Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 97.7% → 99.0%

Time: 13.5s

Alternatives: 13

Speedup: 1.0×

• 32.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \frac{a \cdot b}{-4}\right)\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (fma x y (fma z (/ t 16.0) (/ (* a b) -4.0))) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, y, fma(z, (t / 16.0), ((a * b) / -4.0))) + c;
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(fma(x, y, fma(z, Float64(t / 16.0), Float64(Float64(a * b) / -4.0))) + c)
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(x * y + N[(z * N[(t / 16.0), $MachinePrecision] + N[(N[(a * b), $MachinePrecision] / -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate--l+ 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \left(\frac{z \cdot t}{16} - \frac{a \cdot b}{4}\right)\right)} + c \]

   2. fma-define 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \frac{a \cdot b}{4}\right)} + c \]

   3. associate-/l* 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{z \cdot \frac{t}{16}} - \frac{a \cdot b}{4}\right) + c \]

   4. fma-neg 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(z, \frac{t}{16}, -\frac{a \cdot b}{4}\right)}\right) + c \]

   5. distribute-neg-frac2 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \color{blue}{\frac{a \cdot b}{-4}}\right)\right) + c \]

   6. metadata-eval 98.8%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \frac{a \cdot b}{\color{blue}{-4}}\right)\right) + c \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \frac{a \cdot b}{-4}\right)\right) + c} \]
4. Add Preprocessing

5. Final simplification 98.8%

   \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(z, \frac{t}{16}, \frac{a \cdot b}{-4}\right)\right) + c \]
6. Add Preprocessing

Alternative 2: 98.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ c + \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \frac{b}{4}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (- (fma x y (* z (/ t 16.0))) (* a (/ b 4.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + (fma(x, y, (z * (t / 16.0))) - (a * (b / 4.0)));
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(fma(x, y, Float64(z * Float64(t / 16.0))) - Float64(a * Float64(b / 4.0))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(N[(x * y + N[(z * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(b / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. *-commutative 98.4%

      \[\leadsto \left(x \cdot y + \frac{\color{blue}{t \cdot z}}{16}\right) - \left(\frac{a \cdot b}{4} - c\right) \]

   3. associate-+l- 98.4%

      \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{t \cdot z}{16}\right) - \frac{a \cdot b}{4}\right) + c} \]

   4. fma-define 98.8%

      \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, y, \frac{t \cdot z}{16}\right)} - \frac{a \cdot b}{4}\right) + c \]

   5. *-commutative 98.8%

      \[\leadsto \left(\mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot t}}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   6. associate-/l* 98.8%

      \[\leadsto \left(\mathsf{fma}\left(x, y, \color{blue}{z \cdot \frac{t}{16}}\right) - \frac{a \cdot b}{4}\right) + c \]

   7. associate-/l* 98.8%

      \[\leadsto \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - \color{blue}{a \cdot \frac{b}{4}}\right) + c \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \frac{b}{4}\right) + c} \]
4. Add Preprocessing

5. Final simplification 98.8%

   \[\leadsto c + \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \frac{b}{4}\right) \]
6. Add Preprocessing

