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

Percentage Accurate: 95.5% → 97.4%

Time: 8.7s

Alternatives: 15

Speedup: 0.5×

• 41.0% 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: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. fma-def 99.6%

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

      3. associate-+l+ 99.6%

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

      4. fma-def 99.6%

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

      5. fma-def 99.6%

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

   3. Simplified 99.6%

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

      1. fma-udef 99.6%

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

      2. fma-udef 99.6%

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

      3. associate-+l+ 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+r+ 99.6%

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

   5. Applied egg-rr 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around 0 42.9%

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

   3. Taylor expanded in y around 0 71.5%

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

4. Final simplification 98.8%

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

Alternative 2: 97.7% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

   1. +-commutative 96.0%

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

   2. fma-def 96.8%

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

   3. associate-+l+ 96.8%

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

   4. fma-def 98.0%

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

   5. fma-def 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 97.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 20.0%

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

      3. associate-+l+ 20.0%

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

      4. fma-def 50.0%

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

      5. fma-def 50.0%

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

   3. Simplified 50.0%

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

      1. fma-udef 20.0%

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

      2. fma-udef 20.0%

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

      3. associate-+l+ 20.0%

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

      4. +-commutative 20.0%

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

      5. associate-+r+ 20.0%

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

   5. Applied egg-rr 20.0%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 98.8%

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

Alternative 4: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + c \cdot i\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq -7.2 \cdot 10^{+114}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -5.3 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 1.9 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq 6.5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.4 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* c i))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* c i) -1.05e+149)
     t_1
     (if (<= (* c i) -7.2e+114)
       (* x y)
       (if (<= (* c i) -5.3e+70)
         t_1
         (if (<= (* c i) 1.9e-292)
           t_2
           (if (<= (* c i) 6.5e-253)
             (* x y)
             (if (<= (* c i) 3.4e+74) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -1.05e+149) {
		tmp = t_1;
	} else if ((c * i) <= -7.2e+114) {
		tmp = x * y;
	} else if ((c * i) <= -5.3e+70) {
		tmp = t_1;
	} else if ((c * i) <= 1.9e-292) {
		tmp = t_2;
	} else if ((c * i) <= 6.5e-253) {
		tmp = x * y;
	} else if ((c * i) <= 3.4e+74) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (c * i)
    t_2 = (a * b) + (z * t)
    if ((c * i) <= (-1.05d+149)) then
        tmp = t_1
    else if ((c * i) <= (-7.2d+114)) then
        tmp = x * y
    else if ((c * i) <= (-5.3d+70)) then
        tmp = t_1
    else if ((c * i) <= 1.9d-292) then
        tmp = t_2
    else if ((c * i) <= 6.5d-253) then
        tmp = x * y
    else if ((c * i) <= 3.4d+74) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (c * i);
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((c * i) <= -1.05e+149) {
		tmp = t_1;
	} else if ((c * i) <= -7.2e+114) {
		tmp = x * y;
	} else if ((c * i) <= -5.3e+70) {
		tmp = t_1;
	} else if ((c * i) <= 1.9e-292) {
		tmp = t_2;
	} else if ((c * i) <= 6.5e-253) {
		tmp = x * y;
	} else if ((c * i) <= 3.4e+74) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (c * i)
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (c * i) <= -1.05e+149:
		tmp = t_1
	elif (c * i) <= -7.2e+114:
		tmp = x * y
	elif (c * i) <= -5.3e+70:
		tmp = t_1
	elif (c * i) <= 1.9e-292:
		tmp = t_2
	elif (c * i) <= 6.5e-253:
		tmp = x * y
	elif (c * i) <= 3.4e+74:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(c * i))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1.05e+149)
		tmp = t_1;
	elseif (Float64(c * i) <= -7.2e+114)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -5.3e+70)
		tmp = t_1;
	elseif (Float64(c * i) <= 1.9e-292)
		tmp = t_2;
	elseif (Float64(c * i) <= 6.5e-253)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 3.4e+74)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (c * i);
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1.05e+149)
		tmp = t_1;
	elseif ((c * i) <= -7.2e+114)
		tmp = x * y;
	elseif ((c * i) <= -5.3e+70)
		tmp = t_1;
	elseif ((c * i) <= 1.9e-292)
		tmp = t_2;
	elseif ((c * i) <= 6.5e-253)
		tmp = x * y;
	elseif ((c * i) <= 3.4e+74)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.05e+149], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], -7.2e+114], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -5.3e+70], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 1.9e-292], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], 6.5e-253], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.4e+74], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.0500000000000001e149 or -7.2000000000000001e114 < (*.f64 c i) < -5.3e70 or 3.3999999999999999e74 < (*.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 a around inf 73.9%

