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

Percentage Accurate: 96.1% → 97.3%

Time: 10.7s

Alternatives: 16

Speedup: 0.5×

• 42.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.1% 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: 97.3% accurate, 0.5× speedup

Math

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

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 (+ (* c i) (* 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 = (c * i) + (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 = (c * i) + (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 = (c * i) + (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(c * i) + 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 = (c * i) + (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[(c * i), $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. Taylor expanded in x around inf 57.3%

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

4. Final simplification 98.8%

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

Alternative 2: 98.1% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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%

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

   2. associate-+l+ 97.3%

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

   3. fma-def 98.4%

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

   4. associate-+l+ 98.4%

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

   5. fma-def 98.4%

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

   6. +-commutative 98.4%

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

   7. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 3: 97.1% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

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. associate-+l+ 97.3%

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

   2. +-commutative 97.3%

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

   3. associate-+l+ 97.3%

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

   4. fma-def 98.0%

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

   5. associate-+r+ 98.0%

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

   6. +-commutative 98.0%

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

   7. fma-def 98.0%

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

   8. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 98.4%

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

   2. +-commutative 98.4%

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

5. Applied egg-rr 98.4%

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

6. Final simplification 98.4%

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

Alternative 4: 96.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. associate-+l+ 97.3%

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

   2. +-commutative 97.3%

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

   3. associate-+l+ 97.3%

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

   4. fma-def 98.0%

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

   5. associate-+r+ 98.0%

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

   6. +-commutative 98.0%

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

   7. fma-def 98.0%

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

   8. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 98.4%

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

   2. +-commutative 98.4%

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

5. Applied egg-rr 98.4%

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

   1. fma-udef 97.7%

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

   2. *-commutative 97.7%

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

   3. associate-+r+ 97.7%

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

   4. *-commutative 97.7%

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

7. Applied egg-rr 97.7%

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

8. Final simplification 97.7%

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

Alternative 5: 42.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.2 \cdot 10^{+133}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.55 \cdot 10^{-130}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.6 \cdot 10^{-284}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-309}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 5.5 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.12 \cdot 10^{-129}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 160000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.45 \cdot 10^{+76}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 8 \cdot 10^{+95}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -7.2e+133)
   (* c i)
   (if (<= (* c i) -2.55e-130)
     (* x y)
     (if (<= (* c i) -1.6e-284)
       (* a b)
       (if (<= (* c i) -4e-309)
         (* x y)
         (if (<= (* c i) 5.5e-241)
           (* z t)
           (if (<= (* c i) 1.12e-129)
             (* a b)
             (if (<= (* c i) 160000.0)
               (* x y)
               (if (<= (* c i) 2.45e+76)
                 (* a b)
                 (if (<= (* c i) 8e+95) (* 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) <= -7.2e+133) {
		tmp = c * i;
	} else if ((c * i) <= -2.55e-130) {
		tmp = x * y;
	} else if ((c * i) <= -1.6e-284) {
		tmp = a * b;
	} else if ((c * i) <= -4e-309) {
		tmp = x * y;
	} else if ((c * i) <= 5.5e-241) {
		tmp = z * t;
	} else if ((c * i) <= 1.12e-129) {
		tmp = a * b;
	} else if ((c * i) <= 160000.0) {
		tmp = x * y;
	} else if ((c * i) <= 2.45e+76) {
		tmp = a * b;
	} else if ((c * i) <= 8e+95) {
		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) <= (-7.2d+133)) then
        tmp = c * i
    else if ((c * i) <= (-2.55d-130)) then
        tmp = x * y
    else if ((c * i) <= (-1.6d-284)) then
        tmp = a * b
    else if ((c * i) <= (-4d-309)) then
        tmp = x * y
    else if ((c * i) <= 5.5d-241) then
        tmp = z * t
    else if ((c * i) <= 1.12d-129) then
        tmp = a * b
    else if ((c * i) <= 160000.0d0) then
        tmp = x * y
    else if ((c * i) <= 2.45d+76) then
        tmp = a * b
    else if ((c * i) <= 8d+95) 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) <= -7.2e+133) {
		tmp = c * i;
	} else if ((c * i) <= -2.55e-130) {
		tmp = x * y;
	} else if ((c * i) <= -1.6e-284) {
		tmp = a * b;
	} else if ((c * i) <= -4e-309) {
		tmp = x * y;
	} else if ((c * i) <= 5.5e-241) {
		tmp = z * t;
	} else if ((c * i) <= 1.12e-129) {
		tmp = a * b;
	} else if ((c * i) <= 160000.0) {
		tmp = x * y;
	} else if ((c * i) <= 2.45e+76) {
		tmp = a * b;
	} else if ((c * i) <= 8e+95) {
		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) <= -7.2e+133:
		tmp = c * i
	elif (c * i) <= -2.55e-130:
		tmp = x * y
	elif (c * i) <= -1.6e-284:
		tmp = a * b
	elif (c * i) <= -4e-309:
		tmp = x * y
	elif (c * i) <= 5.5e-241:
		tmp = z * t
	elif (c * i) <= 1.12e-129:
		tmp = a * b
	elif (c * i) <= 160000.0:
		tmp = x * y
	elif (c * i) <= 2.45e+76:
		tmp = a * b
	elif (c * i) <= 8e+95:
		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) <= -7.2e+133)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -2.55e-130)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -1.6e-284)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= -4e-309)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 5.5e-241)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.12e-129)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 160000.0)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 2.45e+76)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 8e+95)
		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) <= -7.2e+133)
		tmp = c * i;
	elseif ((c * i) <= -2.55e-130)
		tmp = x * y;
	elseif ((c * i) <= -1.6e-284)
		tmp = a * b;
	elseif ((c * i) <= -4e-309)
		tmp = x * y;
	elseif ((c * i) <= 5.5e-241)
		tmp = z * t;
	elseif ((c * i) <= 1.12e-129)
		tmp = a * b;
	elseif ((c * i) <= 160000.0)
		tmp = x * y;
	elseif ((c * i) <= 2.45e+76)
		tmp = a * b;
	elseif ((c * i) <= 8e+95)
		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], -7.2e+133], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.55e-130], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.6e-284], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -4e-309], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.5e-241], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.12e-129], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 160000.0], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.45e+76], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8e+95], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -7.19999999999999956e133 or 8.00000000000000016e95 < (*.f64 c i)