Alternative 3: 66.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ t_3 := 0.0625 \cdot \left(z \cdot t\right) - t\_2\\ t_4 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \cdot y \leq -6.1 \cdot 10^{-164}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-316}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{-49}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 17000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y - t\_2\\ \mathbf{elif}\;x \cdot y \leq 10^{+67}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625))))
        (t_2 (* (* a b) 0.25))
        (t_3 (- (* 0.0625 (* z t)) t_2))
        (t_4 (+ c (* x y))))
   (if (<= (* x y) -1.85e+146)
     t_4
     (if (<= (* x y) -6.1e-164)
       t_3
       (if (<= (* x y) -1e-316)
         t_1
         (if (<= (* x y) 6.2e-49)
           t_3
           (if (<= (* x y) 17000.0)
             t_1
             (if (<= (* x y) 2.6e+32)
               (- (* x y) t_2)
               (if (<= (* x y) 1e+67)
                 (+ c (* b (* a -0.25)))
                 (if (<= (* x y) 4e+114) t_1 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (z * (t * 0.0625));
	double t_2 = (a * b) * 0.25;
	double t_3 = (0.0625 * (z * t)) - t_2;
	double t_4 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.85e+146) {
		tmp = t_4;
	} else if ((x * y) <= -6.1e-164) {
		tmp = t_3;
	} else if ((x * y) <= -1e-316) {
		tmp = t_1;
	} else if ((x * y) <= 6.2e-49) {
		tmp = t_3;
	} else if ((x * y) <= 17000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2.6e+32) {
		tmp = (x * y) - t_2;
	} else if ((x * y) <= 1e+67) {
		tmp = c + (b * (a * -0.25));
	} else if ((x * y) <= 4e+114) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = c + (z * (t * 0.0625d0))
    t_2 = (a * b) * 0.25d0
    t_3 = (0.0625d0 * (z * t)) - t_2
    t_4 = c + (x * y)
    if ((x * y) <= (-1.85d+146)) then
        tmp = t_4
    else if ((x * y) <= (-6.1d-164)) then
        tmp = t_3
    else if ((x * y) <= (-1d-316)) then
        tmp = t_1
    else if ((x * y) <= 6.2d-49) then
        tmp = t_3
    else if ((x * y) <= 17000.0d0) then
        tmp = t_1
    else if ((x * y) <= 2.6d+32) then
        tmp = (x * y) - t_2
    else if ((x * y) <= 1d+67) then
        tmp = c + (b * (a * (-0.25d0)))
    else if ((x * y) <= 4d+114) then
        tmp = t_1
    else
        tmp = t_4
    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 t_1 = c + (z * (t * 0.0625));
	double t_2 = (a * b) * 0.25;
	double t_3 = (0.0625 * (z * t)) - t_2;
	double t_4 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.85e+146) {
		tmp = t_4;
	} else if ((x * y) <= -6.1e-164) {
		tmp = t_3;
	} else if ((x * y) <= -1e-316) {
		tmp = t_1;
	} else if ((x * y) <= 6.2e-49) {
		tmp = t_3;
	} else if ((x * y) <= 17000.0) {
		tmp = t_1;
	} else if ((x * y) <= 2.6e+32) {
		tmp = (x * y) - t_2;
	} else if ((x * y) <= 1e+67) {
		tmp = c + (b * (a * -0.25));
	} else if ((x * y) <= 4e+114) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (z * (t * 0.0625))
	t_2 = (a * b) * 0.25
	t_3 = (0.0625 * (z * t)) - t_2
	t_4 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.85e+146:
		tmp = t_4
	elif (x * y) <= -6.1e-164:
		tmp = t_3
	elif (x * y) <= -1e-316:
		tmp = t_1
	elif (x * y) <= 6.2e-49:
		tmp = t_3
	elif (x * y) <= 17000.0:
		tmp = t_1
	elif (x * y) <= 2.6e+32:
		tmp = (x * y) - t_2
	elif (x * y) <= 1e+67:
		tmp = c + (b * (a * -0.25))
	elif (x * y) <= 4e+114:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_2 = Float64(Float64(a * b) * 0.25)
	t_3 = Float64(Float64(0.0625 * Float64(z * t)) - t_2)
	t_4 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.85e+146)
		tmp = t_4;
	elseif (Float64(x * y) <= -6.1e-164)
		tmp = t_3;
	elseif (Float64(x * y) <= -1e-316)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.2e-49)
		tmp = t_3;
	elseif (Float64(x * y) <= 17000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.6e+32)
		tmp = Float64(Float64(x * y) - t_2);
	elseif (Float64(x * y) <= 1e+67)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (Float64(x * y) <= 4e+114)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (z * (t * 0.0625));
	t_2 = (a * b) * 0.25;
	t_3 = (0.0625 * (z * t)) - t_2;
	t_4 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.85e+146)
		tmp = t_4;
	elseif ((x * y) <= -6.1e-164)
		tmp = t_3;
	elseif ((x * y) <= -1e-316)
		tmp = t_1;
	elseif ((x * y) <= 6.2e-49)
		tmp = t_3;
	elseif ((x * y) <= 17000.0)
		tmp = t_1;
	elseif ((x * y) <= 2.6e+32)
		tmp = (x * y) - t_2;
	elseif ((x * y) <= 1e+67)
		tmp = c + (b * (a * -0.25));
	elseif ((x * y) <= 4e+114)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$3 = N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.85e+146], t$95$4, If[LessEqual[N[(x * y), $MachinePrecision], -6.1e-164], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1e-316], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.2e-49], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 17000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.6e+32], N[(N[(x * y), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+67], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+114], t$95$1, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.85000000000000002e146 or 4e114 < (*.f64 x y)

