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

Percentage Accurate: 95.8% → 97.8%

Time: 9.5s

Alternatives: 13

Speedup: 0.5×

• 40.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.0× speedup

Math

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

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 96.5%

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

   1. +-commutative 96.5%

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

   2. associate-+l+ 96.5%

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

   3. fma-def 98.8%

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

   4. associate-+l+ 98.8%

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

   5. fma-def 99.2%

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

   6. +-commutative 99.2%

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

   7. fma-def 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 96.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z t))) (t_2 (+ (+ (* a b) t_1) (* c i))))
   (if (<= t_2 INFINITY) t_2 (+ (* c i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = ((a * b) + t_1) + (c * i);
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (z * t);
	double t_2 = ((a * b) + t_1) + (c * i);
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (c * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (z * t)
	t_2 = ((a * b) + t_1) + (c * i)
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = (c * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(z * t))
	t_2 = Float64(Float64(Float64(a * b) + t_1) + Float64(c * i))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(c * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (z * t);
	t_2 = ((a * b) + t_1) + (c * i);
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = (c * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a * b), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(c * i), $MachinePrecision] + t$95$1), $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 a around 0 66.7%

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

4. Final simplification 98.8%

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

Alternative 3: 42.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.4 \cdot 10^{+98}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.75 \cdot 10^{-183}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5.7 \cdot 10^{+76}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.4e+98)
   (* c i)
   (if (<= (* c i) -1.75e-183)
     (* z t)
     (if (<= (* c i) 0.0)
       (* a b)
       (if (<= (* c i) 2.05e-38)
         (* z t)
         (if (<= (* c i) 5.7e+76) (* a b) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.4e+98) {
		tmp = c * i;
	} else if ((c * i) <= -1.75e-183) {
		tmp = z * t;
	} else if ((c * i) <= 0.0) {
		tmp = a * b;
	} else if ((c * i) <= 2.05e-38) {
		tmp = z * t;
	} else if ((c * i) <= 5.7e+76) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-1.4d+98)) then
        tmp = c * i
    else if ((c * i) <= (-1.75d-183)) then
        tmp = z * t
    else if ((c * i) <= 0.0d0) then
        tmp = a * b
    else if ((c * i) <= 2.05d-38) then
        tmp = z * t
    else if ((c * i) <= 5.7d+76) then
        tmp = a * b
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.4e+98) {
		tmp = c * i;
	} else if ((c * i) <= -1.75e-183) {
		tmp = z * t;
	} else if ((c * i) <= 0.0) {
		tmp = a * b;
	} else if ((c * i) <= 2.05e-38) {
		tmp = z * t;
	} else if ((c * i) <= 5.7e+76) {
		tmp = a * b;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.4e+98:
		tmp = c * i
	elif (c * i) <= -1.75e-183:
		tmp = z * t
	elif (c * i) <= 0.0:
		tmp = a * b
	elif (c * i) <= 2.05e-38:
		tmp = z * t
	elif (c * i) <= 5.7e+76:
		tmp = a * b
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.4e+98)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.75e-183)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 0.0)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 2.05e-38)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 5.7e+76)
		tmp = Float64(a * b);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -1.4e+98)
		tmp = c * i;
	elseif ((c * i) <= -1.75e-183)
		tmp = z * t;
	elseif ((c * i) <= 0.0)
		tmp = a * b;
	elseif ((c * i) <= 2.05e-38)
		tmp = z * t;
	elseif ((c * i) <= 5.7e+76)
		tmp = a * b;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.4e+98], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.75e-183], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 0.0], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.05e-38], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 5.7e+76], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.4e98 or 5.70000000000000004e76 < (*.f64 c i)

   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 c around inf 74.4%

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

   if -1.4e98 < (*.f64 c i) < -1.74999999999999996e-183 or -0.0 < (*.f64 c i) < 2.0499999999999999e-38

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. fma-def 97.7%

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

      3. associate-+l+ 97.7%

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

      4. fma-def 98.9%

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

      5. fma-def 98.9%

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

   3. Simplified 98.9%

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

      1. fma-udef 97.7%

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

      2. fma-udef 97.7%

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

      3. associate-+l+ 97.7%

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

      4. +-commutative 97.7%

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

      5. associate-+r+ 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in z around inf 39.3%

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

   if -1.74999999999999996e-183 < (*.f64 c i) < -0.0 or 2.0499999999999999e-38 < (*.f64 c i) < 5.70000000000000004e76

