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

Percentage Accurate: 95.5% → 97.7%

Time: 8.4s

Alternatives: 12

Speedup: 0.5×

• 41.2% 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: 95.5% 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: 97.7% 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 96.1%

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

   1. +-commutative 96.1%

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

   2. associate-+l+ 96.1%

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

   3. fma-def 97.3%

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

   4. associate-+l+ 97.3%

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

   5. fma-def 98.0%

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

   6. +-commutative 98.0%

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

   7. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 97.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l+ 0.0%

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

      2. +-commutative 0.0%

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

      3. associate-+l+ 0.0%

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

      4. fma-def 20.0%

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

      5. associate-+r+ 20.0%

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

      6. +-commutative 20.0%

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

      7. fma-def 40.0%

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

      8. fma-def 40.0%

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

   3. Simplified 40.0%

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

   4. Taylor expanded in x around 0 30.0%

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

   5. Taylor expanded in a around 0 40.0%

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

      1. +-commutative 40.0%

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

      2. *-commutative 40.0%

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

      3. fma-udef 50.0%

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

   7. Simplified 50.0%

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

4. Final simplification 98.0%

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

Alternative 3: 65.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ t_2 := z \cdot t + c \cdot i\\ t_3 := a \cdot b + c \cdot i\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b)))
        (t_2 (+ (* z t) (* c i)))
        (t_3 (+ (* a b) (* c i))))
   (if (<= (* z t) -1e+179)
     t_2
     (if (<= (* z t) -5e+40)
       t_1
       (if (<= (* z t) -1e-44)
         t_3
         (if (<= (* z t) -1e-108)
           t_1
           (if (<= (* z t) -1e-180) t_3 (if (<= (* z t) 2e+23) 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 = (z * t) + (c * i);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((z * t) <= -1e+179) {
		tmp = t_2;
	} else if ((z * t) <= -5e+40) {
		tmp = t_1;
	} else if ((z * t) <= -1e-44) {
		tmp = t_3;
	} else if ((z * t) <= -1e-108) {
		tmp = t_1;
	} else if ((z * t) <= -1e-180) {
		tmp = t_3;
	} else if ((z * t) <= 2e+23) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (x * y) + (a * b)
    t_2 = (z * t) + (c * i)
    t_3 = (a * b) + (c * i)
    if ((z * t) <= (-1d+179)) then
        tmp = t_2
    else if ((z * t) <= (-5d+40)) then
        tmp = t_1
    else if ((z * t) <= (-1d-44)) then
        tmp = t_3
    else if ((z * t) <= (-1d-108)) then
        tmp = t_1
    else if ((z * t) <= (-1d-180)) then
        tmp = t_3
    else if ((z * t) <= 2d+23) 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 = (z * t) + (c * i);
	double t_3 = (a * b) + (c * i);
	double tmp;
	if ((z * t) <= -1e+179) {
		tmp = t_2;
	} else if ((z * t) <= -5e+40) {
		tmp = t_1;
	} else if ((z * t) <= -1e-44) {
		tmp = t_3;
	} else if ((z * t) <= -1e-108) {
		tmp = t_1;
	} else if ((z * t) <= -1e-180) {
		tmp = t_3;
	} else if ((z * t) <= 2e+23) {
		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 = (z * t) + (c * i)
	t_3 = (a * b) + (c * i)
	tmp = 0
	if (z * t) <= -1e+179:
		tmp = t_2
	elif (z * t) <= -5e+40:
		tmp = t_1
	elif (z * t) <= -1e-44:
		tmp = t_3
	elif (z * t) <= -1e-108:
		tmp = t_1
	elif (z * t) <= -1e-180:
		tmp = t_3
	elif (z * t) <= 2e+23:
		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(z * t) + Float64(c * i))
	t_3 = Float64(Float64(a * b) + Float64(c * i))
	tmp = 0.0
	if (Float64(z * t) <= -1e+179)
		tmp = t_2;
	elseif (Float64(z * t) <= -5e+40)
		tmp = t_1;
	elseif (Float64(z * t) <= -1e-44)
		tmp = t_3;
	elseif (Float64(z * t) <= -1e-108)
		tmp = t_1;
	elseif (Float64(z * t) <= -1e-180)
		tmp = t_3;
	elseif (Float64(z * t) <= 2e+23)
		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 = (z * t) + (c * i);
	t_3 = (a * b) + (c * i);
	tmp = 0.0;
	if ((z * t) <= -1e+179)
		tmp = t_2;
	elseif ((z * t) <= -5e+40)
		tmp = t_1;
	elseif ((z * t) <= -1e-44)
		tmp = t_3;
	elseif ((z * t) <= -1e-108)
		tmp = t_1;
	elseif ((z * t) <= -1e-180)
		tmp = t_3;
	elseif ((z * t) <= 2e+23)
		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[(z * t), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+179], t$95$2, If[LessEqual[N[(z * t), $MachinePrecision], -5e+40], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -1e-44], t$95$3, If[LessEqual[N[(z * t), $MachinePrecision], -1e-108], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -1e-180], t$95$3, If[LessEqual[N[(z * t), $MachinePrecision], 2e+23], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -9.9999999999999998e178 or 1.9999999999999998e23 < (*.f64 z t)