   1. Initial program 96.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.9%

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

   if -1.85000000000000002e146 < (*.f64 x y) < -6.10000000000000013e-164 or -9.999999837e-317 < (*.f64 x y) < 6.2e-49

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.5%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 73.5%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -6.10000000000000013e-164 < (*.f64 x y) < -9.999999837e-317 or 6.2e-49 < (*.f64 x y) < 17000 or 9.99999999999999983e66 < (*.f64 x y) < 4e114

   1. Initial program 97.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 85.6%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 85.6%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 85.6%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 85.6%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 85.6%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   5. Simplified 85.6%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   if 17000 < (*.f64 x y) < 2.6000000000000002e32

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 84.7%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 84.7%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   if 2.6000000000000002e32 < (*.f64 x y) < 9.99999999999999983e66

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 99.6%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -6.1 \cdot 10^{-164}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-316}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{-49}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 17000:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.6 \cdot 10^{+32}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 10^{+67}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+114}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 44.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.1 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-316}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5.3 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))) (t_2 (* 0.0625 (* z t))))
   (if (<= (* x y) -2.6e+145)
     (* x y)
     (if (<= (* x y) -3.1e-164)
       t_1
       (if (<= (* x y) -1e-316)
         c
         (if (<= (* x y) 7.6e-169)
           t_1
           (if (<= (* x y) 5.3e-15)
             t_2
             (if (<= (* x y) 9.5e+66)
               t_1
               (if (<= (* x y) 4.1e+123) t_2 (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -2.6e+145) {
		tmp = x * y;
	} else if ((x * y) <= -3.1e-164) {
		tmp = t_1;
	} else if ((x * y) <= -1e-316) {
		tmp = c;
	} else if ((x * y) <= 7.6e-169) {
		tmp = t_1;
	} else if ((x * y) <= 5.3e-15) {
		tmp = t_2;
	} else if ((x * y) <= 9.5e+66) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e+123) {
		tmp = t_2;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    t_2 = 0.0625d0 * (z * t)
    if ((x * y) <= (-2.6d+145)) then
        tmp = x * y
    else if ((x * y) <= (-3.1d-164)) then
        tmp = t_1
    else if ((x * y) <= (-1d-316)) then
        tmp = c
    else if ((x * y) <= 7.6d-169) then
        tmp = t_1
    else if ((x * y) <= 5.3d-15) then
        tmp = t_2
    else if ((x * y) <= 9.5d+66) then
        tmp = t_1
    else if ((x * y) <= 4.1d+123) then
        tmp = t_2
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -2.6e+145) {
		tmp = x * y;
	} else if ((x * y) <= -3.1e-164) {
		tmp = t_1;
	} else if ((x * y) <= -1e-316) {
		tmp = c;
	} else if ((x * y) <= 7.6e-169) {
		tmp = t_1;
	} else if ((x * y) <= 5.3e-15) {
		tmp = t_2;
	} else if ((x * y) <= 9.5e+66) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e+123) {
		tmp = t_2;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (x * y) <= -2.6e+145:
		tmp = x * y
	elif (x * y) <= -3.1e-164:
		tmp = t_1
	elif (x * y) <= -1e-316:
		tmp = c
	elif (x * y) <= 7.6e-169:
		tmp = t_1
	elif (x * y) <= 5.3e-15:
		tmp = t_2
	elif (x * y) <= 9.5e+66:
		tmp = t_1
	elif (x * y) <= 4.1e+123:
		tmp = t_2
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -2.6e+145)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.1e-164)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-316)
		tmp = c;
	elseif (Float64(x * y) <= 7.6e-169)
		tmp = t_1;
	elseif (Float64(x * y) <= 5.3e-15)
		tmp = t_2;
	elseif (Float64(x * y) <= 9.5e+66)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.1e+123)
		tmp = t_2;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((x * y) <= -2.6e+145)
		tmp = x * y;
	elseif ((x * y) <= -3.1e-164)
		tmp = t_1;
	elseif ((x * y) <= -1e-316)
		tmp = c;
	elseif ((x * y) <= 7.6e-169)
		tmp = t_1;
	elseif ((x * y) <= 5.3e-15)
		tmp = t_2;
	elseif ((x * y) <= 9.5e+66)
		tmp = t_1;
	elseif ((x * y) <= 4.1e+123)
		tmp = t_2;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.6e+145], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.1e-164], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-316], c, If[LessEqual[N[(x * y), $MachinePrecision], 7.6e-169], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5.3e-15], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 9.5e+66], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.1e+123], t$95$2, N[(x * y), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.60000000000000003e145 or 4.09999999999999989e123 < (*.f64 x y)