   1. Initial program 95.2%

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

   2. Taylor expanded in c around inf 74.0%

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

   if -7.19999999999999956e133 < (*.f64 c i) < -2.5499999999999999e-130 or -1.60000000000000012e-284 < (*.f64 c i) < -3.9999999999999977e-309 or 1.12000000000000006e-129 < (*.f64 c i) < 1.6e5

   1. Initial program 98.9%

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

      1. associate-+l+ 98.9%

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

      2. +-commutative 98.9%

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

      3. associate-+l+ 98.9%

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

      4. fma-def 98.9%

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

      5. associate-+r+ 98.9%

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

      6. +-commutative 98.9%

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

      7. fma-def 98.9%

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

      8. fma-def 98.9%

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

   3. Simplified 98.9%

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

      1. fma-udef 98.9%

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

      2. +-commutative 98.9%

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

   5. Applied egg-rr 98.9%

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

      1. fma-udef 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-+r+ 98.9%

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

      4. *-commutative 98.9%

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

   7. Applied egg-rr 98.9%

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

   8. Taylor expanded in x around inf 48.7%

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

   if -2.5499999999999999e-130 < (*.f64 c i) < -1.60000000000000012e-284 or 5.4999999999999998e-241 < (*.f64 c i) < 1.12000000000000006e-129 or 1.6e5 < (*.f64 c i) < 2.45000000000000013e76

   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. associate-+l+ 97.5%

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

      2. +-commutative 97.5%

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

      3. associate-+l+ 97.5%

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

      4. fma-def 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. fma-udef 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-+r+ 97.5%

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

      4. *-commutative 97.5%

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

   7. Applied egg-rr 97.5%

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

   8. Taylor expanded in a around inf 62.1%

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

   if -3.9999999999999977e-309 < (*.f64 c i) < 5.4999999999999998e-241 or 2.45000000000000013e76 < (*.f64 c i) < 8.00000000000000016e95