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

   if -1.0500000000000001e149 < (*.f64 c i) < -7.2000000000000001e114 or 1.9000000000000001e-292 < (*.f64 c i) < 6.4999999999999998e-253

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 100.0%

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

   3. Taylor expanded in t around 0 88.0%

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

   4. Taylor expanded in c around 0 81.9%

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

   if -5.3e70 < (*.f64 c i) < 1.9000000000000001e-292 or 6.4999999999999998e-253 < (*.f64 c i) < 3.3999999999999999e74

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 77.2%

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

      1. associate-+r+ 77.2%

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

      2. +-commutative 77.2%

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

      3. fma-def 77.2%

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

      4. *-commutative 77.2%

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

      5. +-commutative 77.2%

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

      6. fma-def 77.3%

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

   4. Simplified 77.3%

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

      1. fma-def 77.3%

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

      2. fma-udef 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-+r+ 77.2%

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

   6. Applied egg-rr 77.2%

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

   7. Taylor expanded in c around 0 73.6%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{+149}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.2 \cdot 10^{+114}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -5.3 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.9 \cdot 10^{-292}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 6.5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 3.4 \cdot 10^{+74}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 5: 64.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot b + z \cdot t\\ t_2 := c \cdot i + z \cdot t\\ \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \cdot i \leq -6.4 \cdot 10^{+114}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -4.9 \cdot 10^{+73}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.9 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 750000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* a b) (* z t))) (t_2 (+ (* c i) (* z t))))
   (if (<= (* c i) -1.05e+149)
     t_2
     (if (<= (* c i) -6.4e+114)
       (* x y)
       (if (<= (* c i) -4.9e+73)
         (+ (* a b) (* c i))
         (if (<= (* c i) 1.9e-292)
           t_1
           (if (<= (* c i) 7.5e-253)
             (* x y)
             (if (<= (* c i) 750000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -1.05e+149) {
		tmp = t_2;
	} else if ((c * i) <= -6.4e+114) {
		tmp = x * y;
	} else if ((c * i) <= -4.9e+73) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 1.9e-292) {
		tmp = t_1;
	} else if ((c * i) <= 7.5e-253) {
		tmp = x * y;
	} else if ((c * i) <= 750000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) + (z * t)
    t_2 = (c * i) + (z * t)
    if ((c * i) <= (-1.05d+149)) then
        tmp = t_2
    else if ((c * i) <= (-6.4d+114)) then
        tmp = x * y
    else if ((c * i) <= (-4.9d+73)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= 1.9d-292) then
        tmp = t_1
    else if ((c * i) <= 7.5d-253) then
        tmp = x * y
    else if ((c * i) <= 750000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (a * b) + (z * t);
	double t_2 = (c * i) + (z * t);
	double tmp;
	if ((c * i) <= -1.05e+149) {
		tmp = t_2;
	} else if ((c * i) <= -6.4e+114) {
		tmp = x * y;
	} else if ((c * i) <= -4.9e+73) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= 1.9e-292) {
		tmp = t_1;
	} else if ((c * i) <= 7.5e-253) {
		tmp = x * y;
	} else if ((c * i) <= 750000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (a * b) + (z * t)
	t_2 = (c * i) + (z * t)
	tmp = 0
	if (c * i) <= -1.05e+149:
		tmp = t_2
	elif (c * i) <= -6.4e+114:
		tmp = x * y
	elif (c * i) <= -4.9e+73:
		tmp = (a * b) + (c * i)
	elif (c * i) <= 1.9e-292:
		tmp = t_1
	elif (c * i) <= 7.5e-253:
		tmp = x * y
	elif (c * i) <= 750000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(a * b) + Float64(z * t))
	t_2 = Float64(Float64(c * i) + Float64(z * t))
	tmp = 0.0
	if (Float64(c * i) <= -1.05e+149)
		tmp = t_2;
	elseif (Float64(c * i) <= -6.4e+114)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= -4.9e+73)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= 1.9e-292)
		tmp = t_1;
	elseif (Float64(c * i) <= 7.5e-253)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 750000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (a * b) + (z * t);
	t_2 = (c * i) + (z * t);
	tmp = 0.0;
	if ((c * i) <= -1.05e+149)
		tmp = t_2;
	elseif ((c * i) <= -6.4e+114)
		tmp = x * y;
	elseif ((c * i) <= -4.9e+73)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= 1.9e-292)
		tmp = t_1;
	elseif ((c * i) <= 7.5e-253)
		tmp = x * y;
	elseif ((c * i) <= 750000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(c * i), $MachinePrecision], -1.05e+149], t$95$2, If[LessEqual[N[(c * i), $MachinePrecision], -6.4e+114], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -4.9e+73], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.9e-292], t$95$1, If[LessEqual[N[(c * i), $MachinePrecision], 7.5e-253], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 750000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -1.0500000000000001e149 or 7.5e8 < (*.f64 c i)