   1. Initial program 91.6%

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

      1. associate-+l+ 91.6%

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

      2. +-commutative 91.6%

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

      3. associate-+l+ 91.6%

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

      4. fma-def 93.7%

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

      5. associate-+r+ 93.7%

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

      6. +-commutative 93.7%

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

      7. fma-def 95.8%

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

      8. fma-def 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around 0 84.3%

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

   5. Taylor expanded in a around 0 77.3%

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

   if -9.9999999999999998e178 < (*.f64 z t) < -5.00000000000000003e40 or -9.99999999999999953e-45 < (*.f64 z t) < -1.00000000000000004e-108 or -1e-180 < (*.f64 z t) < 1.9999999999999998e23

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. associate-+l+ 98.4%

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

      3. fma-def 99.2%

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

      4. associate-+l+ 99.2%

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

      5. fma-def 100.0%

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

      6. +-commutative 100.0%

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

      7. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 93.2%

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

   5. Taylor expanded in c around 0 75.4%

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

   if -5.00000000000000003e40 < (*.f64 z t) < -9.99999999999999953e-45 or -1.00000000000000004e-108 < (*.f64 z t) < -1e-180

   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. Taylor expanded in x around 0 88.8%

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

   5. Taylor expanded in z around 0 85.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+179}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+40}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-44}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-108}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-180}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+23}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;z \cdot t + c \cdot i\\ \end{array} \]

Alternative 4: 96.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x * y), $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 40.9%

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

4. Final simplification 97.7%

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

Alternative 5: 59.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -3.1 \cdot 10^{-19} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -7e+97)
   (* x y)
   (if (<= (* x y) -1.7e-10)
     (* z t)
     (if (or (<= (* x y) -3.1e-19) (not (<= (* x y) 1.35e+138)))
       (* 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) <= -7e+97) {
		tmp = x * y;
	} else if ((x * y) <= -1.7e-10) {
		tmp = z * t;
	} else if (((x * y) <= -3.1e-19) || !((x * y) <= 1.35e+138)) {
		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) <= (-7d+97)) then
        tmp = x * y
    else if ((x * y) <= (-1.7d-10)) then
        tmp = z * t
    else if (((x * y) <= (-3.1d-19)) .or. (.not. ((x * y) <= 1.35d+138))) 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) <= -7e+97) {
		tmp = x * y;
	} else if ((x * y) <= -1.7e-10) {
		tmp = z * t;
	} else if (((x * y) <= -3.1e-19) || !((x * y) <= 1.35e+138)) {
		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) <= -7e+97:
		tmp = x * y
	elif (x * y) <= -1.7e-10:
		tmp = z * t
	elif ((x * y) <= -3.1e-19) or not ((x * y) <= 1.35e+138):
		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) <= -7e+97)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.7e-10)
		tmp = Float64(z * t);
	elseif ((Float64(x * y) <= -3.1e-19) || !(Float64(x * y) <= 1.35e+138))
		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) <= -7e+97)
		tmp = x * y;
	elseif ((x * y) <= -1.7e-10)
		tmp = z * t;
	elseif (((x * y) <= -3.1e-19) || ~(((x * y) <= 1.35e+138)))
		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[LessEqual[N[(x * y), $MachinePrecision], -7e+97], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.7e-10], N[(z * t), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.1e-19], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.35e+138]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.0000000000000001e97 or -1.70000000000000007e-10 < (*.f64 x y) < -3.0999999999999999e-19 or 1.35000000000000004e138 < (*.f64 x y)

