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

Percentage Accurate: 95.9% → 97.4%

Time: 13.4s

Alternatives: 16

Speedup: 0.4×

• 40.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+228}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1e+228)
   (fma a b (* c i))
   (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) {
	double tmp;
	if ((a * b) <= -1e+228) {
		tmp = fma(a, b, (c * i));
	} else {
		tmp = fma(c, i, fma(a, b, fma(x, y, (z * t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1e+228)
		tmp = fma(a, b, Float64(c * i));
	else
		tmp = fma(c, i, fma(a, b, fma(x, y, Float64(z * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -1e+228], N[(a * b + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(c * i + N[(a * b + N[(x * y + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.9999999999999992e227

   1. Initial program 74.9%

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

   3. Taylor expanded in z around 0 78.5%

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

   4. Taylor expanded in x around 0 92.8%

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

      1. fma-def 96.4%

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

   6. Simplified 96.4%

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

   if -9.9999999999999992e227 < (*.f64 a b)

   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 97.8%

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

      3. +-commutative 97.8%

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

      4. fma-def 98.7%

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

      5. fma-def 98.7%

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

   3. Simplified 98.7%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+228}:\\ \;\;\;\;\mathsf{fma}\left(a, b, c \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(c, i, \mathsf{fma}\left(a, b, \mathsf{fma}\left(x, y, z \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

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 95.3%

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

   3. associate-+l+ 95.3%

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

   4. fma-def 97.3%

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

   5. fma-def 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 97.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+r+ 100.0%

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

      8. fma-def 100.0%

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

   6. Applied egg-rr 100.0%

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

   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 20.0%

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

      3. +-commutative 20.0%

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

      4. fma-def 40.0%

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

      5. fma-def 40.0%

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

   3. Simplified 40.0%

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

      1. fma-udef 20.0%

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

      2. fma-def 20.0%

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

      3. associate-+r+ 20.0%

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

   6. Applied egg-rr 20.0%

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

   7. Taylor expanded in z around 0 33.3%

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

   8. Taylor expanded in a around inf 53.8%

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

4. Final simplification 97.3%

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

Alternative 4: 97.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. fma-def 99.6%

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

      3. +-commutative 99.6%

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

      4. fma-def 99.6%

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

      5. fma-def 99.6%

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

   3. Simplified 99.6%

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

      1. fma-udef 99.6%

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

      2. fma-def 99.6%

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

      3. associate-+r+ 99.6%

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

   6. Applied egg-rr 99.6%

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

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

   1. Initial program 0.0%

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

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

      3. +-commutative 0.0%

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

      4. fma-def 27.3%

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

      5. fma-def 27.3%

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

   3. Simplified 27.3%

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

      1. fma-udef 0.0%

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

      2. fma-def 0.0%

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

      3. associate-+r+ 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in z around 0 27.3%