   1. Initial program 97.6%

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

      1. associate-+l+ 97.6%

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

      2. +-commutative 97.6%

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

      3. associate-+l+ 97.6%

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

      4. fma-def 97.6%

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

      5. associate-+r+ 97.6%

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

      6. +-commutative 97.6%

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

      7. fma-def 97.6%

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

      8. fma-def 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 97.6%

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

      2. +-commutative 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in z around inf 51.5%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.2 \cdot 10^{+133}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -2.55 \cdot 10^{-130}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -1.6 \cdot 10^{-284}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-309}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 5.5 \cdot 10^{-241}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.12 \cdot 10^{-129}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 160000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.45 \cdot 10^{+76}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 8 \cdot 10^{+95}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 6: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := x \cdot y + z \cdot t\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 5800000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 1.75 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y)))
        (t_2 (+ (* x y) (* z t)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* c i) -8.5e+64)
     t_3
     (if (<= (* c i) -4e-279)
       t_1
       (if (<= (* c i) 9.2e-242)
         t_2
         (if (<= (* c i) 9.5e-67)
           t_1
           (if (<= (* c i) 5800000.0)
             t_2
             (if (<= (* c i) 1.75e+51) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (x * y) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -8.5e+64) {
		tmp = t_3;
	} else if ((c * i) <= -4e-279) {
		tmp = t_1;
	} else if ((c * i) <= 9.2e-242) {
		tmp = t_2;
	} else if ((c * i) <= 9.5e-67) {
		tmp = t_1;
	} else if ((c * i) <= 5800000.0) {
		tmp = t_2;
	} else if ((c * i) <= 1.75e+51) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    t_2 = (x * y) + (z * t)
    t_3 = (a * b) + (c * i)
    if ((c * i) <= (-8.5d+64)) then
        tmp = t_3
    else if ((c * i) <= (-4d-279)) then
        tmp = t_1
    else if ((c * i) <= 9.2d-242) then
        tmp = t_2
    else if ((c * i) <= 9.5d-67) then
        tmp = t_1
    else if ((c * i) <= 5800000.0d0) then
        tmp = t_2
    else if ((c * i) <= 1.75d+51) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (x * y) + (z * t);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -8.5e+64) {
		tmp = t_3;
	} else if ((c * i) <= -4e-279) {
		tmp = t_1;
	} else if ((c * i) <= 9.2e-242) {
		tmp = t_2;
	} else if ((c * i) <= 9.5e-67) {
		tmp = t_1;
	} else if ((c * i) <= 5800000.0) {
		tmp = t_2;
	} else if ((c * i) <= 1.75e+51) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (x * y) + (z * t)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -8.5e+64:
		tmp = t_3
	elif (c * i) <= -4e-279:
		tmp = t_1
	elif (c * i) <= 9.2e-242:
		tmp = t_2
	elif (c * i) <= 9.5e-67:
		tmp = t_1
	elif (c * i) <= 5800000.0:
		tmp = t_2
	elif (c * i) <= 1.75e+51:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -8.5e+64)
		tmp = t_3;
	elseif (Float64(c * i) <= -4e-279)
		tmp = t_1;
	elseif (Float64(c * i) <= 9.2e-242)
		tmp = t_2;
	elseif (Float64(c * i) <= 9.5e-67)
		tmp = t_1;
	elseif (Float64(c * i) <= 5800000.0)
		tmp = t_2;
	elseif (Float64(c * i) <= 1.75e+51)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	t_2 = (x * y) + (z * t);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -8.5e+64)
		tmp = t_3;
	elseif ((c * i) <= -4e-279)
		tmp = t_1;
	elseif ((c * i) <= 9.2e-242)
		tmp = t_2;
	elseif ((c * i) <= 9.5e-67)
		tmp = t_1;
	elseif ((c * i) <= 5800000.0)
		tmp = t_2;
	elseif ((c * i) <= 1.75e+51)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -8.5e+64], t$95$3, If[LessEqual[N[(c * i), $MachinePrecision], -4e-279], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 9.2e-242], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 9.5e-67], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 5800000.0], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 1.75e+51], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -8.4999999999999998e64 or 1.75e51 < (*.f64 c i)

   1. Initial program 94.3%

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

   2. Taylor expanded in a around inf 79.5%

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

   if -8.4999999999999998e64 < (*.f64 c i) < -4.00000000000000022e-279 or 9.19999999999999939e-242 < (*.f64 c i) < 9.4999999999999994e-67 or 5.8e6 < (*.f64 c i) < 1.75e51

   1. Initial program 98.8%

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

      1. associate-+l+ 98.8%

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

      2. +-commutative 98.8%

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

      3. associate-+l+ 98.8%

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

      4. fma-def 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. fma-udef 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-+r+ 98.8%

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

      4. *-commutative 98.8%

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

   7. Applied egg-rr 98.8%

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

   8. Taylor expanded in z around 0 87.6%

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

      1. +-commutative 87.6%

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

      2. fma-udef 87.6%

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

   10. Simplified 87.6%

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

   11. Taylor expanded in c around 0 83.0%

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

   if -4.00000000000000022e-279 < (*.f64 c i) < 9.19999999999999939e-242 or 9.4999999999999994e-67 < (*.f64 c i) < 5.8e6