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0 81.1%

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

   3. Taylor expanded in a around inf 46.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.4 \cdot 10^{+98}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.75 \cdot 10^{-183}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 0:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 5.7 \cdot 10^{+76}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 4: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -7.8 \cdot 10^{+29}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -7.5e+139)
   (* x y)
   (if (<= (* x y) -7.8e+29)
     (+ (* a b) (* z t))
     (if (<= (* x y) -8.2e+27)
       (* x y)
       (if (<= (* x y) 3e+140) (+ (* a b) (* c i)) (+ (* x y) (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -7.5e+139) {
		tmp = x * y;
	} else if ((x * y) <= -7.8e+29) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= -8.2e+27) {
		tmp = x * y;
	} else if ((x * y) <= 3e+140) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (x * y) + (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 ((x * y) <= (-7.5d+139)) then
        tmp = x * y
    else if ((x * y) <= (-7.8d+29)) then
        tmp = (a * b) + (z * t)
    else if ((x * y) <= (-8.2d+27)) then
        tmp = x * y
    else if ((x * y) <= 3d+140) then
        tmp = (a * b) + (c * i)
    else
        tmp = (x * y) + (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 ((x * y) <= -7.5e+139) {
		tmp = x * y;
	} else if ((x * y) <= -7.8e+29) {
		tmp = (a * b) + (z * t);
	} else if ((x * y) <= -8.2e+27) {
		tmp = x * y;
	} else if ((x * y) <= 3e+140) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -7.5e+139:
		tmp = x * y
	elif (x * y) <= -7.8e+29:
		tmp = (a * b) + (z * t)
	elif (x * y) <= -8.2e+27:
		tmp = x * y
	elif (x * y) <= 3e+140:
		tmp = (a * b) + (c * i)
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -7.5e+139)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -7.8e+29)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(x * y) <= -8.2e+27)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 3e+140)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -7.5e+139)
		tmp = x * y;
	elseif ((x * y) <= -7.8e+29)
		tmp = (a * b) + (z * t);
	elseif ((x * y) <= -8.2e+27)
		tmp = x * y;
	elseif ((x * y) <= 3e+140)
		tmp = (a * b) + (c * i);
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -7.5e+139], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -7.8e+29], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8.2e+27], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3e+140], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -7.49999999999999992e139 or -7.79999999999999937e29 < (*.f64 x y) < -8.2000000000000005e27

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 86.6%

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

   3. Taylor expanded in x around inf 82.6%

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

   if -7.49999999999999992e139 < (*.f64 x y) < -7.79999999999999937e29

   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 x around 0 90.5%

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

      1. *-commutative 90.5%

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

      2. fma-def 95.3%

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

      3. *-commutative 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in c around 0 76.8%

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

   if -8.2000000000000005e27 < (*.f64 x y) < 2.99999999999999997e140

   1. Initial program 98.7%

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

   2. Taylor expanded in a around inf 66.8%

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

   if 2.99999999999999997e140 < (*.f64 x y)

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 92.1%

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

   3. Taylor expanded in c around 0 85.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.5 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -7.8 \cdot 10^{+29}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -8.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+140}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]

Alternative 5: 64.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -33000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{-220}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))) (t_2 (+ (* c i) (* z t))))
   (if (<= (* c i) -33000000.0)
     t_2
     (if (<= (* c i) 9.5e-300)
       t_1
       (if (<= (* c i) 7e-220)
         (+ (* a b) (* z t))
         (if (<= (* c i) 8.5e+138) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -33000000.0) {
		tmp = t_2;
	} else if ((c * i) <= 9.5e-300) {
		tmp = t_1;
	} else if ((c * i) <= 7e-220) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 8.5e+138) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) + (a * b)
    t_2 = (c * i) + (z * t)
    if ((c * i) <= (-33000000.0d0)) then
        tmp = t_2
    else if ((c * i) <= 9.5d-300) then
        tmp = t_1
    else if ((c * i) <= 7d-220) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 8.5d+138) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -33000000.0) {
		tmp = t_2;
	} else if ((c * i) <= 9.5e-300) {
		tmp = t_1;
	} else if ((c * i) <= 7e-220) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 8.5e+138) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (a * b)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -33000000.0:
		tmp = t_2
	elif (c * i) <= 9.5e-300:
		tmp = t_1
	elif (c * i) <= 7e-220:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 8.5e+138:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(a * b))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -33000000.0)
		tmp = t_2;
	elseif (Float64(c * i) <= 9.5e-300)
		tmp = t_1;
	elseif (Float64(c * i) <= 7e-220)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 8.5e+138)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (a * b);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -33000000.0)
		tmp = t_2;
	elseif ((c * i) <= 9.5e-300)
		tmp = t_1;
	elseif ((c * i) <= 7e-220)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 8.5e+138)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -33000000.0], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 9.5e-300], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 7e-220], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.5e+138], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.3e7 or 8.5000000000000006e138 < (*.f64 c i)