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

   8. Taylor expanded in a around inf 63.9%

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

4. Final simplification 98.0%

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

Alternative 5: 65.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -7 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -7 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{-163}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.2 \cdot 10^{+45} \lor \neg \left(a \cdot b \leq 5.5 \cdot 10^{+62}\right) \land a \cdot b \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* a b) -7e+155)
     t_2
     (if (<= (* a b) -7e-85)
       t_1
       (if (<= (* a b) 9e-163)
         (+ (* c i) (* z t))
         (if (or (<= (* a b) 2.2e+45)
                 (and (not (<= (* a b) 5.5e+62)) (<= (* a b) 1.45e+140)))
           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 = (x * y) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -7e+155) {
		tmp = t_2;
	} else if ((a * b) <= -7e-85) {
		tmp = t_1;
	} else if ((a * b) <= 9e-163) {
		tmp = (c * i) + (z * t);
	} else if (((a * b) <= 2.2e+45) || (!((a * b) <= 5.5e+62) && ((a * b) <= 1.45e+140))) {
		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 = (x * y) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((a * b) <= (-7d+155)) then
        tmp = t_2
    else if ((a * b) <= (-7d-85)) then
        tmp = t_1
    else if ((a * b) <= 9d-163) then
        tmp = (c * i) + (z * t)
    else if (((a * b) <= 2.2d+45) .or. (.not. ((a * b) <= 5.5d+62)) .and. ((a * b) <= 1.45d+140)) 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 = (x * y) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -7e+155) {
		tmp = t_2;
	} else if ((a * b) <= -7e-85) {
		tmp = t_1;
	} else if ((a * b) <= 9e-163) {
		tmp = (c * i) + (z * t);
	} else if (((a * b) <= 2.2e+45) || (!((a * b) <= 5.5e+62) && ((a * b) <= 1.45e+140))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -7e+155:
		tmp = t_2
	elif (a * b) <= -7e-85:
		tmp = t_1
	elif (a * b) <= 9e-163:
		tmp = (c * i) + (z * t)
	elif ((a * b) <= 2.2e+45) or (not ((a * b) <= 5.5e+62) and ((a * b) <= 1.45e+140)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -7e+155)
		tmp = t_2;
	elseif (Float64(a * b) <= -7e-85)
		tmp = t_1;
	elseif (Float64(a * b) <= 9e-163)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif ((Float64(a * b) <= 2.2e+45) || (!(Float64(a * b) <= 5.5e+62) && (Float64(a * b) <= 1.45e+140)))
		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 = (x * y) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -7e+155)
		tmp = t_2;
	elseif ((a * b) <= -7e-85)
		tmp = t_1;
	elseif ((a * b) <= 9e-163)
		tmp = (c * i) + (z * t);
	elseif (((a * b) <= 2.2e+45) || (~(((a * b) <= 5.5e+62)) && ((a * b) <= 1.45e+140)))
		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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -7e+155], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -7e-85], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 9e-163], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 2.2e+45], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 5.5e+62]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 1.45e+140]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6.99999999999999969e155 or 2.2e45 < (*.f64 a b) < 5.4999999999999997e62 or 1.4499999999999999e140 < (*.f64 a b)

   1. Initial program 87.1%

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

   3. Taylor expanded in a around inf 87.2%

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

   if -6.99999999999999969e155 < (*.f64 a b) < -6.99999999999999956e-85 or 8.9999999999999995e-163 < (*.f64 a b) < 2.2e45 or 5.4999999999999997e62 < (*.f64 a b) < 1.4499999999999999e140

   1. Initial program 97.9%

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

   3. Taylor expanded in a around 0 84.9%

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

   4. Taylor expanded in c around 0 71.5%

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

   if -6.99999999999999956e-85 < (*.f64 a b) < 8.9999999999999995e-163

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 71.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7 \cdot 10^{+155}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -7 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{-163}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 2.2 \cdot 10^{+45} \lor \neg \left(a \cdot b \leq 5.5 \cdot 10^{+62}\right) \land a \cdot b \leq 1.45 \cdot 10^{+140}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -1.05 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -7.8 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 3.6 \cdot 10^{-257}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.6 \cdot 10^{+45} \lor \neg \left(a \cdot b \leq 2.4 \cdot 10^{+63}\right) \land a \cdot b \leq 1.12 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* a b) -1.05e+157)
     t_2
     (if (<= (* a b) -7.8e-38)
       t_1
       (if (<= (* a b) 3.6e-257)
         (+ (* c i) (* x y))
         (if (or (<= (* a b) 1.6e+45)
                 (and (not (<= (* a b) 2.4e+63)) (<= (* a b) 1.12e+144)))
           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 = (x * y) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -1.05e+157) {
		tmp = t_2;
	} else if ((a * b) <= -7.8e-38) {
		tmp = t_1;
	} else if ((a * b) <= 3.6e-257) {
		tmp = (c * i) + (x * y);
	} else if (((a * b) <= 1.6e+45) || (!((a * b) <= 2.4e+63) && ((a * b) <= 1.12e+144))) {
		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 = (x * y) + (z * t)
    t_2 = (a * b) + (c * i)
    if ((a * b) <= (-1.05d+157)) then
        tmp = t_2
    else if ((a * b) <= (-7.8d-38)) then
        tmp = t_1
    else if ((a * b) <= 3.6d-257) then
        tmp = (c * i) + (x * y)
    else if (((a * b) <= 1.6d+45) .or. (.not. ((a * b) <= 2.4d+63)) .and. ((a * b) <= 1.12d+144)) 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 = (x * y) + (z * t);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if ((a * b) <= -1.05e+157) {
		tmp = t_2;
	} else if ((a * b) <= -7.8e-38) {
		tmp = t_1;
	} else if ((a * b) <= 3.6e-257) {
		tmp = (c * i) + (x * y);
	} else if (((a * b) <= 1.6e+45) || (!((a * b) <= 2.4e+63) && ((a * b) <= 1.12e+144))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if (a * b) <= -1.05e+157:
		tmp = t_2
	elif (a * b) <= -7.8e-38:
		tmp = t_1
	elif (a * b) <= 3.6e-257:
		tmp = (c * i) + (x * y)
	elif ((a * b) <= 1.6e+45) or (not ((a * b) <= 2.4e+63) and ((a * b) <= 1.12e+144)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -1.05e+157)
		tmp = t_2;
	elseif (Float64(a * b) <= -7.8e-38)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.6e-257)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif ((Float64(a * b) <= 1.6e+45) || (!(Float64(a * b) <= 2.4e+63) && (Float64(a * b) <= 1.12e+144)))
		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 = (x * y) + (z * t);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -1.05e+157)
		tmp = t_2;
	elseif ((a * b) <= -7.8e-38)
		tmp = t_1;
	elseif ((a * b) <= 3.6e-257)
		tmp = (c * i) + (x * y);
	elseif (((a * b) <= 1.6e+45) || (~(((a * b) <= 2.4e+63)) && ((a * b) <= 1.12e+144)))
		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[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.05e+157], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -7.8e-38], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.6e-257], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], 1.6e+45], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.4e+63]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 1.12e+144]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.05e157 or 1.6000000000000001e45 < (*.f64 a b) < 2.4e63 or 1.11999999999999999e144 < (*.f64 a b)