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 81.0%

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

   3. Taylor expanded in c around 0 80.9%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -8.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -4 \cdot 10^{-279}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 9.2 \cdot 10^{-242}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 5800000:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.75 \cdot 10^{+51}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 7: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := x \cdot y + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+67}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -2.35 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* x y))) (t_2 (+ (* x y) (* z t))))
   (if (<= (* c i) -3.7e+67)
     (+ (* c i) (* x y))
     (if (<= (* c i) -2.35e-281)
       t_1
       (if (<= (* c i) 2.5e-241)
         t_2
         (if (<= (* c i) 2.5e-68)
           t_1
           (if (<= (* c i) 500000.0)
             t_2
             (if (<= (* c i) 3e+47) t_1 (+ (* a b) (* c i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -3.7e+67) {
		tmp = (c * i) + (x * y);
	} else if ((c * i) <= -2.35e-281) {
		tmp = t_1;
	} else if ((c * i) <= 2.5e-241) {
		tmp = t_2;
	} else if ((c * i) <= 2.5e-68) {
		tmp = t_1;
	} else if ((c * i) <= 500000.0) {
		tmp = t_2;
	} else if ((c * i) <= 3e+47) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (x * y)
    t_2 = (x * y) + (z * t)
    if ((c * i) <= (-3.7d+67)) then
        tmp = (c * i) + (x * y)
    else if ((c * i) <= (-2.35d-281)) then
        tmp = t_1
    else if ((c * i) <= 2.5d-241) then
        tmp = t_2
    else if ((c * i) <= 2.5d-68) then
        tmp = t_1
    else if ((c * i) <= 500000.0d0) then
        tmp = t_2
    else if ((c * i) <= 3d+47) then
        tmp = t_1
    else
        tmp = (a * b) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (x * y);
	double t_2 = (x * y) + (z * t);
	double tmp;
	if ((c * i) <= -3.7e+67) {
		tmp = (c * i) + (x * y);
	} else if ((c * i) <= -2.35e-281) {
		tmp = t_1;
	} else if ((c * i) <= 2.5e-241) {
		tmp = t_2;
	} else if ((c * i) <= 2.5e-68) {
		tmp = t_1;
	} else if ((c * i) <= 500000.0) {
		tmp = t_2;
	} else if ((c * i) <= 3e+47) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (x * y)
	t_2 = (x * y) + (z * t)
	tmp = 0
	if (c * i) <= -3.7e+67:
		tmp = (c * i) + (x * y)
	elif (c * i) <= -2.35e-281:
		tmp = t_1
	elif (c * i) <= 2.5e-241:
		tmp = t_2
	elif (c * i) <= 2.5e-68:
		tmp = t_1
	elif (c * i) <= 500000.0:
		tmp = t_2
	elif (c * i) <= 3e+47:
		tmp = t_1
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -3.7e+67)
		tmp = Float64(Float64(c * i) + Float64(x * y));
	elseif (Float64(c * i) <= -2.35e-281)
		tmp = t_1;
	elseif (Float64(c * i) <= 2.5e-241)
		tmp = t_2;
	elseif (Float64(c * i) <= 2.5e-68)
		tmp = t_1;
	elseif (Float64(c * i) <= 500000.0)
		tmp = t_2;
	elseif (Float64(c * i) <= 3e+47)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (x * y);
	t_2 = (x * y) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -3.7e+67)
		tmp = (c * i) + (x * y);
	elseif ((c * i) <= -2.35e-281)
		tmp = t_1;
	elseif ((c * i) <= 2.5e-241)
		tmp = t_2;
	elseif ((c * i) <= 2.5e-68)
		tmp = t_1;
	elseif ((c * i) <= 500000.0)
		tmp = t_2;
	elseif ((c * i) <= 3e+47)
		tmp = t_1;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -3.7e+67], N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -2.35e-281], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 2.5e-241], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 2.5e-68], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 500000.0], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 3e+47], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -3.6999999999999997e67

   1. Initial program 90.7%

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

   2. Taylor expanded in x around inf 83.6%

      \[\leadsto \color{blue}{x \cdot y} + c \cdot i \]

   if -3.6999999999999997e67 < (*.f64 c i) < -2.3500000000000001e-281 or 2.4999999999999999e-241 < (*.f64 c i) < 2.49999999999999986e-68 or 5e5 < (*.f64 c i) < 3.0000000000000001e47

   1. Initial program 98.8%

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

      1. associate-+l+ 98.8%

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

      2. +-commutative 98.8%

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

      3. associate-+l+ 98.8%

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

      4. fma-def 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. fma-udef 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-+r+ 98.8%

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

      4. *-commutative 98.8%

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

   7. Applied egg-rr 98.8%

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

   8. Taylor expanded in z around 0 87.6%

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

      1. +-commutative 87.6%

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

      2. fma-udef 87.6%

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

   10. Simplified 87.6%

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

   11. Taylor expanded in c around 0 83.0%

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

   if -2.3500000000000001e-281 < (*.f64 c i) < 2.4999999999999999e-241 or 2.49999999999999986e-68 < (*.f64 c i) < 5e5

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 81.0%

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

   3. Taylor expanded in c around 0 80.9%

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

   if 3.0000000000000001e47 < (*.f64 c i)

