 6.8e-134) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 4.7e+32) {
		tmp = (c * i) + (z * t);
	} else if ((x * y) <= 1.6e+84) {
		tmp = (a * b) + (x * y);
	} else if ((x * y) <= 1.9e+161) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (x * y) <= -3.2e+64:
		tmp = t_2
	elif (x * y) <= -4.35e+18:
		tmp = t_1
	elif (x * y) <= 6.8e-134:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 4.7e+32:
		tmp = (c * i) + (z * t)
	elif (x * y) <= 1.6e+84:
		tmp = (a * b) + (x * y)
	elif (x * y) <= 1.9e+161:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -3.2e+64)
		tmp = t_2;
	elseif (Float64(x * y) <= -4.35e+18)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.8e-134)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 4.7e+32)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(x * y) <= 1.6e+84)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(x * y) <= 1.9e+161)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((x * y) <= -3.2e+64)
		tmp = t_2;
	elseif ((x * y) <= -4.35e+18)
		tmp = t_1;
	elseif ((x * y) <= 6.8e-134)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 4.7e+32)
		tmp = (c * i) + (z * t);
	elseif ((x * y) <= 1.6e+84)
		tmp = (a * b) + (x * y);
	elseif ((x * y) <= 1.9e+161)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.2e+64], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -4.35e+18], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.8e-134], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.7e+32], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.6e+84], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.9e+161], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -3.20000000000000019e64 or 1.9000000000000001e161 < (*.f64 x y)

   1. Initial program 94.4%

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

      1. +-commutative 94.4%

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

      2. fma-def 95.5%

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

      3. +-commutative 95.5%

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

      4. associate-+r+ 95.5%

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

      5. +-commutative 95.5%

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

      6. fma-def 96.6%

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

      7. +-commutative 96.6%

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

      8. fma-def 97.8%

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

   3. Simplified 97.8%

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

      1. fma-udef 96.6%

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

      2. fma-udef 95.5%

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

      3. associate-+r+ 95.5%

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

      4. +-commutative 95.5%

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

      5. fma-def 96.6%

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

      6. flip-+ 13.4%

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

      7. clear-num 13.4%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 13.4%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 96.5%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 95.4%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 95.4%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 95.4%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 96.5%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 97.7%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 97.7%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-+r+ 91.3%

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

      4. fma-udef 92.4%

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

      5. *-commutative 92.4%

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

      6. fma-udef 93.5%

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

      7. fma-udef 92.4%

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

      8. +-commutative 92.4%

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

      9. fma-def 92.4%

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

   8. Simplified 92.4%

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

   9. Taylor expanded in a around 0 83.3%

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

   if -3.20000000000000019e64 < (*.f64 x y) < -4.35e18 or 1.60000000000000005e84 < (*.f64 x y) < 1.9000000000000001e161

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. fma-def 87.5%

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

      3. +-commutative 87.5%

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

      4. associate-+r+ 87.5%

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

      5. +-commutative 87.5%

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

      6. fma-def 87.5%

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

      7. +-commutative 87.5%

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

      8. fma-def 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in x around 0 87.5%

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

   5. Taylor expanded in t around 0 83.6%

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

   if -4.35e18 < (*.f64 x y) < 6.79999999999999954e-134

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. fma-def 97.1%

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

      3. +-commutative 97.1%

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

      4. associate-+r+ 97.1%

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

      5. +-commutative 97.1%

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

      6. fma-def 99.0%

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

      7. +-commutative 99.0%

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

      8. fma-def 99.0%

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

   3. Simplified 99.0%

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

      1. fma-udef 97.1%

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

      2. fma-udef 97.1%

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

      3. associate-+r+ 97.1%

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

      4. +-commutative 97.1%

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

      5. fma-def 97.1%

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

      6. flip-+ 45.8%

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

      7. clear-num 45.8%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 45.8%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 96.8%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 98.7%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 98.7%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 83.0%