   1. Initial program 93.9%

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

   2. Taylor expanded in a around 0 86.6%

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

   3. Taylor expanded in y around 0 72.3%

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

   if -1.0500000000000001e149 < (*.f64 c i) < -6.4e114 or 1.9000000000000001e-292 < (*.f64 c i) < 7.49999999999999987e-253

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 100.0%

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

   3. Taylor expanded in t around 0 88.0%

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

   4. Taylor expanded in c around 0 81.9%

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

   if -6.4e114 < (*.f64 c i) < -4.8999999999999999e73

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 88.1%

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

   if -4.8999999999999999e73 < (*.f64 c i) < 1.9000000000000001e-292 or 7.49999999999999987e-253 < (*.f64 c i) < 7.5e8

   1. Initial program 96.6%

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

   2. Taylor expanded in x around 0 77.0%

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

      1. associate-+r+ 77.0%

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

      2. +-commutative 77.0%

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

      3. fma-def 77.0%

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

      4. *-commutative 77.0%

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

      5. +-commutative 77.0%

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

      6. fma-def 77.1%

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

   4. Simplified 77.1%

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

      1. fma-def 77.1%

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

      2. fma-udef 77.0%

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

      3. +-commutative 77.0%

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

      4. associate-+r+ 77.0%

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

   6. Applied egg-rr 77.0%

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

   7. Taylor expanded in c around 0 74.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.05 \cdot 10^{+149}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -6.4 \cdot 10^{+114}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq -4.9 \cdot 10^{+73}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 1.9 \cdot 10^{-292}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.5 \cdot 10^{-253}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 750000000:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \end{array} \]

Alternative 6: 96.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(a * b), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(z * t), $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 0 40.0%

