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

Percentage Accurate: 95.8% → 97.7%

Time: 9.9s

Alternatives: 14

Speedup: 0.4×

• 40.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

      1. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y + \left(z \cdot t + a \cdot b\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z \cdot t + a \cdot b\right) + x \cdot y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot t + a \cdot b\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot t\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(a, b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      7. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(a, b\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   4. Applied egg-rr 100.0%

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

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 42.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 42.9%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x + \frac{c \cdot i}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{c \cdot i}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(c \cdot i\right), \color{blue}{y}\right)\right)\right) \]

      4. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), y\right)\right)\right) \]

   8. Simplified 71.4%

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

4. Final simplification 99.2%

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

Alternative 2: 42.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.6 \cdot 10^{+238}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -4.3 \cdot 10^{-184}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.6 \cdot 10^{-296}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{-65}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.6e+238)
   (* c i)
   (if (<= (* c i) -4.3e-184)
     (* z t)
     (if (<= (* c i) 4.6e-296)
       (* a b)
       (if (<= (* c i) 4.4e-65)
         (* x y)
         (if (<= (* c i) 1.5e+64) (* 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) <= -2.6e+238) {
		tmp = c * i;
	} else if ((c * i) <= -4.3e-184) {
		tmp = z * t;
	} else if ((c * i) <= 4.6e-296) {
		tmp = a * b;
	} else if ((c * i) <= 4.4e-65) {
		tmp = x * y;
	} else if ((c * i) <= 1.5e+64) {
		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) <= (-2.6d+238)) then
        tmp = c * i
    else if ((c * i) <= (-4.3d-184)) then
        tmp = z * t
    else if ((c * i) <= 4.6d-296) then
        tmp = a * b
    else if ((c * i) <= 4.4d-65) then
        tmp = x * y
    else if ((c * i) <= 1.5d+64) 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) <= -2.6e+238) {
		tmp = c * i;
	} else if ((c * i) <= -4.3e-184) {
		tmp = z * t;
	} else if ((c * i) <= 4.6e-296) {
		tmp = a * b;
	} else if ((c * i) <= 4.4e-65) {
		tmp = x * y;
	} else if ((c * i) <= 1.5e+64) {
		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) <= -2.6e+238:
		tmp = c * i
	elif (c * i) <= -4.3e-184:
		tmp = z * t
	elif (c * i) <= 4.6e-296:
		tmp = a * b
	elif (c * i) <= 4.4e-65:
		tmp = x * y
	elif (c * i) <= 1.5e+64:
		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) <= -2.6e+238)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -4.3e-184)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 4.6e-296)
		tmp = Float64(a * b);
	elseif (Float64(c * i) <= 4.4e-65)
		tmp = Float64(x * y);
	elseif (Float64(c * i) <= 1.5e+64)
		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) <= -2.6e+238)
		tmp = c * i;
	elseif ((c * i) <= -4.3e-184)
		tmp = z * t;
	elseif ((c * i) <= 4.6e-296)
		tmp = a * b;
	elseif ((c * i) <= 4.4e-65)
		tmp = x * y;
	elseif ((c * i) <= 1.5e+64)
		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], -2.6e+238], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -4.3e-184], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.6e-296], N[(a * b), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.4e-65], N[(x * y), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.5e+64], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 c i) < -2.6e238 or 1.5000000000000001e64 < (*.f64 c i)

   1. Initial program 94.5%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 71.4%

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

   if -2.6e238 < (*.f64 c i) < -4.30000000000000007e-184

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 44.0%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 44.0%

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

   if -4.30000000000000007e-184 < (*.f64 c i) < 4.60000000000000008e-296 or 4.40000000000000042e-65 < (*.f64 c i) < 1.5000000000000001e64

   1. Initial program 98.6%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 54.3%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 54.3%