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

      1. +-commutative 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-+r+ 83.0%

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

      4. fma-udef 83.0%

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

      5. *-commutative 83.0%

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

      6. fma-udef 84.9%

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

      7. fma-udef 84.9%

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

      8. +-commutative 84.9%

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

      9. fma-def 84.9%

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

   8. Simplified 84.9%

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

   9. Taylor expanded in x around 0 80.3%

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

   if 6.79999999999999954e-134 < (*.f64 x y) < 4.70000000000000023e32

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. +-commutative 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 94.7%

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

   5. Taylor expanded in a around 0 81.2%

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

   if 4.70000000000000023e32 < (*.f64 x y) < 1.60000000000000005e84

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. +-commutative 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. flip-+ 75.0%

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

      7. clear-num 74.6%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 74.8%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 99.6%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 99.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 99.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 99.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 99.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 99.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 99.6%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+r+ 100.0%

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

      4. fma-udef 100.0%

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

      5. *-commutative 100.0%

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

      6. fma-udef 100.0%

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

      7. fma-udef 100.0%

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

      8. +-commutative 100.0%

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

      9. fma-def 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in t around 0 87.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.2 \cdot 10^{+64}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -4.35 \cdot 10^{+18}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{-134}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 4.7 \cdot 10^{+32}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.6 \cdot 10^{+84}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]

Alternative 11: 97.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 28.6%

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

      3. +-commutative 28.6%

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

      4. associate-+r+ 28.6%

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

      5. +-commutative 28.6%

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

      6. fma-def 50.0%

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

      7. +-commutative 50.0%

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

      8. fma-def 57.1%

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

   3. Simplified 57.1%

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

      1. fma-udef 35.7%

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

      2. fma-udef 28.6%

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

      3. associate-+r+ 28.6%

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

      4. +-commutative 28.6%

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

      5. fma-def 35.7%

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

      6. flip-+ 0.0%

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

      7. clear-num 0.0%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 0.0%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 35.7%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 28.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 35.7%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 57.1%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 57.1%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 28.6%

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

      1. +-commutative 28.6%

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

      2. *-commutative 28.6%

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

      3. associate-+r+ 28.6%

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

      4. fma-udef 35.7%

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

      5. *-commutative 35.7%

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

      6. fma-udef 57.1%

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

      7. fma-udef 50.0%

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

      8. +-commutative 50.0%

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

      9. fma-def 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in t around 0 44.5%

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

4. Final simplification 96.9%

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

Alternative 12: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.9 \cdot 10^{+135}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+36} \lor \neg \left(x \cdot y \leq 10^{+84}\right) \land x \cdot y \leq 9.5 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.9e+135)
   (+ (* a b) (* x y))
   (if (or (<= (* x y) 2.1e+36)
           (and (not (<= (* x y) 1e+84)) (<= (* x y) 9.5e+161)))
     (+ (* a b) (+ (* c i) (* 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) <= -1.9e+135) {
		tmp = (a * b) + (x * y);
	} else if (((x * y) <= 2.1e+36) || (!((x * y) <= 1e+84) && ((x * y) <= 9.5e+161))) {
		tmp = (a * b) + ((c * i) + (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) <= (-1.9d+135)) then
        tmp = (a * b) + (x * y)
    else if (((x * y) <= 2.1d+36) .or. (.not. ((x * y) <= 1d+84)) .and. ((x * y) <= 9.5d+161)) then
        tmp = (a * b) + ((c * i) + (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) <= -1.9e+135) {
		tmp = (a * b) + (x * y);
	} else if (((x * y) <= 2.1e+36) || (!((x * y) <= 1e+84) && ((x * y) <= 9.5e+161))) {
		tmp = (a * b) + ((c * i) + (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) <= -1.9e+135:
		tmp = (a * b) + (x * y)
	elif ((x * y) <= 2.1e+36) or (not ((x * y) <= 1e+84) and ((x * y) <= 9.5e+161)):
		tmp = (a * b) + ((c * i) + (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) <= -1.9e+135)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif ((Float64(x * y) <= 2.1e+36) || (!(Float64(x * y) <= 1e+84) && (Float64(x * y) <= 9.5e+161)))
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + 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) <= -1.9e+135)
		tmp = (a * b) + (x * y);
	elseif (((x * y) <= 2.1e+36) || (~(((x * y) <= 1e+84)) && ((x * y) <= 9.5e+161)))
		tmp = (a * b) + ((c * i) + (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], -1.9e+135], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 2.1e+36], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+84]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 9.5e+161]]], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $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) < -1.9000000000000001e135