   1. Initial program 92.5%

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

   2. Taylor expanded in x around inf 73.1%

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

   if -7.0000000000000001e97 < (*.f64 x y) < -1.70000000000000007e-10

   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 inf 61.2%

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

   if -3.0999999999999999e-19 < (*.f64 x y) < 1.35000000000000004e138

   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 98.2%

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

      5. associate-+r+ 98.2%

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

      6. +-commutative 98.2%

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

      7. fma-def 98.8%

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

      8. fma-def 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around 0 91.9%

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

   5. Taylor expanded in z around 0 62.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -3.1 \cdot 10^{-19} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 6: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + a \cdot b\\ \mathbf{if}\;x \cdot y \leq -7.1 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -8 \cdot 10^{-34} \lor \neg \left(x \cdot y \leq 1.9 \cdot 10^{+61}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* a b))))
   (if (<= (* x y) -7.1e+33)
     t_1
     (if (<= (* x y) -3.3e-9)
       (* z t)
       (if (or (<= (* x y) -8e-34) (not (<= (* x y) 1.9e+61)))
         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 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -7.1e+33) {
		tmp = t_1;
	} else if ((x * y) <= -3.3e-9) {
		tmp = z * t;
	} else if (((x * y) <= -8e-34) || !((x * y) <= 1.9e+61)) {
		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) :: tmp
    t_1 = (x * y) + (a * b)
    if ((x * y) <= (-7.1d+33)) then
        tmp = t_1
    else if ((x * y) <= (-3.3d-9)) then
        tmp = z * t
    else if (((x * y) <= (-8d-34)) .or. (.not. ((x * y) <= 1.9d+61))) 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 = (x * y) + (a * b);
	double tmp;
	if ((x * y) <= -7.1e+33) {
		tmp = t_1;
	} else if ((x * y) <= -3.3e-9) {
		tmp = z * t;
	} else if (((x * y) <= -8e-34) || !((x * y) <= 1.9e+61)) {
		tmp = t_1;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * y) + (a * b)
	tmp = 0
	if (x * y) <= -7.1e+33:
		tmp = t_1
	elif (x * y) <= -3.3e-9:
		tmp = z * t
	elif ((x * y) <= -8e-34) or not ((x * y) <= 1.9e+61):
		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(x * y) + Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -7.1e+33)
		tmp = t_1;
	elseif (Float64(x * y) <= -3.3e-9)
		tmp = Float64(z * t);
	elseif ((Float64(x * y) <= -8e-34) || !(Float64(x * y) <= 1.9e+61))
		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 = (x * y) + (a * b);
	tmp = 0.0;
	if ((x * y) <= -7.1e+33)
		tmp = t_1;
	elseif ((x * y) <= -3.3e-9)
		tmp = z * t;
	elseif (((x * y) <= -8e-34) || ~(((x * y) <= 1.9e+61)))
		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[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7.1e+33], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -3.3e-9], N[(z * t), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -8e-34], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.9e+61]], $MachinePrecision]], t$95$1, N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.09999999999999979e33 or -3.30000000000000018e-9 < (*.f64 x y) < -7.99999999999999942e-34 or 1.89999999999999998e61 < (*.f64 x y)