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

   if 4.60000000000000008e-296 < (*.f64 c i) < 4.40000000000000042e-65

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 49.2%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 49.2%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.6 \cdot 10^{+238}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -4.3 \cdot 10^{-184}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 4.6 \cdot 10^{-296}:\\ \;\;\;\;a \cdot b\\ \mathbf{elif}\;c \cdot i \leq 4.4 \cdot 10^{-65}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;c \cdot i \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.5 \cdot 10^{+159}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -8 \cdot 10^{+143}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.06 \cdot 10^{-192}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -7.5e+159)
   (+ (* c i) (* z t))
   (if (<= (* c i) -8e+143)
     (+ (* a b) (* c i))
     (if (<= (* c i) -1.06e-192)
       (+ (* x y) (* z t))
       (if (<= (* c i) 8.2e+67) (+ (* x y) (* a b)) (+ (* x y) (* c i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -7.5e+159) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= -8e+143) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -1.06e-192) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 8.2e+67) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-7.5d+159)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= (-8d+143)) then
        tmp = (a * b) + (c * i)
    else if ((c * i) <= (-1.06d-192)) then
        tmp = (x * y) + (z * t)
    else if ((c * i) <= 8.2d+67) then
        tmp = (x * y) + (a * b)
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -7.5e+159) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= -8e+143) {
		tmp = (a * b) + (c * i);
	} else if ((c * i) <= -1.06e-192) {
		tmp = (x * y) + (z * t);
	} else if ((c * i) <= 8.2e+67) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -7.5e+159:
		tmp = (c * i) + (z * t)
	elif (c * i) <= -8e+143:
		tmp = (a * b) + (c * i)
	elif (c * i) <= -1.06e-192:
		tmp = (x * y) + (z * t)
	elif (c * i) <= 8.2e+67:
		tmp = (x * y) + (a * b)
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -7.5e+159)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= -8e+143)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	elseif (Float64(c * i) <= -1.06e-192)
		tmp = Float64(Float64(x * y) + Float64(z * t));
	elseif (Float64(c * i) <= 8.2e+67)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -7.5e+159)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= -8e+143)
		tmp = (a * b) + (c * i);
	elseif ((c * i) <= -1.06e-192)
		tmp = (x * y) + (z * t);
	elseif ((c * i) <= 8.2e+67)
		tmp = (x * y) + (a * b);
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -7.5e+159], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -8e+143], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.06e-192], N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 8.2e+67], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 c i) < -7.4999999999999997e159

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 94.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 94.2%

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

   if -7.4999999999999997e159 < (*.f64 c i) < -8.0000000000000002e143

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 88.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 88.1%

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

   if -8.0000000000000002e143 < (*.f64 c i) < -1.06e-192

   1. Initial program 98.5%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 86.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 86.5%

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

   6. Taylor expanded in a around 0

      \[\leadsto \color{blue}{t \cdot z + x \cdot y} \]
   7. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot z\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot z\right)\right) \]

      4. *-lowering-*.f64 74.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 74.9%

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

   if -1.06e-192 < (*.f64 c i) < 8.19999999999999959e67

   1. Initial program 98.0%

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

      1. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y + \left(z \cdot t + a \cdot b\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z \cdot t + a \cdot b\right) + x \cdot y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot t + a \cdot b\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot t\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(a, b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      7. *-lowering-*.f64 98.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(a, b\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(a + \frac{t \cdot z}{b}\right)\right)}, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{t \cdot z}{b}\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\frac{t \cdot z}{b}\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(t \cdot z\right), b\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      4. *-lowering-*.f64 95.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), b\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   7. Simplified 95.3%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot \left(a + \frac{t \cdot z}{b}\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(a + \frac{t \cdot z}{b}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{t \cdot z}{b}\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{t \cdot z}{b}\right)}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{b}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 92.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), b\right)\right)\right)\right) \]

   10. Simplified 92.4%

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

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 72.3%

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

   if 8.19999999999999959e67 < (*.f64 c i)

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 75.6%

      \[\leadsto \color{blue}{x \cdot y} + c \cdot i \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -7.5 \cdot 10^{+159}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq -8 \cdot 10^{+143}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.06 \cdot 10^{-192}:\\ \;\;\;\;x \cdot y + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 8.2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + \frac{c \cdot i}{y}\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   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. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 42.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 42.9%