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

      1. associate-+r+ 40.0%

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

      2. +-commutative 40.0%

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

      3. fma-def 40.0%

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

      4. *-commutative 40.0%

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

      5. +-commutative 40.0%

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

      6. fma-def 40.0%

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

   4. Simplified 40.0%

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

      1. fma-def 40.0%

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

      2. fma-udef 40.0%

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

      3. +-commutative 40.0%

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

      4. associate-+r+ 40.0%

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

   6. Applied egg-rr 40.0%

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

   7. Taylor expanded in z around inf 60.2%

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

4. Final simplification 98.4%

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

Alternative 7: 43.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.2 \cdot 10^{-130}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -8.4 \cdot 10^{-284}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 10^{-237}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.22 \cdot 10^{-73}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.3 \cdot 10^{+74}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -6.8e+69)
   (* c i)
   (if (<= (* c i) -7.2e-130)
     (* z t)
     (if (<= (* c i) -8.4e-284)
       (* a b)
       (if (<= (* c i) 1e-237)
         (* z t)
         (if (<= (* c i) 1.22e-73)
           (* a b)
           (if (<= (* c i) 3.3e+74) (* z t) (* c i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -6.8e+69) {
		tmp = c * i;
	} else if ((c * i) <= -7.2e-130) {
		tmp = z * t;
	} else if ((c * i) <= -8.4e-284) {
		tmp = a * b;
	} else if ((c * i) <= 1e-237) {
		tmp = z * t;
	} else if ((c * i) <= 1.22e-73) {
		tmp = a * b;
	} else if ((c * i) <= 3.3e+74) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-6.8d+69)) then
        tmp = c * i
    else if ((c * i) <= (-7.2d-130)) then
        tmp = z * t
    else if ((c * i) <= (-8.4d-284)) then
        tmp = a * b
    else if ((c * i) <= 1d-237) then
        tmp = z * t
    else if ((c * i) <= 1.22d-73) then
        tmp = a * b
    else if ((c * i) <= 3.3d+74) then
        tmp = z * t
    else
        tmp = c * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -6.8e+69) {
		tmp = c * i;
	} else if ((c * i) <= -7.2e-130) {
		tmp = z * t;
	} else if ((c * i) <= -8.4e-284) {
		tmp = a * b;
	} else if ((c * i) <= 1e-237) {
		tmp = z * t;
	} else if ((c * i) <= 1.22e-73) {
		tmp = a * b;
	} else if ((c * i) <= 3.3e+74) {
		tmp = z * t;
	} else {
		tmp = c * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -6.8e+69:
		tmp = c * i
	elif (c * i) <= -7.2e-130:
		tmp = z * t
	elif (c * i) <= -8.4e-284:
		tmp = a * b
	elif (c * i) <= 1e-237:
		tmp = z * t
	elif (c * i) <= 1.22e-73:
		tmp = a * b
	elif (c * i) <= 3.3e+74:
		tmp = z * t
	else:
		tmp = c * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -6.8e+69)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -7.2e-130)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= -8.4e-284)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 1e-237)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.22e-73)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 3.3e+74)
		tmp = Float64(z * t);
	else
		tmp = Float64(c * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -6.8e+69)
		tmp = c * i;
	elseif ((c * i) <= -7.2e-130)
		tmp = z * t;
	elseif ((c * i) <= -8.4e-284)
		tmp = a * b;
	elseif ((c * i) <= 1e-237)
		tmp = z * t;
	elseif ((c * i) <= 1.22e-73)
		tmp = a * b;
	elseif ((c * i) <= 3.3e+74)
		tmp = z * t;
	else
		tmp = c * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -6.8e+69], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -7.2e-130], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -8.4e-284], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e-237], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.22e-73], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.3e+74], N[(z * t), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -6.79999999999999973e69 or 3.3000000000000002e74 < (*.f64 c i)

   1. Initial program 95.1%

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

   2. Taylor expanded in c around inf 56.4%

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

   if -6.79999999999999973e69 < (*.f64 c i) < -7.2000000000000003e-130 or -8.39999999999999965e-284 < (*.f64 c i) < 9.9999999999999999e-238 or 1.22e-73 < (*.f64 c i) < 3.3000000000000002e74

   1. Initial program 95.6%

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

   2. Taylor expanded in x around 0 69.9%

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

      1. associate-+r+ 69.9%

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

      2. +-commutative 69.9%

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

      3. fma-def 69.9%

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

      4. *-commutative 69.9%

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

      5. +-commutative 69.9%

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

      6. fma-def 69.9%

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

   4. Simplified 69.9%

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

      1. fma-def 69.9%

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

      2. fma-udef 69.9%

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

      3. +-commutative 69.9%

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

      4. associate-+r+ 69.9%

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

   6. Applied egg-rr 69.9%

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

   7. Taylor expanded in z around inf 50.0%

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

   if -7.2000000000000003e-130 < (*.f64 c i) < -8.39999999999999965e-284 or 9.9999999999999999e-238 < (*.f64 c i) < 1.22e-73