   1. Initial program 87.1%

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

   3. Taylor expanded in a around inf 87.2%

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

   if -1.05e157 < (*.f64 a b) < -7.7999999999999998e-38 or 3.60000000000000007e-257 < (*.f64 a b) < 1.6000000000000001e45 or 2.4e63 < (*.f64 a b) < 1.11999999999999999e144

   1. Initial program 98.0%

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

   3. Taylor expanded in a around 0 87.4%

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

   4. Taylor expanded in c around 0 72.6%

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

   if -7.7999999999999998e-38 < (*.f64 a b) < 3.60000000000000007e-257

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf 71.8%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.05 \cdot 10^{+157}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq -7.8 \cdot 10^{-38}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.6 \cdot 10^{-257}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.6 \cdot 10^{+45} \lor \neg \left(a \cdot b \leq 2.4 \cdot 10^{+63}\right) \land a \cdot b \leq 1.12 \cdot 10^{+144}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 42.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+155}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.15 \cdot 10^{-35}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.5 \cdot 10^{-170}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+161}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5e+155)
   (* a b)
   (if (<= (* a b) -1.15e-35)
     (* z t)
     (if (<= (* a b) 5.5e-170)
       (* c i)
       (if (<= (* a b) 9e+35)
         (* x y)
         (if (<= (* a b) 5.4e+161) (* z t) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+155) {
		tmp = a * b;
	} else if ((a * b) <= -1.15e-35) {
		tmp = z * t;
	} else if ((a * b) <= 5.5e-170) {
		tmp = c * i;
	} else if ((a * b) <= 9e+35) {
		tmp = x * y;
	} else if ((a * b) <= 5.4e+161) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-5d+155)) then
        tmp = a * b
    else if ((a * b) <= (-1.15d-35)) then
        tmp = z * t
    else if ((a * b) <= 5.5d-170) then
        tmp = c * i
    else if ((a * b) <= 9d+35) then
        tmp = x * y
    else if ((a * b) <= 5.4d+161) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5e+155) {
		tmp = a * b;
	} else if ((a * b) <= -1.15e-35) {
		tmp = z * t;
	} else if ((a * b) <= 5.5e-170) {
		tmp = c * i;
	} else if ((a * b) <= 9e+35) {
		tmp = x * y;
	} else if ((a * b) <= 5.4e+161) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5e+155:
		tmp = a * b
	elif (a * b) <= -1.15e-35:
		tmp = z * t
	elif (a * b) <= 5.5e-170:
		tmp = c * i
	elif (a * b) <= 9e+35:
		tmp = x * y
	elif (a * b) <= 5.4e+161:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -5e+155)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -1.15e-35)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 5.5e-170)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 9e+35)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 5.4e+161)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -5e+155)
		tmp = a * b;
	elseif ((a * b) <= -1.15e-35)
		tmp = z * t;
	elseif ((a * b) <= 5.5e-170)
		tmp = c * i;
	elseif ((a * b) <= 9e+35)
		tmp = x * y;
	elseif ((a * b) <= 5.4e+161)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+155], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1.15e-35], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.5e-170], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 9e+35], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.4e+161], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.9999999999999999e155 or 5.3999999999999995e161 < (*.f64 a b)