   1. Initial program 94.5%

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

      1. +-commutative 94.5%

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

      2. fma-def 94.6%

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

      3. +-commutative 94.6%

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

      4. associate-+r+ 94.6%

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

      5. +-commutative 94.6%

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

      6. fma-def 97.3%

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

      7. +-commutative 97.3%

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

      8. fma-def 97.3%

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

   3. Simplified 97.3%

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

      1. fma-udef 94.6%

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

      2. fma-udef 94.6%

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

      3. associate-+r+ 94.6%

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

      4. +-commutative 94.6%

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

      5. fma-def 94.6%

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

      6. flip-+ 10.2%

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

      7. clear-num 10.2%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 10.2%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 94.3%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 94.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 94.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 94.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 94.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 97.0%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 97.0%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 91.9%

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

      1. +-commutative 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-+r+ 91.9%

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

      4. fma-udef 91.9%

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

      5. *-commutative 91.9%

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

      6. fma-udef 94.6%

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

      7. fma-udef 94.6%

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

      8. +-commutative 94.6%

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

      9. fma-def 94.6%

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

   8. Simplified 94.6%

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

   9. Taylor expanded in t around 0 86.8%

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

   if -1.9000000000000001e135 < (*.f64 x y) < 2.10000000000000004e36 or 1.00000000000000006e84 < (*.f64 x y) < 9.50000000000000061e161

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. fma-def 96.6%

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

      3. +-commutative 96.6%

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

      4. associate-+r+ 96.6%

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

      5. +-commutative 96.6%

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

      6. fma-def 97.7%

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

      7. +-commutative 97.7%

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

      8. fma-def 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around 0 90.1%

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

   if 2.10000000000000004e36 < (*.f64 x y) < 1.00000000000000006e84 or 9.50000000000000061e161 < (*.f64 x y)

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. fma-def 95.4%

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

      3. +-commutative 95.4%

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

      4. associate-+r+ 95.4%

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

      5. +-commutative 95.4%

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

      6. fma-def 95.4%

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

      7. +-commutative 95.4%

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

      8. fma-def 97.7%

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

   3. Simplified 97.7%

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

      1. fma-udef 97.7%

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

      2. fma-udef 95.4%

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

      3. associate-+r+ 95.4%

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

      4. +-commutative 95.4%

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

      5. fma-def 97.7%

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

      6. flip-+ 13.8%

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

      7. clear-num 13.8%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 13.8%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 97.6%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 95.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 95.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 95.3%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 97.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 97.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 97.6%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-+r+ 93.4%

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

      4. fma-udef 95.7%

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

      5. *-commutative 95.7%

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

      6. fma-udef 95.7%

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

      7. fma-udef 93.4%

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

      8. +-commutative 93.4%

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

      9. fma-def 93.4%

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

   8. Simplified 93.4%

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

   9. Taylor expanded in a around 0 88.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.9 \cdot 10^{+135}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+36} \lor \neg \left(x \cdot y \leq 10^{+84}\right) \land x \cdot y \leq 9.5 \cdot 10^{+161}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \end{array} \]