   1. Initial program 95.0%

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

   2. Taylor expanded in z around inf 83.9%

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

   if -3.3e7 < (*.f64 c i) < 9.5000000000000007e-300 or 6.99999999999999975e-220 < (*.f64 c i) < 8.5000000000000006e138

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0 75.9%

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

   3. Taylor expanded in c around 0 70.3%

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

   if 9.5000000000000007e-300 < (*.f64 c i) < 6.99999999999999975e-220

   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 92.8%

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

      1. *-commutative 92.8%

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

      2. fma-def 92.8%

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

      3. *-commutative 92.8%

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

   4. Applied egg-rr 92.8%

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

   5. Taylor expanded in c around 0 80.1%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -33000000:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{-300}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 7 \cdot 10^{-220}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{+138}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 6: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ \mathbf{if}\;c \cdot i \leq -33000000:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{-220}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))))
   (if (<= (* c i) -33000000.0)
     (+ (* c i) (* z t))
     (if (<= (* c i) 8.5e-300)
       t_1
       (if (<= (* c i) 1.05e-220)
         (+ (* a b) (* z t))
         (if (<= (* c i) 2.7e+75) t_1 (+ (* x y) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double tmp;
	if ((c * i) <= -33000000.0) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 8.5e-300) {
		tmp = t_1;
	} else if ((c * i) <= 1.05e-220) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 2.7e+75) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) + (a * b)
    if ((c * i) <= (-33000000.0d0)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 8.5d-300) then
        tmp = t_1
    else if ((c * i) <= 1.05d-220) then
        tmp = (a * b) + (z * t)
    else if ((c * i) <= 2.7d+75) then
        tmp = t_1
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * y) + (a * b);
	double tmp;
	if ((c * i) <= -33000000.0) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 8.5e-300) {
		tmp = t_1;
	} else if ((c * i) <= 1.05e-220) {
		tmp = (a * b) + (z * t);
	} else if ((c * i) <= 2.7e+75) {
		tmp = t_1;
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (a * b)
	tmp = 0
	if (c * i) <= -33000000.0:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 8.5e-300:
		tmp = t_1
	elif (c * i) <= 1.05e-220:
		tmp = (a * b) + (z * t)
	elif (c * i) <= 2.7e+75:
		tmp = t_1
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(c * i) <= -33000000.0)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 8.5e-300)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.05e-220)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (Float64(c * i) <= 2.7e+75)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * y) + (a * b);
	tmp = 0.0;
	if ((c * i) <= -33000000.0)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 8.5e-300)
		tmp = t_1;
	elseif ((c * i) <= 1.05e-220)
		tmp = (a * b) + (z * t);
	elseif ((c * i) <= 2.7e+75)
		tmp = t_1;
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -33000000.0], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.5e-300], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.05e-220], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.7e+75], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -3.3e7

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 82.2%

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

   if -3.3e7 < (*.f64 c i) < 8.4999999999999995e-300 or 1.04999999999999996e-220 < (*.f64 c i) < 2.69999999999999998e75

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 75.7%

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

   3. Taylor expanded in c around 0 71.6%

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

   if 8.4999999999999995e-300 < (*.f64 c i) < 1.04999999999999996e-220

   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 92.8%

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

      1. *-commutative 92.8%

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

      2. fma-def 92.8%

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

      3. *-commutative 92.8%

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

   4. Applied egg-rr 92.8%

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

   5. Taylor expanded in c around 0 80.1%

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

   if 2.69999999999999998e75 < (*.f64 c i)

   1. Initial program 93.5%

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

   2. Taylor expanded in x around inf 85.2%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -33000000:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.5 \cdot 10^{-300}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 1.05 \cdot 10^{-220}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 2.7 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]

Alternative 7: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.8 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+140}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -6.8e+139)
   (+ (* x y) (* c i))
   (if (<= (* x y) 2.5e+140)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* x y) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -6.8e+139) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 2.5e+140) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (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 ((x * y) <= (-6.8d+139)) then
        tmp = (x * y) + (c * i)
    else if ((x * y) <= 2.5d+140) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (x * y) + (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 ((x * y) <= -6.8e+139) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 2.5e+140) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -6.8e+139:
		tmp = (x * y) + (c * i)
	elif (x * y) <= 2.5e+140:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -6.8e+139)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(x * y) <= 2.5e+140)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -6.8e+139)
		tmp = (x * y) + (c * i);
	elseif ((x * y) <= 2.5e+140)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (x * y) + (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -6.8e+139], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+140], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.8000000000000005e139