   1. Initial program 96.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 90.7%

      \[\leadsto \color{blue}{\left(x \cdot y - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fma-neg 90.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -0.25 \cdot \left(a \cdot b\right)\right)} + c \]

      2. distribute-lft-neg-in 90.7%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25\right) \cdot \left(a \cdot b\right)}\right) + c \]

      3. metadata-eval 90.7%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{-0.25} \cdot \left(a \cdot b\right)\right) + c \]

      4. associate-*r* 90.7%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25 \cdot a\right) \cdot b}\right) + c \]

   5. Simplified 90.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} + c \]
   6. Step-by-step derivation

      1. +-commutative 90.7%

         \[\leadsto \color{blue}{c + \mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} \]

      2. fma-undefine 90.7%

         \[\leadsto c + \color{blue}{\left(x \cdot y + \left(-0.25 \cdot a\right) \cdot b\right)} \]

      3. associate-+r+ 90.7%

         \[\leadsto \color{blue}{\left(c + x \cdot y\right) + \left(-0.25 \cdot a\right) \cdot b} \]

      4. *-commutative 90.7%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      5. associate-*r* 90.7%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

      6. *-commutative 90.7%

         \[\leadsto \left(c + x \cdot y\right) + a \cdot \color{blue}{\left(b \cdot -0.25\right)} \]

      7. +-commutative 90.7%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right) + \left(c + x \cdot y\right)} \]

      8. *-commutative 90.7%

         \[\leadsto \color{blue}{\left(b \cdot -0.25\right) \cdot a} + \left(c + x \cdot y\right) \]

      9. fma-define 91.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot -0.25, a, c + x \cdot y\right)} \]

      10. *-commutative 91.7%

          \[\leadsto \mathsf{fma}\left(\color{blue}{-0.25 \cdot b}, a, c + x \cdot y\right) \]

      11. +-commutative 91.7%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{x \cdot y + c}\right) \]

      12. fma-undefine 91.7%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{\mathsf{fma}\left(x, y, c\right)}\right) \]

   7. Applied egg-rr 91.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.25 \cdot b, a, \mathsf{fma}\left(x, y, c\right)\right)} \]

   8. Taylor expanded in x around inf 78.6%

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

   if -2.60000000000000003e145 < (*.f64 x y) < -3.1000000000000001e-164 or -9.999999837e-317 < (*.f64 x y) < 7.6000000000000001e-169 or 5.3000000000000001e-15 < (*.f64 x y) < 9.50000000000000051e66

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 75.4%

      \[\leadsto \color{blue}{\left(x \cdot y - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fma-neg 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -0.25 \cdot \left(a \cdot b\right)\right)} + c \]

      2. distribute-lft-neg-in 75.4%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25\right) \cdot \left(a \cdot b\right)}\right) + c \]

      3. metadata-eval 75.4%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{-0.25} \cdot \left(a \cdot b\right)\right) + c \]

      4. associate-*r* 75.4%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25 \cdot a\right) \cdot b}\right) + c \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} + c \]
   6. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto \color{blue}{c + \mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} \]

      2. fma-undefine 75.4%

         \[\leadsto c + \color{blue}{\left(x \cdot y + \left(-0.25 \cdot a\right) \cdot b\right)} \]