   1. Initial program 96.8%

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

   2. Taylor expanded in a around inf 78.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+67}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -2.35 \cdot 10^{-281}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{-241}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.5 \cdot 10^{-68}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 500000:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3 \cdot 10^{+47}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 8: 42.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.1 \cdot 10^{-21}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 6.9 \cdot 10^{+87}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.5 \cdot 10^{+120}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -9.5e+26)
   (* a b)
   (if (<= (* a b) -2.3e-39)
     (* z t)
     (if (<= (* a b) 5.1e-21)
       (* c i)
       (if (<= (* a b) 6.9e+87)
         (* z t)
         (if (<= (* a b) 6.5e+120) (* c i) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -9.5e+26) {
		tmp = a * b;
	} else if ((a * b) <= -2.3e-39) {
		tmp = z * t;
	} else if ((a * b) <= 5.1e-21) {
		tmp = c * i;
	} else if ((a * b) <= 6.9e+87) {
		tmp = z * t;
	} else if ((a * b) <= 6.5e+120) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-9.5d+26)) then
        tmp = a * b
    else if ((a * b) <= (-2.3d-39)) then
        tmp = z * t
    else if ((a * b) <= 5.1d-21) then
        tmp = c * i
    else if ((a * b) <= 6.9d+87) then
        tmp = z * t
    else if ((a * b) <= 6.5d+120) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -9.5e+26) {
		tmp = a * b;
	} else if ((a * b) <= -2.3e-39) {
		tmp = z * t;
	} else if ((a * b) <= 5.1e-21) {
		tmp = c * i;
	} else if ((a * b) <= 6.9e+87) {
		tmp = z * t;
	} else if ((a * b) <= 6.5e+120) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -9.5e+26:
		tmp = a * b
	elif (a * b) <= -2.3e-39:
		tmp = z * t
	elif (a * b) <= 5.1e-21:
		tmp = c * i
	elif (a * b) <= 6.9e+87:
		tmp = z * t
	elif (a * b) <= 6.5e+120:
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -9.5e+26)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= -2.3e-39)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 5.1e-21)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 6.9e+87)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 6.5e+120)
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -9.5e+26)
		tmp = a * b;
	elseif ((a * b) <= -2.3e-39)
		tmp = z * t;
	elseif ((a * b) <= 5.1e-21)
		tmp = c * i;
	elseif ((a * b) <= 6.9e+87)
		tmp = z * t;
	elseif ((a * b) <= 6.5e+120)
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -9.5e+26], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.3e-39], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5.1e-21], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6.9e+87], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 6.5e+120], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.50000000000000054e26 or 6.4999999999999997e120 < (*.f64 a b)

   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. associate-+l+ 95.2%

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

      2. +-commutative 95.2%

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

      3. associate-+l+ 95.2%

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

      4. fma-def 96.2%

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

      5. associate-+r+ 96.2%

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

      6. +-commutative 96.2%

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

      7. fma-def 96.2%

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

      8. fma-def 97.1%

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

   3. Simplified 97.1%

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

      1. fma-udef 97.1%

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

      2. +-commutative 97.1%

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

   5. Applied egg-rr 97.1%

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

      1. fma-udef 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-+r+ 96.2%

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

      4. *-commutative 96.2%

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

   7. Applied egg-rr 96.2%

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

   8. Taylor expanded in a around inf 60.9%

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

   if -9.50000000000000054e26 < (*.f64 a b) < -2.30000000000000008e-39 or 5.10000000000000004e-21 < (*.f64 a b) < 6.89999999999999963e87

   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. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 47.8%

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

   if -2.30000000000000008e-39 < (*.f64 a b) < 5.10000000000000004e-21 or 6.89999999999999963e87 < (*.f64 a b) < 6.4999999999999997e120