   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 83.4%

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

      1. associate-+r+ 83.4%

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

      2. +-commutative 83.4%

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

      3. fma-def 83.4%

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

      4. *-commutative 83.4%

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

      5. +-commutative 83.4%

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

      6. fma-def 83.4%

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

   4. Simplified 83.4%

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

      1. fma-def 83.4%

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

      2. fma-udef 83.4%

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

      3. +-commutative 83.4%

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

      4. associate-+r+ 83.4%

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

   6. Applied egg-rr 83.4%

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

   7. Taylor expanded in a around inf 66.6%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -7.2 \cdot 10^{-130}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -8.4 \cdot 10^{-284}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 10^{-237}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.22 \cdot 10^{-73}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 3.3 \cdot 10^{+74}:\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 8: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + \left(z \cdot t + x \cdot y\right)\\ t_2 := a \cdot b + z \cdot t\\ \mathbf{if}\;a \cdot b \leq -2.7 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (+ (* z t) (* x y)))) (t_2 (+ (* a b) (* z t))))
   (if (<= (* a b) -2.7e+128)
     t_2
     (if (<= (* a b) 4e+28)
       t_1
       (if (<= (* a b) 3.8e+103)
         (+ (* a b) (* c i))
         (if (<= (* a b) 3e+139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((z * t) + (x * y));
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -2.7e+128) {
		tmp = t_2;
	} else if ((a * b) <= 4e+28) {
		tmp = t_1;
	} else if ((a * b) <= 3.8e+103) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= 3e+139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * i) + ((z * t) + (x * y))
    t_2 = (a * b) + (z * t)
    if ((a * b) <= (-2.7d+128)) then
        tmp = t_2
    else if ((a * b) <= 4d+28) then
        tmp = t_1
    else if ((a * b) <= 3.8d+103) then
        tmp = (a * b) + (c * i)
    else if ((a * b) <= 3d+139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + ((z * t) + (x * y));
	double t_2 = (a * b) + (z * t);
	double tmp;
	if ((a * b) <= -2.7e+128) {
		tmp = t_2;
	} else if ((a * b) <= 4e+28) {
		tmp = t_1;
	} else if ((a * b) <= 3.8e+103) {
		tmp = (a * b) + (c * i);
	} else if ((a * b) <= 3e+139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + ((z * t) + (x * y))
	t_2 = (a * b) + (z * t)
	tmp = 0
	if (a * b) <= -2.7e+128:
		tmp = t_2
	elif (a * b) <= 4e+28:
		tmp = t_1
	elif (a * b) <= 3.8e+103:
		tmp = (a * b) + (c * i)
	elif (a * b) <= 3e+139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(x * y)))
	t_2 = Float64(Float64(a * b) + Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -2.7e+128)
		tmp = t_2;
	elseif (Float64(a * b) <= 4e+28)
		tmp = t_1;
	elseif (Float64(a * b) <= 3.8e+103)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(a * b) <= 3e+139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + ((z * t) + (x * y));
	t_2 = (a * b) + (z * t);
	tmp = 0.0;
	if ((a * b) <= -2.7e+128)
		tmp = t_2;
	elseif ((a * b) <= 4e+28)
		tmp = t_1;
	elseif ((a * b) <= 3.8e+103)
		tmp = (a * b) + (c * i);
	elseif ((a * b) <= 3e+139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2.7e+128], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 4e+28], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 3.8e+103], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 3e+139], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.70000000000000001e128 or 3e139 < (*.f64 a b)

   1. Initial program 92.0%

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

   2. Taylor expanded in x around 0 82.0%

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

      1. associate-+r+ 82.0%

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

      2. +-commutative 82.0%

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

      3. fma-def 82.0%

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

      4. *-commutative 82.0%

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

      5. +-commutative 82.0%

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

      6. fma-def 82.0%

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

   4. Simplified 82.0%

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

      1. fma-def 82.0%

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

      2. fma-udef 82.0%

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

      3. +-commutative 82.0%

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

      4. associate-+r+ 82.0%

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

   6. Applied egg-rr 82.0%

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

   7. Taylor expanded in c around 0 79.6%

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

   if -2.70000000000000001e128 < (*.f64 a b) < 3.99999999999999983e28 or 3.7999999999999997e103 < (*.f64 a b) < 3e139

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0 89.3%

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

   if 3.99999999999999983e28 < (*.f64 a b) < 3.7999999999999997e103

   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 a around inf 80.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.7 \cdot 10^{+128}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;a \cdot b \leq 4 \cdot 10^{+28}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{elif}\;a \cdot b \leq 3.8 \cdot 10^{+103}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;a \cdot b \leq 3 \cdot 10^{+139}:\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \end{array} \]

Alternative 9: 88.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+91} \lor \neg \left(z \cdot t \leq 10^{+43}\right):\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (* z t) -2e+91) (not (<= (* z t) 1e+43)))
   (+ (* c i) (+ (* z t) (* x y)))
   (+ (* c i) (+ (* a b) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -2e+91) || !((z * t) <= 1e+43)) {
		tmp = (c * i) + ((z * t) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((z * t) <= (-2d+91)) .or. (.not. ((z * t) <= 1d+43))) then
        tmp = (c * i) + ((z * t) + (x * y))
    else
        tmp = (c * i) + ((a * b) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((z * t) <= -2e+91) || !((z * t) <= 1e+43)) {
		tmp = (c * i) + ((z * t) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((z * t) <= -2e+91) or not ((z * t) <= 1e+43):
		tmp = (c * i) + ((z * t) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(z * t) <= -2e+91) || !(Float64(z * t) <= 1e+43))
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((z * t) <= -2e+91) || ~(((z * t) <= 1e+43)))
		tmp = (c * i) + ((z * t) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -2e+91], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+43]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2.00000000000000016e91 or 1.00000000000000001e43 < (*.f64 z t)