   1. Initial program 92.7%

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

   2. Taylor expanded in x around inf 92.8%

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

   if -6.8000000000000005e139 < (*.f64 x y) < 2.50000000000000004e140

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 90.5%

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

   if 2.50000000000000004e140 < (*.f64 x y)

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 92.1%

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

   3. Taylor expanded in c around 0 85.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.8 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+140}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]

Alternative 8: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+139}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -1.75e+139)
   (+ (* x y) (* c i))
   (if (<= (* x y) 7.5e+139)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* c i) (+ (* x y) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -1.75e+139) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 7.5e+139) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (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 ((x * y) <= (-1.75d+139)) then
        tmp = (x * y) + (c * i)
    else if ((x * y) <= 7.5d+139) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((x * y) + (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 ((x * y) <= -1.75e+139) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 7.5e+139) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -1.75e+139:
		tmp = (x * y) + (c * i)
	elif (x * y) <= 7.5e+139:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((x * y) + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -1.75e+139)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(x * y) <= 7.5e+139)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -1.75e+139)
		tmp = (x * y) + (c * i);
	elseif ((x * y) <= 7.5e+139)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((x * y) + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.75e+139], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.5e+139], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.74999999999999989e139

   1. Initial program 92.7%

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

   2. Taylor expanded in x around inf 92.8%

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

   if -1.74999999999999989e139 < (*.f64 x y) < 7.49999999999999992e139

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 90.5%

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

   if 7.49999999999999992e139 < (*.f64 x y)

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 92.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.75 \cdot 10^{+139}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+139}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \end{array} \]

Alternative 9: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.1 \cdot 10^{+138}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+139}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -4.1e+138)
   (+ (* c i) (+ (* x y) (* z t)))
   (if (<= (* x y) 6.8e+139)
     (+ (* c i) (+ (* a b) (* z t)))
     (+ (* c i) (+ (* x y) (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -4.1e+138) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else if ((x * y) <= 6.8e+139) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (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 ((x * y) <= (-4.1d+138)) then
        tmp = (c * i) + ((x * y) + (z * t))
    else if ((x * y) <= 6.8d+139) then
        tmp = (c * i) + ((a * b) + (z * t))
    else
        tmp = (c * i) + ((x * y) + (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 ((x * y) <= -4.1e+138) {
		tmp = (c * i) + ((x * y) + (z * t));
	} else if ((x * y) <= 6.8e+139) {
		tmp = (c * i) + ((a * b) + (z * t));
	} else {
		tmp = (c * i) + ((x * y) + (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -4.1e+138:
		tmp = (c * i) + ((x * y) + (z * t))
	elif (x * y) <= 6.8e+139:
		tmp = (c * i) + ((a * b) + (z * t))
	else:
		tmp = (c * i) + ((x * y) + (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -4.1e+138)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(z * t)));
	elseif (Float64(x * y) <= 6.8e+139)
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -4.1e+138)
		tmp = (c * i) + ((x * y) + (z * t));
	elseif ((x * y) <= 6.8e+139)
		tmp = (c * i) + ((a * b) + (z * t));
	else
		tmp = (c * i) + ((x * y) + (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -4.1e+138], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.8e+139], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0999999999999998e138

   1. Initial program 92.7%

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

   2. Taylor expanded in a around 0 100.0%

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

   if -4.0999999999999998e138 < (*.f64 x y) < 6.8000000000000005e139

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 90.5%

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

   if 6.8000000000000005e139 < (*.f64 x y)

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 92.1%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.1 \cdot 10^{+138}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+139}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \end{array} \]