   1. Initial program 86.0%

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

      1. +-commutative 86.0%

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

      2. fma-def 87.2%

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

      3. +-commutative 87.2%

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

      4. fma-def 90.7%

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

      5. fma-def 90.7%

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

   3. Simplified 90.7%

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

      1. fma-udef 87.2%

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

      2. fma-def 87.2%

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

      3. associate-+r+ 87.2%

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

   6. Applied egg-rr 87.2%

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

   7. Taylor expanded in z around 0 86.2%

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

   8. Taylor expanded in a around inf 75.9%

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

   if -4.9999999999999999e155 < (*.f64 a b) < -1.1499999999999999e-35 or 8.9999999999999993e35 < (*.f64 a b) < 5.3999999999999995e161

   1. Initial program 95.7%

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

   3. Taylor expanded in a around 0 78.1%

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

   4. Taylor expanded in t around inf 49.0%

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

   if -1.1499999999999999e-35 < (*.f64 a b) < 5.50000000000000018e-170

   1. Initial program 98.7%

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

   3. Taylor expanded in c around inf 38.7%

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

   if 5.50000000000000018e-170 < (*.f64 a b) < 8.9999999999999993e35

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+r+ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 73.6%

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

   8. Taylor expanded in x around inf 44.0%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+155}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -1.15 \cdot 10^{-35}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.5 \cdot 10^{-170}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 9 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5.4 \cdot 10^{+161}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + z \cdot t\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 480000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* z t))) (t_2 (+ (* a b) (* c i))))
   (if (<= (* a b) -1.15e+157)
     t_2
     (if (<= (* a b) 480000000000.0)
       t_1
       (if (<= (* a b) 3.5e+32)
         (+ (* a b) (* x y))
         (if (<= (* a b) 5e+140) 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) + (c * i);
	double tmp;
	if ((a * b) <= -1.15e+157) {
		tmp = t_2;
	} else if ((a * b) <= 480000000000.0) {
		tmp = t_1;
	} else if ((a * b) <= 3.5e+32) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 5e+140) {
		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) + (c * i)
    if ((a * b) <= (-1.15d+157)) then
        tmp = t_2
    else if ((a * b) <= 480000000000.0d0) then
        tmp = t_1
    else if ((a * b) <= 3.5d+32) then
        tmp = (a * b) + (x * y)
    else if ((a * b) <= 5d+140) 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) + (c * i);
	double tmp;
	if ((a * b) <= -1.15e+157) {
		tmp = t_2;
	} else if ((a * b) <= 480000000000.0) {
		tmp = t_1;
	} else if ((a * b) <= 3.5e+32) {
		tmp = (a * b) + (x * y);
	} else if ((a * b) <= 5e+140) {
		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) + (c * i)
	tmp = 0
	if (a * b) <= -1.15e+157:
		tmp = t_2
	elif (a * b) <= 480000000000.0:
		tmp = t_1
	elif (a * b) <= 3.5e+32:
		tmp = (a * b) + (x * y)
	elif (a * b) <= 5e+140:
		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(c * i))
	tmp = 0.0
	if (Float64(a * b) <= -1.15e+157)
		tmp = t_2;
	elseif (Float64(a * b) <= 480000000000.0)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.5e+32)
		tmp = Float64(Float64(a * b) + Float64(x * y));
	elseif (Float64(a * b) <= 5e+140)
		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) + (c * i);
	tmp = 0.0;
	if ((a * b) <= -1.15e+157)
		tmp = t_2;
	elseif ((a * b) <= 480000000000.0)
		tmp = t_1;
	elseif ((a * b) <= 3.5e+32)
		tmp = (a * b) + (x * y);
	elseif ((a * b) <= 5e+140)
		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[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.15e+157], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 480000000000.0], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.5e+32], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+140], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.15000000000000002e157 or 5.00000000000000008e140 < (*.f64 a b)

   1. Initial program 86.3%

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

   3. Taylor expanded in a around inf 86.4%

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

   if -1.15000000000000002e157 < (*.f64 a b) < 4.8e11 or 3.5000000000000001e32 < (*.f64 a b) < 5.00000000000000008e140