   1. Initial program 92.3%

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

   2. Taylor expanded in a around 0 87.9%

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

   if -2.00000000000000016e91 < (*.f64 z t) < 1.00000000000000001e43

   1. Initial program 98.6%

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

   2. Taylor expanded in x around inf 94.3%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+91} \lor \neg \left(z \cdot t \leq 10^{+43}\right):\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + x \cdot y\right)\\ \end{array} \]

Alternative 10: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+88} \lor \neg \left(x \leq 3.1 \cdot 10^{-127}\right):\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -8.8e+88) (not (<= x 3.1e-127)))
   (+ (* c i) (+ (* z t) (* x y)))
   (+ (* c i) (+ (* a b) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.8e+88) || !(x <= 3.1e-127)) {
		tmp = (c * i) + ((z * t) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-8.8d+88)) .or. (.not. (x <= 3.1d-127))) then
        tmp = (c * i) + ((z * t) + (x * y))
    else
        tmp = (c * i) + ((a * b) + (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.8e+88) || !(x <= 3.1e-127)) {
		tmp = (c * i) + ((z * t) + (x * y));
	} else {
		tmp = (c * i) + ((a * b) + (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -8.8e+88) or not (x <= 3.1e-127):
		tmp = (c * i) + ((z * t) + (x * y))
	else:
		tmp = (c * i) + ((a * b) + (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -8.8e+88) || !(x <= 3.1e-127))
		tmp = Float64(Float64(c * i) + Float64(Float64(z * t) + Float64(x * y)));
	else
		tmp = Float64(Float64(c * i) + Float64(Float64(a * b) + Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -8.8e+88) || ~((x <= 3.1e-127)))
		tmp = (c * i) + ((z * t) + (x * y));
	else
		tmp = (c * i) + ((a * b) + (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -8.8e+88], N[Not[LessEqual[x, 3.1e-127]], $MachinePrecision]], N[(N[(c * i), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * i), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.80000000000000035e88 or 3.1e-127 < x

   1. Initial program 93.6%

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

   2. Taylor expanded in a around 0 78.6%

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

   if -8.80000000000000035e88 < x < 3.1e-127

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0 88.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+88} \lor \neg \left(x \leq 3.1 \cdot 10^{-127}\right):\\ \;\;\;\;c \cdot i + \left(z \cdot t + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + \left(a \cdot b + z \cdot t\right)\\ \end{array} \]

Alternative 11: 61.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot i + x \cdot y\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-303}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-82}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* c i) (* x y))))
   (if (<= x -4.5e+84)
     t_1
     (if (<= x 1.95e-303)
       (+ (* a b) (* z t))
       (if (<= x 4.2e-82) (+ (* c i) (* z t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (x * y);
	double tmp;
	if (x <= -4.5e+84) {
		tmp = t_1;
	} else if (x <= 1.95e-303) {
		tmp = (a * b) + (z * t);
	} else if (x <= 4.2e-82) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (c * i) + (x * y)
    if (x <= (-4.5d+84)) then
        tmp = t_1
    else if (x <= 1.95d-303) then
        tmp = (a * b) + (z * t)
    else if (x <= 4.2d-82) then
        tmp = (c * i) + (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (c * i) + (x * y);
	double tmp;
	if (x <= -4.5e+84) {
		tmp = t_1;
	} else if (x <= 1.95e-303) {
		tmp = (a * b) + (z * t);
	} else if (x <= 4.2e-82) {
		tmp = (c * i) + (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (c * i) + (x * y)
	tmp = 0
	if x <= -4.5e+84:
		tmp = t_1
	elif x <= 1.95e-303:
		tmp = (a * b) + (z * t)
	elif x <= 4.2e-82:
		tmp = (c * i) + (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(c * i) + Float64(x * y))
	tmp = 0.0
	if (x <= -4.5e+84)
		tmp = t_1;
	elseif (x <= 1.95e-303)
		tmp = Float64(Float64(a * b) + Float64(z * t));
	elseif (x <= 4.2e-82)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (c * i) + (x * y);
	tmp = 0.0;
	if (x <= -4.5e+84)
		tmp = t_1;
	elseif (x <= 1.95e-303)
		tmp = (a * b) + (z * t);
	elseif (x <= 4.2e-82)
		tmp = (c * i) + (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(c * i), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+84], t$95$1, If[LessEqual[x, 1.95e-303], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-82], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.4999999999999997e84 or 4.2000000000000001e-82 < x