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

   6. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x + \frac{c \cdot i}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{c \cdot i}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(c \cdot i\right), \color{blue}{y}\right)\right)\right) \]

      4. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(c, i\right), y\right)\right)\right) \]

   8. Simplified 71.4%

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

Alternative 5: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.6 \cdot 10^{+238}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.7 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.6e+238)
   (+ (* c i) (* z t))
   (if (<= (* c i) 3.7e+112)
     (+ (* x y) (+ (* a b) (* z t)))
     (+ (* x y) (* 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) <= -2.6e+238) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 3.7e+112) {
		tmp = (x * y) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2.6d+238)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 3.7d+112) then
        tmp = (x * y) + ((a * b) + (z * t))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.6e+238) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 3.7e+112) {
		tmp = (x * y) + ((a * b) + (z * t));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.6e+238:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 3.7e+112:
		tmp = (x * y) + ((a * b) + (z * t))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.6e+238)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 3.7e+112)
		tmp = Float64(Float64(x * y) + Float64(Float64(a * b) + Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2.6e+238)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 3.7e+112)
		tmp = (x * y) + ((a * b) + (z * t));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2.6e+238], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 3.7e+112], N[(N[(x * y), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.6e238

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 96.5%

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

   if -2.6e238 < (*.f64 c i) < 3.70000000000000004e112

   1. Initial program 98.4%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 90.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 90.7%

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

         \[\leadsto \left(x \cdot y + a \cdot b\right) + \left(t \cdot z\right) \cdot \color{blue}{1} \]

      4. lft-mult-inverse N/A

         \[\leadsto \left(x \cdot y + a \cdot b\right) + \left(t \cdot z\right) \cdot \left(\frac{1}{b} \cdot \color{blue}{b}\right) \]

      5. associate-*l* N/A

         \[\leadsto \left(x \cdot y + a \cdot b\right) + \left(\left(t \cdot z\right) \cdot \frac{1}{b}\right) \cdot \color{blue}{b} \]

      6. div-inv N/A

         \[\leadsto \left(x \cdot y + a \cdot b\right) + \frac{t \cdot z}{b} \cdot b \]

      7. associate-+r+ N/A

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

      8. distribute-rgt-in N/A

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(b \cdot \left(a + \frac{t \cdot z}{b}\right)\right), \color{blue}{\left(x \cdot y\right)}\right) \]

      11. distribute-rgt-in N/A

          \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b + \frac{t \cdot z}{b} \cdot b\right), \left(\color{blue}{x} \cdot y\right)\right) \]

      12. div-inv N/A

          \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b + \left(\left(t \cdot z\right) \cdot \frac{1}{b}\right) \cdot b\right), \left(x \cdot y\right)\right) \]

      13. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b + \left(t \cdot z\right) \cdot \left(\frac{1}{b} \cdot b\right)\right), \left(x \cdot y\right)\right) \]

      14. lft-mult-inverse N/A

          \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b + \left(t \cdot z\right) \cdot 1\right), \left(x \cdot y\right)\right) \]

      15. *-rgt-identity N/A

          \[\leadsto \mathsf{+.f64}\left(\left(a \cdot b + t \cdot z\right), \left(x \cdot y\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z + a \cdot b\right), \left(\color{blue}{x} \cdot y\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(t \cdot z\right), \left(a \cdot b\right)\right), \left(\color{blue}{x} \cdot y\right)\right) \]

      18. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right) \]

      19. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(a, b\right)\right), \left(x \cdot y\right)\right) \]

      20. *-lowering-*.f64 90.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(a, b\right)\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 90.7%

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

   if 3.70000000000000004e112 < (*.f64 c i)