Alternative 13: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.38 \cdot 10^{+134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* x y))))
   (if (<= (* x y) -1.38e+134)
     t_2
     (if (<= (* x y) -2800000000000.0)
       t_1
       (if (<= (* x y) 6.5e-136)
         (+ (* a b) (* z t))
         (if (<= (* x y) 3.8e+32) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -1.38e+134) {
		tmp = t_2;
	} else if ((x * y) <= -2800000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 6.5e-136) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 3.8e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + (z * t)
    t_2 = (a * b) + (x * y)
    if ((x * y) <= (-1.38d+134)) then
        tmp = t_2
    else if ((x * y) <= (-2800000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 6.5d-136) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= 3.8d+32) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (z * t);
	double t_2 = (a * b) + (x * y);
	double tmp;
	if ((x * y) <= -1.38e+134) {
		tmp = t_2;
	} else if ((x * y) <= -2800000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 6.5e-136) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= 3.8e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (z * t)
	t_2 = (a * b) + (x * y)
	tmp = 0
	if (x * y) <= -1.38e+134:
		tmp = t_2
	elif (x * y) <= -2800000000000.0:
		tmp = t_1
	elif (x * y) <= 6.5e-136:
		tmp = (a * b) + (z * t)
	elif (x * y) <= 3.8e+32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.38e+134)
		tmp = t_2;
	elseif (Float64(x * y) <= -2800000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.5e-136)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= 3.8e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (z * t);
	t_2 = (a * b) + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.38e+134)
		tmp = t_2;
	elseif ((x * y) <= -2800000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 6.5e-136)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= 3.8e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.38e+134], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2800000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.5e-136], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+32], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.38e134 or 3.8000000000000003e32 < (*.f64 x y)

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. fma-def 94.6%

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

      3. +-commutative 94.6%

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

      4. associate-+r+ 94.6%

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

      5. +-commutative 94.6%

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

      6. fma-def 95.7%

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

      7. +-commutative 95.7%

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

      8. fma-def 96.8%

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

   3. Simplified 96.8%

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

      1. fma-udef 95.7%

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

      2. fma-udef 94.6%

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

      3. associate-+r+ 94.6%

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

      4. +-commutative 94.6%

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

      5. fma-def 95.7%

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

      6. flip-+ 15.2%

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

      7. clear-num 15.2%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 15.2%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 95.5%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 94.4%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 94.4%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 94.4%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 95.5%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 96.6%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 96.6%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 89.4%

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

      1. +-commutative 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-+r+ 89.4%

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

      4. fma-udef 90.5%

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

      5. *-commutative 90.5%

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

      6. fma-udef 91.6%

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

      7. fma-udef 90.5%

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

      8. +-commutative 90.5%

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

      9. fma-def 90.5%

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

   8. Simplified 90.5%

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

   9. Taylor expanded in t around 0 79.8%

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

   if -1.38e134 < (*.f64 x y) < -2.8e12 or 6.50000000000000011e-136 < (*.f64 x y) < 3.8000000000000003e32

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. fma-def 96.6%

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

      3. +-commutative 96.6%

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

      4. associate-+r+ 96.6%

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

      5. +-commutative 96.6%

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

      6. fma-def 96.6%

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

      7. +-commutative 96.6%

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

      8. fma-def 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around 0 87.2%

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

   5. Taylor expanded in a around 0 77.6%

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

   if -2.8e12 < (*.f64 x y) < 6.50000000000000011e-136

   1. Initial program 95.2%

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

      1. +-commutative 95.2%

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

      2. fma-def 97.1%

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

      3. +-commutative 97.1%

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

      4. associate-+r+ 97.1%

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

      5. +-commutative 97.1%

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

      6. fma-def 99.0%

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

      7. +-commutative 99.0%

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

      8. fma-def 99.0%

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

   3. Simplified 99.0%

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

      1. fma-udef 97.1%

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

      2. fma-udef 97.1%

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

      3. associate-+r+ 97.1%

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

      4. +-commutative 97.1%

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

      5. fma-def 97.1%

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

      6. flip-+ 45.8%

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

      7. clear-num 45.8%

         \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}}}\right) \]