   1. Initial program 92.9%

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

   2. Taylor expanded in a around 0 80.6%

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

   3. Taylor expanded in t around 0 63.4%

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

   if -4.4999999999999997e84 < x < 1.95e-303

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0 86.1%

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

      1. associate-+r+ 86.1%

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

      2. +-commutative 86.1%

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

      3. fma-def 86.1%

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

      4. *-commutative 86.1%

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

      5. +-commutative 86.1%

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

      6. fma-def 86.1%

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

   4. Simplified 86.1%

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

      1. fma-def 86.1%

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

      2. fma-udef 86.1%

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

      3. +-commutative 86.1%

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

      4. associate-+r+ 86.1%

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

   6. Applied egg-rr 86.1%

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

   7. Taylor expanded in c around 0 68.7%

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

   if 1.95e-303 < x < 4.2000000000000001e-82

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 61.9%

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

   3. Taylor expanded in y around 0 54.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+84}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-303}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-82}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;c \cdot i + x \cdot y\\ \end{array} \]

Alternative 12: 52.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+133} \lor \neg \left(z \leq 5.8 \cdot 10^{-73}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -2.5e+133) (not (<= z 5.8e-73))) (* 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) {
	double tmp;
	if ((z <= -2.5e+133) || !(z <= 5.8e-73)) {
		tmp = z * t;
	} 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 ((z <= (-2.5d+133)) .or. (.not. (z <= 5.8d-73))) then
        tmp = z * t
    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 ((z <= -2.5e+133) || !(z <= 5.8e-73)) {
		tmp = z * t;
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -2.5e+133) or not (z <= 5.8e-73):
		tmp = z * t
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -2.5e+133) || !(z <= 5.8e-73))
		tmp = Float64(z * t);
	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 ((z <= -2.5e+133) || ~((z <= 5.8e-73)))
		tmp = z * t;
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -2.5e+133], N[Not[LessEqual[z, 5.8e-73]], $MachinePrecision]], N[(z * t), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999998e133 or 5.8e-73 < z

   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 x around 0 76.8%

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

      1. associate-+r+ 76.8%

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

      2. +-commutative 76.8%

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

      3. fma-def 76.8%

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

      4. *-commutative 76.8%

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

      5. +-commutative 76.8%

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

      6. fma-def 76.9%

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

   4. Simplified 76.9%

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

      1. fma-def 76.9%

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

      2. fma-udef 76.8%

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

      3. +-commutative 76.8%

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

      4. associate-+r+ 76.8%

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

   6. Applied egg-rr 76.8%

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

   7. Taylor expanded in z around inf 46.2%

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

   if -2.4999999999999998e133 < z < 5.8e-73

   1. Initial program 98.5%

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

   2. Taylor expanded in a around inf 59.3%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+133} \lor \neg \left(z \leq 5.8 \cdot 10^{-73}\right):\\ \;\;\;\;z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]

Alternative 13: 42.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+118}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 550000000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -6.5e+118)
   (* c i)
   (if (<= (* c i) 550000000.0) (* 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) <= -6.5e+118) {
		tmp = c * i;
	} else if ((c * i) <= 550000000.0) {
		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) <= (-6.5d+118)) then
        tmp = c * i
    else if ((c * i) <= 550000000.0d0) 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) <= -6.5e+118) {
		tmp = c * i;
	} else if ((c * i) <= 550000000.0) {
		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) <= -6.5e+118:
		tmp = c * i
	elif (c * i) <= 550000000.0:
		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) <= -6.5e+118)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 550000000.0)
		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) <= -6.5e+118)
		tmp = c * i;
	elseif ((c * i) <= 550000000.0)
		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], -6.5e+118], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 550000000.0], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -6.5e118 or 5.5e8 < (*.f64 c i)

   1. Initial program 94.2%

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

   2. Taylor expanded in c around inf 53.1%

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

   if -6.5e118 < (*.f64 c i) < 5.5e8

   1. Initial program 97.0%

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

   2. Taylor expanded in x around 0 74.5%

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

      1. associate-+r+ 74.5%

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

      2. +-commutative 74.5%

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

      3. fma-def 74.5%

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

      4. *-commutative 74.5%

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

      5. +-commutative 74.5%

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

      6. fma-def 74.5%

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

   4. Simplified 74.5%

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

      1. fma-def 74.5%

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

      2. fma-udef 74.5%

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

      3. +-commutative 74.5%

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

      4. associate-+r+ 74.5%

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

   6. Applied egg-rr 74.5%

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

   7. Taylor expanded in a around inf 37.3%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -6.5 \cdot 10^{+118}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 550000000:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]