   1. Initial program 98.2%

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

   2. Taylor expanded in c around inf 46.0%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+26}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 5.1 \cdot 10^{-21}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 6.9 \cdot 10^{+87}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 6.5 \cdot 10^{+120}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 9: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + x \cdot y\\ t_2 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq -1.6 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{-236}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (<= (* c i) -5.6e+63)
     t_2
     (if (<= (* c i) -1.6e-155)
       t_1
       (if (<= (* c i) 1.15e-236)
         (+ (* a b) (* z t))
         (if (<= (* c i) 3.8e+51) 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 ((c * i) <= -5.6e+63) {
		tmp = t_2;
	} else if ((c * i) <= -1.6e-155) {
		tmp = t_1;
	} else if ((c * i) <= 1.15e-236) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 3.8e+51) {
		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 ((c * i) <= (-5.6d+63)) then
        tmp = t_2
    else if ((c * i) <= (-1.6d-155)) then
        tmp = t_1
    else if ((c * i) <= 1.15d-236) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 3.8d+51) 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 ((c * i) <= -5.6e+63) {
		tmp = t_2;
	} else if ((c * i) <= -1.6e-155) {
		tmp = t_1;
	} else if ((c * i) <= 1.15e-236) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 3.8e+51) {
		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 (c * i) <= -5.6e+63:
		tmp = t_2
	elif (c * i) <= -1.6e-155:
		tmp = t_1
	elif (c * i) <= 1.15e-236:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 3.8e+51:
		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 (Float64(c * i) <= -5.6e+63)
		tmp = t_2;
	elseif (Float64(c * i) <= -1.6e-155)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.15e-236)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 3.8e+51)
		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 ((c * i) <= -5.6e+63)
		tmp = t_2;
	elseif ((c * i) <= -1.6e-155)
		tmp = t_1;
	elseif ((c * i) <= 1.15e-236)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 3.8e+51)
		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[N[(c * i), $MachinePrecision], -5.6e+63], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -1.6e-155], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.15e-236], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.8e+51], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.59999999999999974e63 or 3.7999999999999997e51 < (*.f64 c i)

   1. Initial program 94.3%

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

   2. Taylor expanded in a around inf 79.5%

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

   if -5.59999999999999974e63 < (*.f64 c i) < -1.60000000000000006e-155 or 1.15000000000000003e-236 < (*.f64 c i) < 3.7999999999999997e51

   1. Initial program 98.9%

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

      1. associate-+l+ 98.9%

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

      2. +-commutative 98.9%

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

      3. associate-+l+ 98.9%

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

      4. fma-def 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. fma-udef 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-+r+ 98.9%

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

      4. *-commutative 98.9%

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

   7. Applied egg-rr 98.9%

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

   8. Taylor expanded in z around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. fma-udef 84.7%

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

   10. Simplified 84.7%

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

   11. Taylor expanded in c around 0 80.6%

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

   if -1.60000000000000006e-155 < (*.f64 c i) < 1.15000000000000003e-236

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.4%

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

   3. Taylor expanded in c around 0 72.4%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5.6 \cdot 10^{+63}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.6 \cdot 10^{-155}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.15 \cdot 10^{-236}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 10: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -1.45 \cdot 10^{-125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))))
   (if (<= (* c i) -6.8e-25)
     t_1
     (if (<= (* c i) -1.45e-125)
       (* x y)
       (if (<= (* c i) 3.4e+90) (+ (* a b) (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -6.8e-25) {
		tmp = t_1;
	} else if ((c * i) <= -1.45e-125) {
		tmp = x * y;
	} else if ((c * i) <= 3.4e+90) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    if ((c * i) <= (-6.8d-25)) then
        tmp = t_1
    else if ((c * i) <= (-1.45d-125)) then
        tmp = x * y
    else if ((c * i) <= 3.4d+90) then
        tmp = (a * b) + (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double tmp;
	if ((c * i) <= -6.8e-25) {
		tmp = t_1;
	} else if ((c * i) <= -1.45e-125) {
		tmp = x * y;
	} else if ((c * i) <= 3.4e+90) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	tmp = 0
	if (c * i) <= -6.8e-25:
		tmp = t_1
	elif (c * i) <= -1.45e-125:
		tmp = x * y
	elif (c * i) <= 3.4e+90:
		tmp = (a * b) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(c * i) <= -6.8e-25)
		tmp = t_1;
	elseif (Float64(c * i) <= -1.45e-125)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 3.4e+90)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	tmp = 0.0;
	if ((c * i) <= -6.8e-25)
		tmp = t_1;
	elseif ((c * i) <= -1.45e-125)
		tmp = x * y;
	elseif ((c * i) <= 3.4e+90)
		tmp = (a * b) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -6.8e-25], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -1.45e-125], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.4e+90], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.80000000000000003e-25 or 3.40000000000000018e90 < (*.f64 c i)

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 79.4%

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

   if -6.80000000000000003e-25 < (*.f64 c i) < -1.4500000000000001e-125

   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. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. fma-def 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. fma-udef 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-+r+ 100.0%