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 78.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.6 \cdot 10^{+238}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 3.7 \cdot 10^{+112}:\\ \;\;\;\;x \cdot y + \left(a \cdot b + z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.3 \cdot 10^{+228}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 10^{+115}:\\ \;\;\;\;z \cdot t + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.3e+228)
   (+ (* c i) (* z t))
   (if (<= (* c i) 1e+115)
     (+ (* z t) (+ (* x y) (* a b)))
     (+ (* x y) (* 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) <= -2.3e+228) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 1e+115) {
		tmp = (z * t) + ((x * y) + (a * b));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-2.3d+228)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 1d+115) then
        tmp = (z * t) + ((x * y) + (a * b))
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -2.3e+228) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 1e+115) {
		tmp = (z * t) + ((x * y) + (a * b));
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -2.3e+228:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 1e+115:
		tmp = (z * t) + ((x * y) + (a * b))
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -2.3e+228)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 1e+115)
		tmp = Float64(Float64(z * t) + Float64(Float64(x * y) + Float64(a * b)));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -2.3e+228)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 1e+115)
		tmp = (z * t) + ((x * y) + (a * b));
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -2.3e+228], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1e+115], N[(N[(z * t), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.30000000000000013e228

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 96.5%

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

   if -2.30000000000000013e228 < (*.f64 c i) < 1e115

   1. Initial program 98.4%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 90.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 90.7%

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

   if 1e115 < (*.f64 c i)

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 78.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 78.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.3 \cdot 10^{+228}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 10^{+115}:\\ \;\;\;\;z \cdot t + \left(x \cdot y + a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.6 \cdot 10^{+238}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.95 \cdot 10^{-181}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -2.6e+238)
   (* c i)
   (if (<= (* c i) -1.95e-181)
     (* z t)
     (if (<= (* c i) 1.35e+70) (* 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) <= -2.6e+238) {
		tmp = c * i;
	} else if ((c * i) <= -1.95e-181) {
		tmp = z * t;
	} else if ((c * i) <= 1.35e+70) {
		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) <= (-2.6d+238)) then
        tmp = c * i
    else if ((c * i) <= (-1.95d-181)) then
        tmp = z * t
    else if ((c * i) <= 1.35d+70) 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) <= -2.6e+238) {
		tmp = c * i;
	} else if ((c * i) <= -1.95e-181) {
		tmp = z * t;
	} else if ((c * i) <= 1.35e+70) {
		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) <= -2.6e+238:
		tmp = c * i
	elif (c * i) <= -1.95e-181:
		tmp = z * t
	elif (c * i) <= 1.35e+70:
		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) <= -2.6e+238)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= -1.95e-181)
		tmp = Float64(z * t);
	elseif (Float64(c * i) <= 1.35e+70)
		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) <= -2.6e+238)
		tmp = c * i;
	elseif ((c * i) <= -1.95e-181)
		tmp = z * t;
	elseif ((c * i) <= 1.35e+70)
		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], -2.6e+238], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], -1.95e-181], N[(z * t), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.35e+70], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -2.6e238 or 1.35e70 < (*.f64 c i)

   1. Initial program 94.5%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 71.4%

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

   if -2.6e238 < (*.f64 c i) < -1.95e-181

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 44.0%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 44.0%

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

   if -1.95e-181 < (*.f64 c i) < 1.35e70

   1. Initial program 97.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 44.4%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 44.4%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -2.6 \cdot 10^{+238}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq -1.95 \cdot 10^{-181}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+14}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.7e+14)
   (+ (* c i) (* z t))
   (if (<= (* c i) 1.8e+65) (+ (* x y) (* a b)) (+ (* x y) (* 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) <= -3.7e+14) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 1.8e+65) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((c * i) <= (-3.7d+14)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 1.8d+65) then
        tmp = (x * y) + (a * b)
    else
        tmp = (x * y) + (c * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -3.7e+14) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 1.8e+65) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (x * y) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -3.7e+14:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 1.8e+65:
		tmp = (x * y) + (a * b)
	else:
		tmp = (x * y) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -3.7e+14)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 1.8e+65)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	else
		tmp = Float64(Float64(x * y) + Float64(c * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((c * i) <= -3.7e+14)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 1.8e+65)
		tmp = (x * y) + (a * b);
	else
		tmp = (x * y) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -3.7e+14], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 1.8e+65], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -3.7e14