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-+l+ 93.3%

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

      3. fma-def 95.2%

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

      4. associate-+l+ 95.2%

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

      5. fma-def 97.1%

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

      6. +-commutative 97.1%

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

      7. fma-def 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in z around 0 83.8%

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

   5. Taylor expanded in c around 0 73.7%

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

   if -7.09999999999999979e33 < (*.f64 x y) < -3.30000000000000018e-9

   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 inf 75.6%

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

   if -7.99999999999999942e-34 < (*.f64 x y) < 1.89999999999999998e61

   1. Initial program 97.9%

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

      1. associate-+l+ 97.9%

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

      2. +-commutative 97.9%

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

      3. associate-+l+ 97.9%

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

      4. fma-def 97.9%

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

      5. associate-+r+ 97.9%

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

      6. +-commutative 97.9%

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

      7. fma-def 98.6%

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

      8. fma-def 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around 0 95.3%

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

   5. Taylor expanded in z around 0 65.8%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.1 \cdot 10^{+33}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;x \cdot y \leq -8 \cdot 10^{-34} \lor \neg \left(x \cdot y \leq 1.9 \cdot 10^{+61}\right):\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 7: 44.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.62 \cdot 10^{+31}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 95000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8.2 \cdot 10^{+138}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -1.62e+31)
   (* a b)
   (if (<= (* a b) 0.0)
     (* x y)
     (if (<= (* a b) 95000000000.0)
       (* z t)
       (if (<= (* a b) 8.2e+138) (* 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 ((a * b) <= -1.62e+31) {
		tmp = a * b;
	} else if ((a * b) <= 0.0) {
		tmp = x * y;
	} else if ((a * b) <= 95000000000.0) {
		tmp = z * t;
	} else if ((a * b) <= 8.2e+138) {
		tmp = x * y;
	} 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) <= (-1.62d+31)) then
        tmp = a * b
    else if ((a * b) <= 0.0d0) then
        tmp = x * y
    else if ((a * b) <= 95000000000.0d0) then
        tmp = z * t
    else if ((a * b) <= 8.2d+138) then
        tmp = x * y
    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) <= -1.62e+31) {
		tmp = a * b;
	} else if ((a * b) <= 0.0) {
		tmp = x * y;
	} else if ((a * b) <= 95000000000.0) {
		tmp = z * t;
	} else if ((a * b) <= 8.2e+138) {
		tmp = x * y;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -1.62e+31:
		tmp = a * b
	elif (a * b) <= 0.0:
		tmp = x * y
	elif (a * b) <= 95000000000.0:
		tmp = z * t
	elif (a * b) <= 8.2e+138:
		tmp = x * y
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -1.62e+31)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 0.0)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 95000000000.0)
		tmp = Float64(z * t);
	elseif (Float64(a * b) <= 8.2e+138)
		tmp = Float64(x * y);
	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) <= -1.62e+31)
		tmp = a * b;
	elseif ((a * b) <= 0.0)
		tmp = x * y;
	elseif ((a * b) <= 95000000000.0)
		tmp = z * t;
	elseif ((a * b) <= 8.2e+138)
		tmp = x * y;
	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], -1.62e+31], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 0.0], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 95000000000.0], N[(z * t), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 8.2e+138], N[(x * y), $MachinePrecision], N[(a * b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.6199999999999999e31 or 8.19999999999999961e138 < (*.f64 a b)

   1. Initial program 92.5%

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

   2. Taylor expanded in a around inf 60.5%

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

   if -1.6199999999999999e31 < (*.f64 a b) < -0.0 or 9.5e10 < (*.f64 a b) < 8.19999999999999961e138