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 62.0%

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

   if 4.8e11 < (*.f64 a b) < 3.5000000000000001e32

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-def 100.0%

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

      3. associate-+r+ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 81.8%

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

   8. Taylor expanded in c around 0 72.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+157}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 480000000000:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 3.5 \cdot 10^{+32}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+140}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.0% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

   6. Applied egg-rr 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-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 20.0%

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

      3. +-commutative 20.0%

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

      4. fma-def 40.0%

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

      5. fma-def 40.0%

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

   3. Simplified 40.0%

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

      1. fma-udef 20.0%

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

      2. fma-def 20.0%

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

      3. associate-+r+ 20.0%

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

   6. Applied egg-rr 20.0%

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

   7. Taylor expanded in z around 0 33.3%

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

   8. Taylor expanded in a around inf 53.8%

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

4. Final simplification 97.3%

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

Alternative 10: 43.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{+155}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3.1 \cdot 10^{-39}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.26 \cdot 10^{-256}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.4 \cdot 10^{+161}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -6e+155)
   (* a b)
   (if (<= (* a b) -3.1e-39)
     (* z t)
     (if (<= (* a b) 1.26e-256)
       (* c i)
       (if (<= (* a b) 8.4e+161) (* z t) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -6e+155) {
		tmp = a * b;
	} else if ((a * b) <= -3.1e-39) {
		tmp = z * t;
	} else if ((a * b) <= 1.26e-256) {
		tmp = c * i;
	} else if ((a * b) <= 8.4e+161) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-6d+155)) then
        tmp = a * b
    else if ((a * b) <= (-3.1d-39)) then
        tmp = z * t
    else if ((a * b) <= 1.26d-256) then
        tmp = c * i
    else if ((a * b) <= 8.4d+161) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -6e+155) {
		tmp = a * b;
	} else if ((a * b) <= -3.1e-39) {
		tmp = z * t;
	} else if ((a * b) <= 1.26e-256) {
		tmp = c * i;
	} else if ((a * b) <= 8.4e+161) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -6e+155:
		tmp = a * b
	elif (a * b) <= -3.1e-39:
		tmp = z * t
	elif (a * b) <= 1.26e-256:
		tmp = c * i
	elif (a * b) <= 8.4e+161:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -6e+155)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -3.1e-39)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 1.26e-256)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 8.4e+161)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -6e+155)
		tmp = a * b;
	elseif ((a * b) <= -3.1e-39)
		tmp = z * t;
	elseif ((a * b) <= 1.26e-256)
		tmp = c * i;
	elseif ((a * b) <= 8.4e+161)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -6e+155], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -3.1e-39], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.26e-256], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.4e+161], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6.0000000000000003e155 or 8.4e161 < (*.f64 a b)

   1. Initial program 86.0%

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

      1. +-commutative 86.0%

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

      2. fma-def 87.2%

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

      3. +-commutative 87.2%

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

      4. fma-def 90.7%

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

      5. fma-def 90.7%

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

   3. Simplified 90.7%

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

      1. fma-udef 87.2%

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

      2. fma-def 87.2%

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

      3. associate-+r+ 87.2%

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

   6. Applied egg-rr 87.2%

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

   7. Taylor expanded in z around 0 86.2%

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

   8. Taylor expanded in a around inf 75.9%

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

   if -6.0000000000000003e155 < (*.f64 a b) < -3.0999999999999997e-39 or 1.25999999999999999e-256 < (*.f64 a b) < 8.4e161