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 76.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 76.8%

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

   if -3.7e14 < (*.f64 c i) < 1.79999999999999989e65

   1. Initial program 97.9%

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

      1. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y + \left(z \cdot t + a \cdot b\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z \cdot t + a \cdot b\right) + x \cdot y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot t + a \cdot b\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot t\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(a, b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      7. *-lowering-*.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(a, b\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(a + \frac{t \cdot z}{b}\right)\right)}, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{t \cdot z}{b}\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\frac{t \cdot z}{b}\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(t \cdot z\right), b\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      4. *-lowering-*.f64 89.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), b\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   7. Simplified 89.9%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot \left(a + \frac{t \cdot z}{b}\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(a + \frac{t \cdot z}{b}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{t \cdot z}{b}\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{t \cdot z}{b}\right)}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{b}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 86.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), b\right)\right)\right)\right) \]

   10. Simplified 86.5%

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

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 67.7%

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

   if 1.79999999999999989e65 < (*.f64 c i)

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 75.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.7 \cdot 10^{+14}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.3e+15)
   (+ (* c i) (* z t))
   (if (<= (* c i) 9.5e+75) (+ (* x y) (* a b)) (+ (* a b) (* c i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((c * i) <= -1.3e+15) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 9.5e+75) {
		tmp = (x * y) + (a * b);
	} 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 ((c * i) <= (-1.3d+15)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 9.5d+75) then
        tmp = (x * y) + (a * b)
    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 ((c * i) <= -1.3e+15) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 9.5e+75) {
		tmp = (x * y) + (a * b);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.3e+15:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 9.5e+75:
		tmp = (x * y) + (a * b)
	else:
		tmp = (a * b) + (c * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(c * i) <= -1.3e+15)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 9.5e+75)
		tmp = Float64(Float64(x * y) + Float64(a * b));
	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 ((c * i) <= -1.3e+15)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 9.5e+75)
		tmp = (x * y) + (a * b);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.3e+15], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 9.5e+75], N[(N[(x * y), $MachinePrecision] + N[(a * b), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.3e15

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 76.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 76.8%

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

   if -1.3e15 < (*.f64 c i) < 9.50000000000000061e75

   1. Initial program 97.9%

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

      1. associate-+l+ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y + \left(z \cdot t + a \cdot b\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z \cdot t + a \cdot b\right) + x \cdot y\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot t + a \cdot b\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(z \cdot t\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \left(a \cdot b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(a, b\right)\right), \left(x \cdot y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      7. *-lowering-*.f64 97.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, t\right), \mathsf{*.f64}\left(a, b\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   4. Applied egg-rr 97.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(b \cdot \left(a + \frac{t \cdot z}{b}\right)\right)}, \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(a + \frac{t \cdot z}{b}\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\frac{t \cdot z}{b}\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(t \cdot z\right), b\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

      4. *-lowering-*.f64 90.1%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), b\right)\right)\right), \mathsf{*.f64}\left(x, y\right)\right), \mathsf{*.f64}\left(c, i\right)\right) \]

   7. Simplified 90.1%

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

   8. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(b \cdot \left(a + \frac{t \cdot z}{b}\right)\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{b} \cdot \left(a + \frac{t \cdot z}{b}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{t \cdot z}{b}\right)}\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{t \cdot z}{b}\right)}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\left(t \cdot z\right), \color{blue}{b}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 86.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, z\right), b\right)\right)\right)\right) \]

   10. Simplified 86.7%

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

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(b, \color{blue}{a}\right)\right) \]
   12. Step-by-step derivation

   13. Simplified 68.1%

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

   if 9.50000000000000061e75 < (*.f64 c i)