      3. associate-+r+ 75.4%

         \[\leadsto \color{blue}{\left(c + x \cdot y\right) + \left(-0.25 \cdot a\right) \cdot b} \]

      4. *-commutative 75.4%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      5. associate-*r* 75.4%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

      6. *-commutative 75.4%

         \[\leadsto \left(c + x \cdot y\right) + a \cdot \color{blue}{\left(b \cdot -0.25\right)} \]

      7. +-commutative 75.4%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right) + \left(c + x \cdot y\right)} \]

      8. *-commutative 75.4%

         \[\leadsto \color{blue}{\left(b \cdot -0.25\right) \cdot a} + \left(c + x \cdot y\right) \]

      9. fma-define 75.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot -0.25, a, c + x \cdot y\right)} \]

      10. *-commutative 75.4%

          \[\leadsto \mathsf{fma}\left(\color{blue}{-0.25 \cdot b}, a, c + x \cdot y\right) \]

      11. +-commutative 75.4%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{x \cdot y + c}\right) \]

      12. fma-undefine 75.4%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{\mathsf{fma}\left(x, y, c\right)}\right) \]

   7. Applied egg-rr 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.25 \cdot b, a, \mathsf{fma}\left(x, y, c\right)\right)} \]

   8. Taylor expanded in b around inf 43.5%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   9. Step-by-step derivation

      1. *-commutative 43.5%

         \[\leadsto -0.25 \cdot \color{blue}{\left(b \cdot a\right)} \]

      2. associate-*r* 43.5%

         \[\leadsto \color{blue}{\left(-0.25 \cdot b\right) \cdot a} \]

      3. *-commutative 43.5%

         \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

   10. Simplified 43.5%

       \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

   if -3.1000000000000001e-164 < (*.f64 x y) < -9.999999837e-317

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 51.4%

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

   if 7.6000000000000001e-169 < (*.f64 x y) < 5.3000000000000001e-15 or 9.50000000000000051e66 < (*.f64 x y) < 4.09999999999999989e123

   1. Initial program 96.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.5%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 84.5%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 84.5%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 84.5%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 84.5%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   5. Simplified 84.5%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   6. Taylor expanded in z around inf 61.2%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+145}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.1 \cdot 10^{-164}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-316}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{-169}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 5.3 \cdot 10^{-15}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 9.5 \cdot 10^{+66}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{+123}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+135}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-316}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* x y) -1.45e+135)
     (* x y)
     (if (<= (* x y) -1.9e-81)
       t_1
       (if (<= (* x y) -1e-316)
         c
         (if (<= (* x y) 5.2e-30)
           t_1
           (if (<= (* x y) 1.05e+64)
             c
             (if (<= (* x y) 5.8e+123) t_1 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -1.45e+135) {
		tmp = x * y;
	} else if ((x * y) <= -1.9e-81) {
		tmp = t_1;
	} else if ((x * y) <= -1e-316) {
		tmp = c;
	} else if ((x * y) <= 5.2e-30) {
		tmp = t_1;
	} else if ((x * y) <= 1.05e+64) {
		tmp = c;
	} else if ((x * y) <= 5.8e+123) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((x * y) <= (-1.45d+135)) then
        tmp = x * y
    else if ((x * y) <= (-1.9d-81)) then
        tmp = t_1
    else if ((x * y) <= (-1d-316)) then
        tmp = c
    else if ((x * y) <= 5.2d-30) then
        tmp = t_1
    else if ((x * y) <= 1.05d+64) then
        tmp = c
    else if ((x * y) <= 5.8d+123) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -1.45e+135) {
		tmp = x * y;
	} else if ((x * y) <= -1.9e-81) {
		tmp = t_1;
	} else if ((x * y) <= -1e-316) {
		tmp = c;
	} else if ((x * y) <= 5.2e-30) {
		tmp = t_1;
	} else if ((x * y) <= 1.05e+64) {
		tmp = c;
	} else if ((x * y) <= 5.8e+123) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (x * y) <= -1.45e+135:
		tmp = x * y
	elif (x * y) <= -1.9e-81:
		tmp = t_1
	elif (x * y) <= -1e-316:
		tmp = c
	elif (x * y) <= 5.2e-30:
		tmp = t_1
	elif (x * y) <= 1.05e+64:
		tmp = c
	elif (x * y) <= 5.8e+123:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -1.45e+135)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.9e-81)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-316)
		tmp = c;
	elseif (Float64(x * y) <= 5.2e-30)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.05e+64)
		tmp = c;
	elseif (Float64(x * y) <= 5.8e+123)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((x * y) <= -1.45e+135)
		tmp = x * y;
	elseif ((x * y) <= -1.9e-81)
		tmp = t_1;
	elseif ((x * y) <= -1e-316)
		tmp = c;
	elseif ((x * y) <= 5.2e-30)
		tmp = t_1;
	elseif ((x * y) <= 1.05e+64)
		tmp = c;
	elseif ((x * y) <= 5.8e+123)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.45e+135], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.9e-81], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-316], c, If[LessEqual[N[(x * y), $MachinePrecision], 5.2e-30], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.05e+64], c, If[LessEqual[N[(x * y), $MachinePrecision], 5.8e+123], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.4499999999999999e135 or 5.80000000000000019e123 < (*.f64 x y)