   1. Initial program 98.9%

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

   2. Taylor expanded in x around inf 41.3%

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

   if -0.0 < (*.f64 a b) < 9.5e10

   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 inf 48.6%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.62 \cdot 10^{+31}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 95000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 8.2 \cdot 10^{+138}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 8: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+96}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{+123}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* x y) -2.7e+96)
   (+ (* x y) (* c i))
   (if (<= (* x y) 1.65e+123)
     (+ (* c i) (+ (* z t) (* a b)))
     (+ (* 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) <= -2.7e+96) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 1.65e+123) {
		tmp = (c * i) + ((z * t) + (a * b));
	} 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) <= (-2.7d+96)) then
        tmp = (x * y) + (c * i)
    else if ((x * y) <= 1.65d+123) then
        tmp = (c * i) + ((z * t) + (a * b))
    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) <= -2.7e+96) {
		tmp = (x * y) + (c * i);
	} else if ((x * y) <= 1.65e+123) {
		tmp = (c * i) + ((z * t) + (a * b));
	} else {
		tmp = (x * y) + (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x * y) <= -2.7e+96:
		tmp = (x * y) + (c * i)
	elif (x * y) <= 1.65e+123:
		tmp = (c * i) + ((z * t) + (a * b))
	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) <= -2.7e+96)
		tmp = Float64(Float64(x * y) + Float64(c * i));
	elseif (Float64(x * y) <= 1.65e+123)
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(a * b)));
	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) <= -2.7e+96)
		tmp = (x * y) + (c * i);
	elseif ((x * y) <= 1.65e+123)
		tmp = (c * i) + ((z * t) + (a * b));
	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], -2.7e+96], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.65e+123], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(a * b), $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) < -2.70000000000000022e96

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-+l+ 92.5%

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

      3. fma-def 95.0%

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

      4. associate-+l+ 95.0%

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

      5. fma-def 97.5%

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

      6. +-commutative 97.5%

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

      7. fma-def 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 87.8%

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

   5. Taylor expanded in a around 0 83.0%

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

   if -2.70000000000000022e96 < (*.f64 x y) < 1.65000000000000001e123

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 91.1%

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

   if 1.65000000000000001e123 < (*.f64 x y)

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-+l+ 93.0%

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

      3. fma-def 95.3%

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

      4. associate-+l+ 95.3%

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

      5. fma-def 97.7%

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

      6. +-commutative 97.7%

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

      7. fma-def 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around 0 86.1%

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

   5. Taylor expanded in c around 0 79.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.7 \cdot 10^{+96}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \mathbf{elif}\;x \cdot y \leq 1.65 \cdot 10^{+123}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \end{array} \]

Alternative 9: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+133}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+240}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* z t) -5e+133)
   (+ (* c i) (+ (* z t) (* a b)))
   (if (<= (* z t) 4e+240) (+ (* c i) (+ (* 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) {
	double tmp;
	if ((z * t) <= -5e+133) {
		tmp = (c * i) + ((z * t) + (a * b));
	} else if ((z * t) <= 4e+240) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else {
		tmp = 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) <= (-5d+133)) then
        tmp = (c * i) + ((z * t) + (a * b))
    else if ((z * t) <= 4d+240) then
        tmp = (c * i) + ((x * y) + (a * b))
    else
        tmp = 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) <= -5e+133) {
		tmp = (c * i) + ((z * t) + (a * b));
	} else if ((z * t) <= 4e+240) {
		tmp = (c * i) + ((x * y) + (a * b));
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z * t) <= -5e+133:
		tmp = (c * i) + ((z * t) + (a * b))
	elif (z * t) <= 4e+240:
		tmp = (c * i) + ((x * y) + (a * b))
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(z * t) <= -5e+133)
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(a * b)));
	elseif (Float64(z * t) <= 4e+240)
		tmp = Float64(Float64(c * i) + Float64(Float64(x * y) + Float64(a * b)));
	else
		tmp = 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) <= -5e+133)
		tmp = (c * i) + ((z * t) + (a * b));
	elseif ((z * t) <= 4e+240)
		tmp = (c * i) + ((x * y) + (a * b));
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e+133], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 4e+240], N[(N[(c * i), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.99999999999999961e133

   1. Initial program 95.7%

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

   2. Taylor expanded in x around 0 87.4%

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

   if -4.99999999999999961e133 < (*.f64 z t) < 4.00000000000000006e240

   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 z around 0 91.8%

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

   if 4.00000000000000006e240 < (*.f64 z t)