   1. Initial program 95.5%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 74.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.3 \cdot 10^{+15}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 9.5 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y + a \cdot b\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{-16}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.8 \cdot 10^{+91}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -5e-16)
   (+ (* c i) (* z t))
   (if (<= (* c i) 7.8e+91) (+ (* a b) (* 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 ((c * i) <= -5e-16) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 7.8e+91) {
		tmp = (a * b) + (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 ((c * i) <= (-5d-16)) then
        tmp = (c * i) + (z * t)
    else if ((c * i) <= 7.8d+91) then
        tmp = (a * b) + (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 ((c * i) <= -5e-16) {
		tmp = (c * i) + (z * t);
	} else if ((c * i) <= 7.8e+91) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -5e-16:
		tmp = (c * i) + (z * t)
	elif (c * i) <= 7.8e+91:
		tmp = (a * b) + (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 (Float64(c * i) <= -5e-16)
		tmp = Float64(Float64(c * i) + Float64(z * t));
	elseif (Float64(c * i) <= 7.8e+91)
		tmp = Float64(Float64(a * b) + 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 ((c * i) <= -5e-16)
		tmp = (c * i) + (z * t);
	elseif ((c * i) <= 7.8e+91)
		tmp = (a * b) + (z * t);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -5e-16], N[(N[(c * i), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 7.8e+91], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -5.0000000000000004e-16

   1. Initial program 97.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(t \cdot z\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 70.6%

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

   if -5.0000000000000004e-16 < (*.f64 c i) < 7.79999999999999935e91

   1. Initial program 97.8%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 95.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 95.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 68.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 68.2%

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

   if 7.79999999999999935e91 < (*.f64 c i)

   1. Initial program 95.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 75.5%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -5 \cdot 10^{-16}:\\ \;\;\;\;c \cdot i + z \cdot t\\ \mathbf{elif}\;c \cdot i \leq 7.8 \cdot 10^{+91}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+233}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.6 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -1.45e+233)
   (* c i)
   (if (<= (* c i) 2.6e+94) (+ (* a b) (* 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 ((c * i) <= -1.45e+233) {
		tmp = c * i;
	} else if ((c * i) <= 2.6e+94) {
		tmp = (a * b) + (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 ((c * i) <= (-1.45d+233)) then
        tmp = c * i
    else if ((c * i) <= 2.6d+94) then
        tmp = (a * b) + (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 ((c * i) <= -1.45e+233) {
		tmp = c * i;
	} else if ((c * i) <= 2.6e+94) {
		tmp = (a * b) + (z * t);
	} else {
		tmp = (a * b) + (c * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (c * i) <= -1.45e+233:
		tmp = c * i
	elif (c * i) <= 2.6e+94:
		tmp = (a * b) + (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 (Float64(c * i) <= -1.45e+233)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 2.6e+94)
		tmp = Float64(Float64(a * b) + 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 ((c * i) <= -1.45e+233)
		tmp = c * i;
	elseif ((c * i) <= 2.6e+94)
		tmp = (a * b) + (z * t);
	else
		tmp = (a * b) + (c * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(c * i), $MachinePrecision], -1.45e+233], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 2.6e+94], N[(N[(a * b), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c i) < -1.45000000000000006e233

   1. Initial program 92.3%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 93.0%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 93.0%

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

   if -1.45000000000000006e233 < (*.f64 c i) < 2.5999999999999999e94

   1. Initial program 98.4%

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

   3. Taylor expanded in c around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(t \cdot z\right), \color{blue}{\left(a \cdot b + x \cdot y\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \left(\color{blue}{a \cdot b} + x \cdot y\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\left(a \cdot b\right), \color{blue}{\left(x \cdot y\right)}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \left(\color{blue}{x} \cdot y\right)\right)\right) \]

      8. *-lowering-*.f64 91.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 91.0%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \color{blue}{\left(a \cdot b\right)}\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(t, z\right), \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right) \]

   8. Simplified 64.3%

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

   if 2.5999999999999999e94 < (*.f64 c i)