Alternative 14: 37.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-68}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-63}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+134}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= t -5.5e-68)
   (* z t)
   (if (<= t 3.7e-63) (* a b) (if (<= t 3.5e+134) (* x y) (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (t <= -5.5e-68) {
		tmp = z * t;
	} else if (t <= 3.7e-63) {
		tmp = a * b;
	} else if (t <= 3.5e+134) {
		tmp = x * y;
	} 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 (t <= (-5.5d-68)) then
        tmp = z * t
    else if (t <= 3.7d-63) then
        tmp = a * b
    else if (t <= 3.5d+134) then
        tmp = x * y
    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 (t <= -5.5e-68) {
		tmp = z * t;
	} else if (t <= 3.7e-63) {
		tmp = a * b;
	} else if (t <= 3.5e+134) {
		tmp = x * y;
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if t <= -5.5e-68:
		tmp = z * t
	elif t <= 3.7e-63:
		tmp = a * b
	elif t <= 3.5e+134:
		tmp = x * y
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (t <= -5.5e-68)
		tmp = Float64(z * t);
	elseif (t <= 3.7e-63)
		tmp = Float64(a * b);
	elseif (t <= 3.5e+134)
		tmp = Float64(x * y);
	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 (t <= -5.5e-68)
		tmp = z * t;
	elseif (t <= 3.7e-63)
		tmp = a * b;
	elseif (t <= 3.5e+134)
		tmp = x * y;
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[t, -5.5e-68], N[(z * t), $MachinePrecision], If[LessEqual[t, 3.7e-63], N[(a * b), $MachinePrecision], If[LessEqual[t, 3.5e+134], N[(x * y), $MachinePrecision], N[(z * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.5000000000000003e-68 or 3.50000000000000003e134 < t

   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 x around 0 80.0%

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

      1. associate-+r+ 80.0%

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

      2. +-commutative 80.0%

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

      3. fma-def 80.0%

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

      4. *-commutative 80.0%

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

      5. +-commutative 80.0%

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

      6. fma-def 80.0%

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

   4. Simplified 80.0%

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

      1. fma-def 80.0%

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

      2. fma-udef 80.0%

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

      3. +-commutative 80.0%

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

      4. associate-+r+ 80.0%

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

   6. Applied egg-rr 80.0%

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

   7. Taylor expanded in z around inf 48.1%

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

   if -5.5000000000000003e-68 < t < 3.70000000000000012e-63

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 70.8%

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

      1. associate-+r+ 70.8%

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

      2. +-commutative 70.8%

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

      3. fma-def 70.8%

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

      4. *-commutative 70.8%

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

      5. +-commutative 70.8%

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

      6. fma-def 70.9%

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

   4. Simplified 70.9%

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

      1. fma-def 70.9%

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

      2. fma-udef 70.8%

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

      3. +-commutative 70.8%

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

      4. associate-+r+ 70.8%

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

   6. Applied egg-rr 70.8%

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

   7. Taylor expanded in a around inf 41.0%

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

   if 3.70000000000000012e-63 < t < 3.50000000000000003e134

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0 79.6%

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

   3. Taylor expanded in t around 0 44.4%

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

   4. Taylor expanded in c around 0 29.4%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-68}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-63}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+134}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]

Alternative 15: 27.3% 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 96.0%

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

2. Taylor expanded in x around 0 75.4%

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

   1. associate-+r+ 75.4%

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

   2. +-commutative 75.4%

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

   3. fma-def 75.4%

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

   4. *-commutative 75.4%

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

   5. +-commutative 75.4%

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

   6. fma-def 75.4%

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

4. Simplified 75.4%

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

   1. fma-def 75.4%

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

   2. fma-udef 75.4%

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

   3. +-commutative 75.4%

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

   4. associate-+r+ 75.4%

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

6. Applied egg-rr 75.4%

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

7. Taylor expanded in a around inf 28.8%

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

8. Final simplification 28.8%

   \[\leadsto a \cdot b \]

Reproduce

herbie shell --seed 2023242 
(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)))