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

      4. *-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around inf 65.3%

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

   if -1.4500000000000001e-125 < (*.f64 c i) < 3.40000000000000018e90

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 68.9%

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

   3. Taylor expanded in c around 0 65.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{-25}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.45 \cdot 10^{-125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.4 \cdot 10^{+90}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 11: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-48} \lor \neg \left(z \cdot t \leq 10^{-23}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -4e-48) (not (<= (* z t) 1e-23)))
   (+ (* c i) (+ (* a b) (* 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 * t) <= -4e-48) || !((z * t) <= 1e-23)) {
		tmp = (c * i) + ((a * b) + (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 * t) <= (-4d-48)) .or. (.not. ((z * t) <= 1d-23))) then
        tmp = (c * i) + ((a * b) + (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 * t) <= -4e-48) || !((z * t) <= 1e-23)) {
		tmp = (c * i) + ((a * b) + (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 * t) <= -4e-48) or not ((z * t) <= 1e-23):
		tmp = (c * i) + ((a * b) + (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(z * t) <= -4e-48) || !(Float64(z * t) <= 1e-23))
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + 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 * t) <= -4e-48) || ~(((z * t) <= 1e-23)))
		tmp = (c * i) + ((a * b) + (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[N[(z * t), $MachinePrecision], -4e-48], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e-23]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $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 2 regimes

2. if (*.f64 z t) < -3.9999999999999999e-48 or 9.9999999999999996e-24 < (*.f64 z t)

   1. Initial program 94.2%

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

   2. Taylor expanded in x around 0 83.7%

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

   if -3.9999999999999999e-48 < (*.f64 z t) < 9.9999999999999996e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 98.6%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-48} \lor \neg \left(z \cdot t \leq 10^{-23}\right):\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]

Alternative 12: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+185}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+90}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.45e+185)
   (+ (* x y) (* z t))
   (if (<= (* x y) 1.45e+90)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* a b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.45e+185) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 1.45e+90) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-1.45d+185)) then
        tmp = (x * y) + (z * t)
    else if ((x * y) <= 1.45d+90) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (a * b) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.45e+185) {
		tmp = (x * y) + (z * t);
	} else if ((x * y) <= 1.45e+90) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (a * b) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.45e+185:
		tmp = (x * y) + (z * t)
	elif (x * y) <= 1.45e+90:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (a * b) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.45e+185)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(x * y) <= 1.45e+90)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(a * b) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1.45e+185)
		tmp = (x * y) + (z * t);
	elseif ((x * y) <= 1.45e+90)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (a * b) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.45e+185], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.45e+90], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.44999999999999994e185

   1. Initial program 95.8%

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

   2. Taylor expanded in a around 0 100.0%

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

   3. Taylor expanded in c around 0 100.0%

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

   if -1.44999999999999994e185 < (*.f64 x y) < 1.4500000000000001e90

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0 87.9%

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

   if 1.4500000000000001e90 < (*.f64 x y)

   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. associate-+l+ 95.7%

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

      2. +-commutative 95.7%

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

      3. associate-+l+ 95.7%

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

      4. fma-def 95.7%

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

      5. associate-+r+ 95.7%

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

      6. +-commutative 95.7%

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

      7. fma-def 95.7%

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

      8. fma-def 97.9%

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

   3. Simplified 97.9%

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

      1. fma-udef 97.9%

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

      2. +-commutative 97.9%

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

   5. Applied egg-rr 97.9%

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

      1. fma-udef 97.9%

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

      2. *-commutative 97.9%

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

      3. associate-+r+ 97.9%

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

      4. *-commutative 97.9%

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

   7. Applied egg-rr 97.9%

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

   8. Taylor expanded in z around 0 91.8%

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

      1. +-commutative 91.8%

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

      2. fma-udef 94.0%

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

   10. Simplified 94.0%

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

   11. Taylor expanded in c around 0 79.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+185}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+90}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + x \cdot y\\ \end{array} \]

Alternative 13: 87.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+39}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 10^{-23}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -4e+39)
   (+ (* c i) (+ (* x y) (* z t)))
   (if (<= (* z t) 1e-23)
     (+ (* c i) (+ (* a b) (* x y)))
     (+ (* c i) (+ (* a b) (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -4e+39) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else if ((z * t) <= 1e-23) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((z * t) <= (-4d+39)) then
        tmp = (c * i) + ((x * y) + (z * t))
    else if ((z * t) <= 1d-23) then
        tmp = (c * i) + ((a * b) + (x * y))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((z * t) <= -4e+39) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else if ((z * t) <= 1e-23) {
		tmp = (c * i) + ((a * b) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -4e+39:
		tmp = (c * i) + ((x * y) + (z * t))
	elif (z * t) <= 1e-23:
		tmp = (c * i) + ((a * b) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -4e+39)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	elseif (Float64(z * t) <= 1e-23)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((z * t) <= -4e+39)
		tmp = (c * i) + ((x * y) + (z * t));
	elseif ((z * t) <= 1e-23)
		tmp = (c * i) + ((a * b) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -4e+39], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-23], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -3.99999999999999976e39

   1. Initial program 91.1%

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

   2. Taylor expanded in a around 0 87.1%

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

   if -3.99999999999999976e39 < (*.f64 z t) < 9.9999999999999996e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.6%

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

   if 9.9999999999999996e-24 < (*.f64 z t)