Alternative 10: 42.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+138}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.9 \cdot 10^{+46}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+131}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -3.8e+138)
   (* x y)
   (if (<= (* x y) -5.9e+46)
     (* a b)
     (if (<= (* x y) 3.4e+131) (* c i) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -3.8e+138) {
		tmp = x * y;
	} else if ((x * y) <= -5.9e+46) {
		tmp = a * b;
	} else if ((x * y) <= 3.4e+131) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x * y) <= (-3.8d+138)) then
        tmp = x * y
    else if ((x * y) <= (-5.9d+46)) then
        tmp = a * b
    else if ((x * y) <= 3.4d+131) then
        tmp = c * i
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x * y) <= -3.8e+138) {
		tmp = x * y;
	} else if ((x * y) <= -5.9e+46) {
		tmp = a * b;
	} else if ((x * y) <= 3.4e+131) {
		tmp = c * i;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -3.8e+138:
		tmp = x * y
	elif (x * y) <= -5.9e+46:
		tmp = a * b
	elif (x * y) <= 3.4e+131:
		tmp = c * i
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(x * y) <= -3.8e+138)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.9e+46)
		tmp = Float64(a * b);
	elseif (Float64(x * y) <= 3.4e+131)
		tmp = Float64(c * i);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x * y) <= -3.8e+138)
		tmp = x * y;
	elseif ((x * y) <= -5.9e+46)
		tmp = a * b;
	elseif ((x * y) <= 3.4e+131)
		tmp = c * i;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.8e+138], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.9e+46], N[(a * b), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.4e+131], N[(c * i), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.80000000000000012e138 or 3.39999999999999986e131 < (*.f64 x y)

   1. Initial program 92.6%

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

   2. Taylor expanded in z around 0 87.7%

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

   3. Taylor expanded in x around inf 73.9%

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

   if -3.80000000000000012e138 < (*.f64 x y) < -5.8999999999999999e46

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 67.6%

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

   3. Taylor expanded in a around inf 54.0%

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

   if -5.8999999999999999e46 < (*.f64 x y) < 3.39999999999999986e131

   1. Initial program 98.7%

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

   2. Taylor expanded in c around inf 42.9%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+138}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.9 \cdot 10^{+46}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+131}:\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 11: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.04 \cdot 10^{+139} \lor \neg \left(x \cdot y \leq 3.6 \cdot 10^{+141}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* x y) -1.04e+139) (not (<= (* x y) 3.6e+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) <= -1.04e+139) || !((x * y) <= 3.6e+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) <= (-1.04d+139)) .or. (.not. ((x * y) <= 3.6d+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) <= -1.04e+139) || !((x * y) <= 3.6e+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) <= -1.04e+139) or not ((x * y) <= 3.6e+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) <= -1.04e+139) || !(Float64(x * y) <= 3.6e+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) <= -1.04e+139) || ~(((x * y) <= 3.6e+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], -1.04e+139], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.6e+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) < -1.04e139 or 3.6000000000000001e141 < (*.f64 x y)

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 88.7%

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

   3. Taylor expanded in x around inf 75.8%

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

   if -1.04e139 < (*.f64 x y) < 3.6000000000000001e141

   1. Initial program 98.3%

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

   2. Taylor expanded in a around inf 65.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.04 \cdot 10^{+139} \lor \neg \left(x \cdot y \leq 3.6 \cdot 10^{+141}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 12: 41.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -950000 \lor \neg \left(c \cdot i \leq 9.5 \cdot 10^{+75}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* c i) -950000.0) (not (<= (* c i) 9.5e+75))) (* c i) (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -950000.0) || !((c * i) <= 9.5e+75)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((c * i) <= (-950000.0d0)) .or. (.not. ((c * i) <= 9.5d+75))) then
        tmp = c * i
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((c * i) <= -950000.0) || !((c * i) <= 9.5e+75)) {
		tmp = c * i;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((c * i) <= -950000.0) or not ((c * i) <= 9.5e+75):
		tmp = c * i
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(c * i) <= -950000.0) || !(Float64(c * i) <= 9.5e+75))
		tmp = Float64(c * i);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((c * i) <= -950000.0) || ~(((c * i) <= 9.5e+75)))
		tmp = c * i;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(c * i), $MachinePrecision], -950000.0], N[Not[LessEqual[N[(c * i), $MachinePrecision], 9.5e+75]], $MachinePrecision]], N[(c * i), $MachinePrecision], N[(a * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -9.5e5 or 9.50000000000000061e75 < (*.f64 c i)

   1. Initial program 95.5%

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

   2. Taylor expanded in c around inf 66.9%

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

   if -9.5e5 < (*.f64 c i) < 9.50000000000000061e75

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 73.4%

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

   3. Taylor expanded in a around inf 34.0%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -950000 \lor \neg \left(c \cdot i \leq 9.5 \cdot 10^{+75}\right):\\ \;\;\;\;c \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 13: 27.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

2. Taylor expanded in z around 0 78.0%

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

3. Taylor expanded in a around inf 24.1%

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

4. Final simplification 24.1%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023318 
(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)))