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0 85.6%

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

   4. Taylor expanded in t around inf 39.9%

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

   if -3.0999999999999997e-39 < (*.f64 a b) < 1.25999999999999999e-256

   1. Initial program 98.4%

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

   3. Taylor expanded in c around inf 40.3%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -6 \cdot 10^{+155}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -3.1 \cdot 10^{-39}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 1.26 \cdot 10^{-256}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 8.4 \cdot 10^{+161}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;i \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))) (t_2 (+ (* a b) (* c i))))
   (if (<= i -2.5e-12)
     t_2
     (if (<= i 3.6e-69)
       t_1
       (if (<= i 6.8e-17) (* z t) (if (<= i 1.42e+156) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if (i <= -2.5e-12) {
		tmp = t_2;
	} else if (i <= 3.6e-69) {
		tmp = t_1;
	} else if (i <= 6.8e-17) {
		tmp = z * t;
	} else if (i <= 1.42e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    t_2 = (a * b) + (c * i)
    if (i <= (-2.5d-12)) then
        tmp = t_2
    else if (i <= 3.6d-69) then
        tmp = t_1
    else if (i <= 6.8d-17) then
        tmp = z * t
    else if (i <= 1.42d+156) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (a * b) + (c * i);
	double tmp;
	if (i <= -2.5e-12) {
		tmp = t_2;
	} else if (i <= 3.6e-69) {
		tmp = t_1;
	} else if (i <= 6.8e-17) {
		tmp = z * t;
	} else if (i <= 1.42e+156) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (a * b) + (c * i)
	tmp = 0
	if i <= -2.5e-12:
		tmp = t_2
	elif i <= 3.6e-69:
		tmp = t_1
	elif i <= 6.8e-17:
		tmp = z * t
	elif i <= 1.42e+156:
		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(x * y))
	t_2 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (i <= -2.5e-12)
		tmp = t_2;
	elseif (i <= 3.6e-69)
		tmp = t_1;
	elseif (i <= 6.8e-17)
		tmp = Float64(z * t);
	elseif (i <= 1.42e+156)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	t_2 = (a * b) + (c * i);
	tmp = 0.0;
	if (i <= -2.5e-12)
		tmp = t_2;
	elseif (i <= 3.6e-69)
		tmp = t_1;
	elseif (i <= 6.8e-17)
		tmp = z * t;
	elseif (i <= 1.42e+156)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.5e-12], t$95$2, If[LessEqual[i, 3.6e-69], t$95$1, If[LessEqual[i, 6.8e-17], N[(z * t), $MachinePrecision], If[LessEqual[i, 1.42e+156], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.49999999999999985e-12 or 1.41999999999999998e156 < i

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 69.7%

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

   if -2.49999999999999985e-12 < i < 3.60000000000000018e-69 or 6.7999999999999996e-17 < i < 1.41999999999999998e156

   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 95.9%

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

      3. +-commutative 95.9%

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

      4. fma-def 97.2%

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

      5. fma-def 97.2%

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

   3. Simplified 97.2%

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

      1. fma-udef 95.9%

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

      2. fma-def 95.9%

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

      3. associate-+r+ 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in z around 0 74.6%

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

   8. Taylor expanded in c around 0 64.1%

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

   if 3.60000000000000018e-69 < i < 6.7999999999999996e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in a around 0 73.6%

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

   4. Taylor expanded in t around inf 42.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{-69}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-17}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;i \leq 1.42 \cdot 10^{+156}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.6 \cdot 10^{+157}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.75 \cdot 10^{+147}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -5.6e+157)
   (+ (* a b) (* c i))
   (if (<= (* a b) 1.75e+147)
     (+ (* c i) (+ (* x y) (* z t)))
     (+ (* c i) (+ (* a b) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5.6e+157) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= 1.75e+147) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-5.6d+157)) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= 1.75d+147) then
        tmp = (c * i) + ((x * y) + (z * t))
    else
        tmp = (c * i) + ((a * b) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -5.6e+157) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= 1.75e+147) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -5.6e+157:
		tmp = (a * b) + (c * i)
	elif (a * b) <= 1.75e+147:
		tmp = (c * i) + ((x * y) + (z * t))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -5.6e+157)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= 1.75e+147)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -5.6e+157)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= 1.75e+147)
		tmp = (c * i) + ((x * y) + (z * t));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -5.6e+157], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.75e+147], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.6000000000000005e157

   1. Initial program 83.7%

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

   3. Taylor expanded in a around inf 90.8%

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

   if -5.6000000000000005e157 < (*.f64 a b) < 1.74999999999999987e147

   1. Initial program 98.2%

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

   3. Taylor expanded in a around 0 89.0%

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

   if 1.74999999999999987e147 < (*.f64 a b)

   1. Initial program 88.9%

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

   3. Taylor expanded in z around 0 86.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.6 \cdot 10^{+157}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 1.75 \cdot 10^{+147}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.2 \cdot 10^{+175} \lor \neg \left(x \cdot y \leq 3 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -7.2e+175) (not (<= (* x y) 3e+133)))
   (* x y)
   (+ (* a b) (* c i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -7.2e+175) || !((x * y) <= 3e+133)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((x * y) <= (-7.2d+175)) .or. (.not. ((x * y) <= 3d+133))) then
        tmp = x * y
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((x * y) <= -7.2e+175) || !((x * y) <= 3e+133)) {
		tmp = x * y;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((x * y) <= -7.2e+175) or not ((x * y) <= 3e+133):
		tmp = x * y
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(x * y) <= -7.2e+175) || !(Float64(x * y) <= 3e+133))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((x * y) <= -7.2e+175) || ~(((x * y) <= 3e+133)))
		tmp = x * y;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -7.2e+175], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3e+133]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -7.20000000000000067e175 or 3.00000000000000007e133 < (*.f64 x y)