   1. Initial program 96.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 90.9%

      \[\leadsto \color{blue}{\left(x \cdot y - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fma-neg 90.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -0.25 \cdot \left(a \cdot b\right)\right)} + c \]

      2. distribute-lft-neg-in 90.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25\right) \cdot \left(a \cdot b\right)}\right) + c \]

      3. metadata-eval 90.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{-0.25} \cdot \left(a \cdot b\right)\right) + c \]

      4. associate-*r* 90.9%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25 \cdot a\right) \cdot b}\right) + c \]

   5. Simplified 90.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} + c \]
   6. Step-by-step derivation

      1. +-commutative 90.9%

         \[\leadsto \color{blue}{c + \mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} \]

      2. fma-undefine 90.9%

         \[\leadsto c + \color{blue}{\left(x \cdot y + \left(-0.25 \cdot a\right) \cdot b\right)} \]

      3. associate-+r+ 90.9%

         \[\leadsto \color{blue}{\left(c + x \cdot y\right) + \left(-0.25 \cdot a\right) \cdot b} \]

      4. *-commutative 90.9%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      5. associate-*r* 90.9%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

      6. *-commutative 90.9%

         \[\leadsto \left(c + x \cdot y\right) + a \cdot \color{blue}{\left(b \cdot -0.25\right)} \]

      7. +-commutative 90.9%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right) + \left(c + x \cdot y\right)} \]

      8. *-commutative 90.9%

         \[\leadsto \color{blue}{\left(b \cdot -0.25\right) \cdot a} + \left(c + x \cdot y\right) \]

      9. fma-define 91.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot -0.25, a, c + x \cdot y\right)} \]

      10. *-commutative 91.9%

          \[\leadsto \mathsf{fma}\left(\color{blue}{-0.25 \cdot b}, a, c + x \cdot y\right) \]

      11. +-commutative 91.9%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{x \cdot y + c}\right) \]

      12. fma-undefine 91.9%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{\mathsf{fma}\left(x, y, c\right)}\right) \]

   7. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.25 \cdot b, a, \mathsf{fma}\left(x, y, c\right)\right)} \]

   8. Taylor expanded in x around inf 77.1%

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

   if -1.4499999999999999e135 < (*.f64 x y) < -1.8999999999999999e-81 or -9.999999837e-317 < (*.f64 x y) < 5.19999999999999973e-30 or 1.05e64 < (*.f64 x y) < 5.80000000000000019e123

   1. Initial program 99.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 60.6%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 60.6%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 60.6%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 60.6%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   5. Simplified 60.6%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   6. Taylor expanded in z around inf 40.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]

   if -1.8999999999999999e-81 < (*.f64 x y) < -9.999999837e-317 or 5.19999999999999973e-30 < (*.f64 x y) < 1.05e64