   1. Initial program 94.7%

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

   2. Taylor expanded in x around 0 89.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+39}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;z \cdot t \leq 10^{-23}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 14: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{+187} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+141}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -2.4e+187) (not (<= (* x y) 2.4e+141)))
   (* 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) <= -2.4e+187) || !((x * y) <= 2.4e+141)) {
		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) <= (-2.4d+187)) .or. (.not. ((x * y) <= 2.4d+141))) 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) <= -2.4e+187) || !((x * y) <= 2.4e+141)) {
		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) <= -2.4e+187) or not ((x * y) <= 2.4e+141):
		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) <= -2.4e+187) || !(Float64(x * y) <= 2.4e+141))
		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) <= -2.4e+187) || ~(((x * y) <= 2.4e+141)))
		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], -2.4e+187], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.4e+141]], $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) < -2.39999999999999985e187 or 2.39999999999999997e141 < (*.f64 x y)

   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. associate-+l+ 95.1%

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

      2. +-commutative 95.1%

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

      3. associate-+l+ 95.1%

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

      4. fma-def 95.1%

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

      5. associate-+r+ 95.1%

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

      6. +-commutative 95.1%

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

      7. fma-def 95.1%

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

      8. fma-def 96.7%

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

   3. Simplified 96.7%

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

      1. fma-udef 96.7%

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

      2. +-commutative 96.7%

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

   5. Applied egg-rr 96.7%

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

      1. fma-udef 96.7%

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

      2. *-commutative 96.7%

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

      3. associate-+r+ 96.7%

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

      4. *-commutative 96.7%

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

   7. Applied egg-rr 96.7%

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

   8. Taylor expanded in x around inf 77.9%

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

   if -2.39999999999999985e187 < (*.f64 x y) < 2.39999999999999997e141

   1. Initial program 97.9%

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

   2. Taylor expanded in a around inf 65.7%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{+187} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+141}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 15: 40.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.8 \cdot 10^{+145} \lor \neg \left(a \cdot b \leq 3.9 \cdot 10^{-21}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -7.8e+145) (not (<= (* a b) 3.9e-21))) (* a b) (* c i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -7.8e+145) || !((a * b) <= 3.9e-21)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((a * b) <= (-7.8d+145)) .or. (.not. ((a * b) <= 3.9d-21))) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((a * b) <= -7.8e+145) || !((a * b) <= 3.9e-21)) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((a * b) <= -7.8e+145) or not ((a * b) <= 3.9e-21):
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(a * b) <= -7.8e+145) || !(Float64(a * b) <= 3.9e-21))
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((a * b) <= -7.8e+145) || ~(((a * b) <= 3.9e-21)))
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -7.8e+145], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3.9e-21]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -7.7999999999999995e145 or 3.9000000000000001e-21 < (*.f64 a b)

   1. Initial program 95.4%

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

      1. associate-+l+ 95.4%

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

      2. +-commutative 95.4%

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

      3. associate-+l+ 95.4%

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

      4. fma-def 96.3%

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

      5. associate-+r+ 96.3%

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

      6. +-commutative 96.3%

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

      7. fma-def 96.3%

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

      8. fma-def 97.3%

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

   3. Simplified 97.3%

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

      1. fma-udef 97.3%

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

      2. +-commutative 97.3%

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

   5. Applied egg-rr 97.3%

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

      1. fma-udef 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-+r+ 96.4%

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

      4. *-commutative 96.4%

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

   7. Applied egg-rr 96.4%

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

   8. Taylor expanded in a around inf 59.3%

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

   if -7.7999999999999995e145 < (*.f64 a b) < 3.9000000000000001e-21

   1. Initial program 98.6%

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

   2. Taylor expanded in c around inf 40.1%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7.8 \cdot 10^{+145} \lor \neg \left(a \cdot b \leq 3.9 \cdot 10^{-21}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 16: 27.0% 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 97.3%

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

   1. associate-+l+ 97.3%

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

   2. +-commutative 97.3%

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

   3. associate-+l+ 97.3%

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

   4. fma-def 98.0%

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

   5. associate-+r+ 98.0%

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

   6. +-commutative 98.0%

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

   7. fma-def 98.0%

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

   8. fma-def 98.4%

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

3. Simplified 98.4%

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

   1. fma-udef 98.4%

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

   2. +-commutative 98.4%

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

5. Applied egg-rr 98.4%

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

   1. fma-udef 97.7%

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

   2. *-commutative 97.7%

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

   3. associate-+r+ 97.7%

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

   4. *-commutative 97.7%

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

7. Applied egg-rr 97.7%

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

8. Taylor expanded in a around inf 29.5%

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

9. Final simplification 29.5%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023309 
(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)))