   1. Initial program 81.0%

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

   2. Taylor expanded in z around inf 91.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+133}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + a \cdot b\right)\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+240}:\\ \;\;\;\;c \cdot i + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 10: 44.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+62}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 80000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* a b) -4e+62)
   (* a b)
   (if (<= (* a b) 0.0)
     (* c i)
     (if (<= (* a b) 80000000000.0) (* z t) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -4e+62) {
		tmp = a * b;
	} else if ((a * b) <= 0.0) {
		tmp = c * i;
	} else if ((a * b) <= 80000000000.0) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a * b) <= (-4d+62)) then
        tmp = a * b
    else if ((a * b) <= 0.0d0) then
        tmp = c * i
    else if ((a * b) <= 80000000000.0d0) then
        tmp = z * t
    else
        tmp = a * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a * b) <= -4e+62) {
		tmp = a * b;
	} else if ((a * b) <= 0.0) {
		tmp = c * i;
	} else if ((a * b) <= 80000000000.0) {
		tmp = z * t;
	} else {
		tmp = a * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a * b) <= -4e+62:
		tmp = a * b
	elif (a * b) <= 0.0:
		tmp = c * i
	elif (a * b) <= 80000000000.0:
		tmp = z * t
	else:
		tmp = a * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(a * b) <= -4e+62)
		tmp = Float64(a * b);
	elseif (Float64(a * b) <= 0.0)
		tmp = Float64(c * i);
	elseif (Float64(a * b) <= 80000000000.0)
		tmp = Float64(z * t);
	else
		tmp = Float64(a * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a * b) <= -4e+62)
		tmp = a * b;
	elseif ((a * b) <= 0.0)
		tmp = c * i;
	elseif ((a * b) <= 80000000000.0)
		tmp = z * t;
	else
		tmp = a * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(a * b), $MachinePrecision], -4e+62], N[(a * b), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 0.0], N[(c * i), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 80000000000.0], N[(z * t), $MachinePrecision], N[(a * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.00000000000000014e62 or 8e10 < (*.f64 a b)

   1. Initial program 93.2%

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

   2. Taylor expanded in a around inf 56.9%

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

   if -4.00000000000000014e62 < (*.f64 a b) < -0.0

   1. Initial program 98.8%

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

   2. Taylor expanded in c around inf 37.2%

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

   if -0.0 < (*.f64 a b) < 8e10

   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 inf 48.6%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+62}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;a \cdot b \leq 0:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 80000000000:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b\\ \end{array} \]

Alternative 11: 43.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.25 \cdot 10^{+63} \lor \neg \left(a \cdot b \leq 1.8 \cdot 10^{+35}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* a b) -1.25e+63) (not (<= (* a b) 1.8e+35))) (* 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) <= -1.25e+63) || !((a * b) <= 1.8e+35)) {
		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) <= (-1.25d+63)) .or. (.not. ((a * b) <= 1.8d+35))) 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) <= -1.25e+63) || !((a * b) <= 1.8e+35)) {
		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) <= -1.25e+63) or not ((a * b) <= 1.8e+35):
		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) <= -1.25e+63) || !(Float64(a * b) <= 1.8e+35))
		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) <= -1.25e+63) || ~(((a * b) <= 1.8e+35)))
		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], -1.25e+63], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1.8e+35]], $MachinePrecision]], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.25000000000000003e63 or 1.8e35 < (*.f64 a b)

   1. Initial program 93.1%

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

   2. Taylor expanded in a around inf 57.9%

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

   if -1.25000000000000003e63 < (*.f64 a b) < 1.8e35

   1. Initial program 98.0%

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

   2. Taylor expanded in c around inf 31.9%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.25 \cdot 10^{+63} \lor \neg \left(a \cdot b \leq 1.8 \cdot 10^{+35}\right):\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 12: 28.4% 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 96.1%

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

2. Taylor expanded in a around inf 27.3%

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

3. Final simplification 27.3%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023302 
(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)))