   1. Initial program 95.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 75.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 75.5%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \cdot i \leq -1.45 \cdot 10^{+233}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 2.6 \cdot 10^{+94}:\\ \;\;\;\;a \cdot b + z \cdot t\\ \mathbf{else}:\\ \;\;\;\;a \cdot b + c \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+137}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq 12.5:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.9e+137) (* z t) (if (<= z 12.5) (+ (* a b) (* 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 (z <= -1.9e+137) {
		tmp = z * t;
	} else if (z <= 12.5) {
		tmp = (a * b) + (c * i);
	} 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 <= (-1.9d+137)) then
        tmp = z * t
    else if (z <= 12.5d0) then
        tmp = (a * b) + (c * i)
    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 <= -1.9e+137) {
		tmp = z * t;
	} else if (z <= 12.5) {
		tmp = (a * b) + (c * i);
	} else {
		tmp = z * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.9e+137:
		tmp = z * t
	elif z <= 12.5:
		tmp = (a * b) + (c * i)
	else:
		tmp = z * t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.9e+137)
		tmp = Float64(z * t);
	elseif (z <= 12.5)
		tmp = Float64(Float64(a * b) + Float64(c * i));
	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 <= -1.9e+137)
		tmp = z * t;
	elseif (z <= 12.5)
		tmp = (a * b) + (c * i);
	else
		tmp = z * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.9e+137], N[(z * t), $MachinePrecision], If[LessEqual[z, 12.5], N[(N[(a * b), $MachinePrecision] + N[(c * i), $MachinePrecision]), $MachinePrecision], N[(z * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999981e137 or 12.5 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{t \cdot z} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 57.5%

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{z}\right) \]

   5. Simplified 57.5%

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

   if -1.89999999999999981e137 < z < 12.5

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(a \cdot b\right)}, \mathsf{*.f64}\left(c, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 64.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, b\right), \mathsf{*.f64}\left(\color{blue}{c}, i\right)\right) \]

   5. Simplified 64.0%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+137}:\\ \;\;\;\;z \cdot t\\ \mathbf{elif}\;z \leq 12.5:\\ \;\;\;\;a \cdot b + c \cdot i\\ \mathbf{else}:\\ \;\;\;\;z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \cdot i \leq -3.6 \cdot 10^{-17}:\\ \;\;\;\;c \cdot i\\ \mathbf{elif}\;c \cdot i \leq 4.2 \cdot 10^{+68}:\\ \;\;\;\;a \cdot b\\ \mathbf{else}:\\ \;\;\;\;c \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (* c i) -3.6e-17) (* c i) (if (<= (* c i) 4.2e+68) (* 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) <= -3.6e-17) {
		tmp = c * i;
	} else if ((c * i) <= 4.2e+68) {
		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) <= (-3.6d-17)) then
        tmp = c * i
    else if ((c * i) <= 4.2d+68) 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) <= -3.6e-17) {
		tmp = c * i;
	} else if ((c * i) <= 4.2e+68) {
		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) <= -3.6e-17:
		tmp = c * i
	elif (c * i) <= 4.2e+68:
		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) <= -3.6e-17)
		tmp = Float64(c * i);
	elseif (Float64(c * i) <= 4.2e+68)
		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) <= -3.6e-17)
		tmp = c * i;
	elseif ((c * i) <= 4.2e+68)
		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], -3.6e-17], N[(c * i), $MachinePrecision], If[LessEqual[N[(c * i), $MachinePrecision], 4.2e+68], N[(a * b), $MachinePrecision], N[(c * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c i) < -3.59999999999999995e-17 or 4.20000000000000002e68 < (*.f64 c i)

   1. Initial program 96.7%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot i} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 50.5%

         \[\leadsto \mathsf{*.f64}\left(c, \color{blue}{i}\right) \]

   5. Simplified 50.5%

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

   if -3.59999999999999995e-17 < (*.f64 c i) < 4.20000000000000002e68

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a \cdot b} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 39.1%

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

   5. Simplified 39.1%

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

Alternative 14: 26.8% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a \cdot b} \]
4. Step-by-step derivation

   1. *-lowering-*.f64 27.2%

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{b}\right) \]

5. Simplified 27.2%

   \[\leadsto \color{blue}{a \cdot b} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024145 
(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)))