      8. clear-num 45.8%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, y, z \cdot t\right) \cdot \mathsf{fma}\left(x, y, z \cdot t\right) - \left(a \cdot b\right) \cdot \left(a \cdot b\right)}{\mathsf{fma}\left(x, y, z \cdot t\right) - a \cdot b}}}}\right) \]

      9. flip-+ 96.8%

         \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right) + a \cdot b}}}\right) \]

      10. fma-def 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(x \cdot y + z \cdot t\right)} + a \cdot b}}\right) \]

      11. +-commutative 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\left(z \cdot t + x \cdot y\right)} + a \cdot b}}\right) \]

      12. associate-+r+ 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{z \cdot t + \left(x \cdot y + a \cdot b\right)}}}\right) \]

      13. fma-udef 96.8%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{z \cdot t + \color{blue}{\mathsf{fma}\left(x, y, a \cdot b\right)}}}\right) \]

      14. fma-udef 98.7%

          \[\leadsto \mathsf{fma}\left(c, i, \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   5. Applied egg-rr 98.7%

      \[\leadsto \mathsf{fma}\left(c, i, \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, t, \mathsf{fma}\left(x, y, a \cdot b\right)\right)}}}\right) \]

   6. Taylor expanded in c around 0 83.0%

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

      1. +-commutative 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-+r+ 83.0%

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

      4. fma-udef 83.0%

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

      5. *-commutative 83.0%

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

      6. fma-udef 84.9%

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

      7. fma-udef 84.9%

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

      8. +-commutative 84.9%

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

      9. fma-def 84.9%

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

   8. Simplified 84.9%

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

   9. Taylor expanded in x around 0 80.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.38 \cdot 10^{+134}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2800000000000:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{-136}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+32}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 14: 42.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9.5 \cdot 10^{+167}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.6 \cdot 10^{-131}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -3.7 \cdot 10^{-273}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.9 \cdot 10^{+123}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -9.5e+167)
   (* c i)
   (if (<= (* c i) -2.6e-131)
     (* z t)
     (if (<= (* c i) -3.7e-273)
       (* a b)
       (if (<= (* c i) 4.9e+123) (* z t) (* c i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -9.5e+167) {
		tmp = c * i;
	} else if ((c * i) <= -2.6e-131) {
		tmp = z * t;
	} else if ((c * i) <= -3.7e-273) {
		tmp = a * b;
	} else if ((c * i) <= 4.9e+123) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-9.5d+167)) then
        tmp = c * i
    else if ((c * i) <= (-2.6d-131)) then
        tmp = z * t
    else if ((c * i) <= (-3.7d-273)) then
        tmp = a * b
    else if ((c * i) <= 4.9d+123) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -9.5e+167) {
		tmp = c * i;
	} else if ((c * i) <= -2.6e-131) {
		tmp = z * t;
	} else if ((c * i) <= -3.7e-273) {
		tmp = a * b;
	} else if ((c * i) <= 4.9e+123) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -9.5e+167:
		tmp = c * i
	elif (c * i) <= -2.6e-131:
		tmp = z * t
	elif (c * i) <= -3.7e-273:
		tmp = a * b
	elif (c * i) <= 4.9e+123:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -9.5e+167)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.6e-131)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= -3.7e-273)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 4.9e+123)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -9.5e+167)
		tmp = c * i;
	elseif ((c * i) <= -2.6e-131)
		tmp = z * t;
	elseif ((c * i) <= -3.7e-273)
		tmp = a * b;
	elseif ((c * i) <= 4.9e+123)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -9.5e+167], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.6e-131], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -3.7e-273], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.9e+123], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -9.5000000000000006e167 or 4.89999999999999976e123 < (*.f64 c i)

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. fma-def 92.6%

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

      3. +-commutative 92.6%

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

      4. associate-+r+ 92.6%

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

      5. +-commutative 92.6%

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

      6. fma-def 94.1%

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

      7. +-commutative 94.1%

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

      8. fma-def 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in c around inf 67.2%