   1. Initial program 84.9%

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

      1. +-commutative 84.9%

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

      2. fma-def 87.7%

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

      3. +-commutative 87.7%

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

      4. fma-def 91.8%

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

      5. fma-def 91.8%

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

   3. Simplified 91.8%

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

      1. fma-udef 87.7%

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

      2. fma-def 87.7%

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

      3. associate-+r+ 87.7%

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

   6. Applied egg-rr 87.7%

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

   7. Taylor expanded in z around 0 77.4%

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

   8. Taylor expanded in x around inf 67.1%

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

   if -7.20000000000000067e175 < (*.f64 x y) < 3.00000000000000007e133

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf 65.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.2 \cdot 10^{+175} \lor \neg \left(x \cdot y \leq 3 \cdot 10^{+133}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+172} \lor \neg \left(z \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -2.35e+172) (not (<= z 4.5e-17)))
   (+ (* x y) (* z t))
   (+ (* c i) (+ (* a b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -2.35e+172) || !(z <= 4.5e-17)) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z <= (-2.35d+172)) .or. (.not. (z <= 4.5d-17))) then
        tmp = (x * y) + (z * t)
    else
        tmp = (c * i) + ((a * b) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z <= -2.35e+172) || !(z <= 4.5e-17)) {
		tmp = (x * y) + (z * t);
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -2.35e+172) or not (z <= 4.5e-17):
		tmp = (x * y) + (z * t)
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -2.35e+172) || !(z <= 4.5e-17))
		tmp = Float64(Float64(x * y) + Float64(z * t));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z <= -2.35e+172) || ~((z <= 4.5e-17)))
		tmp = (x * y) + (z * t);
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -2.35e+172], N[Not[LessEqual[z, 4.5e-17]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3500000000000001e172 or 4.49999999999999978e-17 < z

   1. Initial program 96.0%

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

   3. Taylor expanded in a around 0 77.8%

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

   4. Taylor expanded in c around 0 66.2%

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

   if -2.3500000000000001e172 < z < 4.49999999999999978e-17

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 86.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+172} \lor \neg \left(z \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.4 \cdot 10^{+166} \lor \neg \left(c \cdot i \leq 2 \cdot 10^{+121}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -2.4e+166) (not (<= (* c i) 2e+121))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2.4e+166) || !((c * i) <= 2e+121)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-2.4d+166)) .or. (.not. ((c * i) <= 2d+121))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -2.4e+166) || !((c * i) <= 2e+121)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -2.4e+166) or not ((c * i) <= 2e+121):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -2.4e+166) || !(Float64(c * i) <= 2e+121))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -2.4e+166) || ~(((c * i) <= 2e+121)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -2.4e+166], N[Not[LessEqual[N[(c * i), $MachinePrecision], 2e+121]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -2.39999999999999992e166 or 2.00000000000000007e121 < (*.f64 c i)

   1. Initial program 91.6%

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

   3. Taylor expanded in c around inf 72.6%

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

   if -2.39999999999999992e166 < (*.f64 c i) < 2.00000000000000007e121

   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 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. fma-def 96.2%

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

      5. fma-def 96.2%

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

   3. Simplified 96.2%

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

      1. fma-udef 95.1%

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

      2. fma-def 95.1%

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

      3. associate-+r+ 95.1%

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

   6. Applied egg-rr 95.1%

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

   7. Taylor expanded in z around 0 68.2%

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

   8. Taylor expanded in a around inf 41.2%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.4 \cdot 10^{+166} \lor \neg \left(c \cdot i \leq 2 \cdot 10^{+121}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 27.9% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 95.3%

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

   3. +-commutative 95.3%

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

   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 96.5%

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

3. Simplified 96.5%

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

   1. fma-udef 95.3%

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

   2. fma-def 95.3%

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

   3. associate-+r+ 95.3%

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

6. Applied egg-rr 95.3%

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

7. Taylor expanded in z around 0 74.5%

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

8. Taylor expanded in a around inf 33.2%

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

9. Final simplification 33.2%

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

Reproduce

herbie shell --seed 2024024 
(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)))