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

   if -9.5000000000000006e167 < (*.f64 c i) < -2.59999999999999996e-131 or -3.7000000000000003e-273 < (*.f64 c i) < 4.89999999999999976e123

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. fma-def 97.5%

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

      3. +-commutative 97.5%

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

      4. associate-+r+ 97.5%

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

      5. +-commutative 97.5%

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

      6. fma-def 98.2%

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

      7. +-commutative 98.2%

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

      8. fma-def 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in z around inf 43.0%

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

   if -2.59999999999999996e-131 < (*.f64 c i) < -3.7000000000000003e-273

   1. Initial program 95.7%

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

      1. +-commutative 95.7%

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

      2. fma-def 95.7%

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

      3. +-commutative 95.7%

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

      4. associate-+r+ 95.7%

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

      5. +-commutative 95.7%

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

      6. fma-def 100.0%

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

      7. +-commutative 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around inf 49.0%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -9.5 \cdot 10^{+167}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.6 \cdot 10^{-131}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -3.7 \cdot 10^{-273}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.9 \cdot 10^{+123}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 15: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.75 \cdot 10^{+134} \lor \neg \left(x \cdot y \leq 2.3 \cdot 10^{+31}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.75e+134) (not (<= (* x y) 2.3e+31)))
   (+ (* a b) (+ (* x y) (* c i)))
   (+ (* a b) (+ (* c i) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.75e+134) || !((x * y) <= 2.3e+31)) {
		tmp = (a * b) + ((x * y) + (c * i));
	} else {
		tmp = (a * b) + ((c * i) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-2.75d+134)) .or. (.not. ((x * y) <= 2.3d+31))) then
        tmp = (a * b) + ((x * y) + (c * i))
    else
        tmp = (a * b) + ((c * i) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -2.75e+134) || !((x * y) <= 2.3e+31)) {
		tmp = (a * b) + ((x * y) + (c * i));
	} else {
		tmp = (a * b) + ((c * i) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -2.75e+134) or not ((x * y) <= 2.3e+31):
		tmp = (a * b) + ((x * y) + (c * i))
	else:
		tmp = (a * b) + ((c * i) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -2.75e+134) || !(Float64(x * y) <= 2.3e+31))
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(c * i)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(c * i) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -2.75e+134) || ~(((x * y) <= 2.3e+31)))
		tmp = (a * b) + ((x * y) + (c * i));
	else
		tmp = (a * b) + ((c * i) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.75e+134], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.3e+31]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.7499999999999999e134 or 2.3e31 < (*.f64 x y)

   1. Initial program 93.6%

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

      1. +-commutative 93.6%

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

      2. fma-def 94.6%

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

      3. +-commutative 94.6%

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

      4. associate-+r+ 94.6%

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

      5. +-commutative 94.6%

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

      6. fma-def 95.7%

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

      7. +-commutative 95.7%

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

      8. fma-def 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 85.0%

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

   if -2.7499999999999999e134 < (*.f64 x y) < 2.3e31

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. fma-def 96.9%

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

      3. +-commutative 96.9%

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

      4. associate-+r+ 96.9%

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

      5. +-commutative 96.9%

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

      6. fma-def 98.1%

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

      7. +-commutative 98.1%

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

      8. fma-def 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in x around 0 90.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.75 \cdot 10^{+134} \lor \neg \left(x \cdot y \leq 2.3 \cdot 10^{+31}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(c \cdot i + z \cdot t\right)\\ \end{array} \]

Alternative 16: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+166} \lor \neg \left(c \cdot i \leq 1.35 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -5.5e+166) (not (<= (* c i) 1.35e+125)))
   (+ (* a b) (+ (* x y) (* c i)))
   (+ (* a b) (+ (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -5.5e+166) || !((c * i) <= 1.35e+125)) {
		tmp = (a * b) + ((x * y) + (c * i));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-5.5d+166)) .or. (.not. ((c * i) <= 1.35d+125))) then
        tmp = (a * b) + ((x * y) + (c * i))
    else
        tmp = (a * b) + ((x * y) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -5.5e+166) || !((c * i) <= 1.35e+125)) {
		tmp = (a * b) + ((x * y) + (c * i));
	} else {
		tmp = (a * b) + ((x * y) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -5.5e+166) or not ((c * i) <= 1.35e+125):
		tmp = (a * b) + ((x * y) + (c * i))
	else:
		tmp = (a * b) + ((x * y) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -5.5e+166) || !(Float64(c * i) <= 1.35e+125))
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(c * i)));
	else
		tmp = Float64(Float64(a * b) + Float64(Float64(x * y) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -5.5e+166) || ~(((c * i) <= 1.35e+125)))
		tmp = (a * b) + ((x * y) + (c * i));
	else
		tmp = (a * b) + ((x * y) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -5.5e+166], N[Not[LessEqual[N[(c * i), $MachinePrecision], 1.35e+125]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -5.50000000000000008e166 or 1.3499999999999999e125 < (*.f64 c i)

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. fma-def 92.6%

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

      3. +-commutative 92.6%

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

      4. associate-+r+ 92.6%

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

      5. +-commutative 92.6%

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

      6. fma-def 94.1%

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

      7. +-commutative 94.1%

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

      8. fma-def 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 86.9%

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

   if -5.50000000000000008e166 < (*.f64 c i) < 1.3499999999999999e125

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. fma-def 97.3%

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

      3. +-commutative 97.3%

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

      4. associate-+r+ 97.3%

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

      5. +-commutative 97.3%

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

      6. fma-def 98.4%

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

      7. +-commutative 98.4%

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

      8. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in c around 0 94.1%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.5 \cdot 10^{+166} \lor \neg \left(c \cdot i \leq 1.35 \cdot 10^{+125}\right):\\ \;\;\;\;a \cdot b + \left(x \cdot y + c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + \left(x \cdot y + z \cdot t\right)\\ \end{array} \]

Alternative 17: 42.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.75 \cdot 10^{+93}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+184}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.75e+93)
   (* c i)
   (if (<= (* c i) 2.7e+184) (* 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) <= -1.75e+93) {
		tmp = c * i;
	} else if ((c * i) <= 2.7e+184) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1.75d+93)) then
        tmp = c * i
    else if ((c * i) <= 2.7d+184) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.75e+93) {
		tmp = c * i;
	} else if ((c * i) <= 2.7e+184) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.75e+93:
		tmp = c * i
	elif (c * i) <= 2.7e+184:
		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(c * i) <= -1.75e+93)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 2.7e+184)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1.75e+93)
		tmp = c * i;
	elseif ((c * i) <= 2.7e+184)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.75e+93], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.7e+184], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -1.74999999999999999e93 or 2.6999999999999999e184 < (*.f64 c i)

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. fma-def 92.5%

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

      3. +-commutative 92.5%

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

      4. associate-+r+ 92.5%

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

      5. +-commutative 92.5%

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

      6. fma-def 94.0%

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

      7. +-commutative 94.0%

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

      8. fma-def 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in c around inf 67.7%

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

   if -1.74999999999999999e93 < (*.f64 c i) < 2.6999999999999999e184

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. fma-def 97.3%

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

      3. +-commutative 97.3%

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

      4. associate-+r+ 97.3%

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

      5. +-commutative 97.3%

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

      6. fma-def 98.4%

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

      7. +-commutative 98.4%

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

      8. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in a around inf 31.1%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.75 \cdot 10^{+93}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+184}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 18: 27.6% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. +-commutative 94.5%

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

   2. fma-def 96.1%

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

   3. +-commutative 96.1%

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

   4. associate-+r+ 96.1%

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

   5. +-commutative 96.1%

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

   6. fma-def 97.2%

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

   7. +-commutative 97.2%

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

   8. fma-def 97.6%

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

3. Simplified 97.6%

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

4. Taylor expanded in a around inf 26.3%

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

5. Final simplification 26.3%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023297 
(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)))