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 43.7%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+135}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.9 \cdot 10^{-81}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-316}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 5.2 \cdot 10^{-30}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+123}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ t_2 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{+145}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 1.52 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2300000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{+120}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25))))
        (t_2 (+ c (* z (* t 0.0625))))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -1.95e+145)
     t_3
     (if (<= (* x y) 1.52e-171)
       t_1
       (if (<= (* x y) 2300000000000.0)
         t_2
         (if (<= (* x y) 1e+67) t_1 (if (<= (* x y) 1.3e+120) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (z * (t * 0.0625));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.95e+145) {
		tmp = t_3;
	} else if ((x * y) <= 1.52e-171) {
		tmp = t_1;
	} else if ((x * y) <= 2300000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 1e+67) {
		tmp = t_1;
	} else if ((x * y) <= 1.3e+120) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    t_2 = c + (z * (t * 0.0625d0))
    t_3 = c + (x * y)
    if ((x * y) <= (-1.95d+145)) then
        tmp = t_3
    else if ((x * y) <= 1.52d-171) then
        tmp = t_1
    else if ((x * y) <= 2300000000000.0d0) then
        tmp = t_2
    else if ((x * y) <= 1d+67) then
        tmp = t_1
    else if ((x * y) <= 1.3d+120) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (z * (t * 0.0625));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.95e+145) {
		tmp = t_3;
	} else if ((x * y) <= 1.52e-171) {
		tmp = t_1;
	} else if ((x * y) <= 2300000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 1e+67) {
		tmp = t_1;
	} else if ((x * y) <= 1.3e+120) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	t_2 = c + (z * (t * 0.0625))
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.95e+145:
		tmp = t_3
	elif (x * y) <= 1.52e-171:
		tmp = t_1
	elif (x * y) <= 2300000000000.0:
		tmp = t_2
	elif (x * y) <= 1e+67:
		tmp = t_1
	elif (x * y) <= 1.3e+120:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_2 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.95e+145)
		tmp = t_3;
	elseif (Float64(x * y) <= 1.52e-171)
		tmp = t_1;
	elseif (Float64(x * y) <= 2300000000000.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 1e+67)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.3e+120)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	t_2 = c + (z * (t * 0.0625));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.95e+145)
		tmp = t_3;
	elseif ((x * y) <= 1.52e-171)
		tmp = t_1;
	elseif ((x * y) <= 2300000000000.0)
		tmp = t_2;
	elseif ((x * y) <= 1e+67)
		tmp = t_1;
	elseif ((x * y) <= 1.3e+120)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.95e+145], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 1.52e-171], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2300000000000.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1e+67], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.3e+120], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.9499999999999999e145 or 1.2999999999999999e120 < (*.f64 x y)

   1. Initial program 96.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.9%

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

   if -1.9499999999999999e145 < (*.f64 x y) < 1.51999999999999995e-171 or 2.3e12 < (*.f64 x y) < 9.99999999999999983e66

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 68.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 68.9%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

   5. Simplified 68.9%

      \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} + c \]

   if 1.51999999999999995e-171 < (*.f64 x y) < 2.3e12 or 9.99999999999999983e66 < (*.f64 x y) < 1.2999999999999999e120

   1. Initial program 97.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.8%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 77.8%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 77.8%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 77.8%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   5. Simplified 77.8%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.95 \cdot 10^{+145}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.52 \cdot 10^{-171}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2300000000000:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+67}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{+120}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+145} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+118}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (or (<= (* x y) -2.6e+145) (not (<= (* x y) 7.5e+118)))
     (- (+ c (* x y)) t_1)
     (- (+ c (* 0.0625 (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -2.6e+145) || !((x * y) <= 7.5e+118)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    if (((x * y) <= (-2.6d+145)) .or. (.not. ((x * y) <= 7.5d+118))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (c + (0.0625d0 * (z * t))) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -2.6e+145) || !((x * y) <= 7.5e+118)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if ((x * y) <= -2.6e+145) or not ((x * y) <= 7.5e+118):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (c + (0.0625 * (z * t))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if ((Float64(x * y) <= -2.6e+145) || !(Float64(x * y) <= 7.5e+118))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(z * t))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if (((x * y) <= -2.6e+145) || ~(((x * y) <= 7.5e+118)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (c + (0.0625 * (z * t))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.6e+145], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7.5e+118]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.60000000000000003e145 or 7.50000000000000003e118 < (*.f64 x y)

   1. Initial program 96.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 90.8%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2.60000000000000003e145 < (*.f64 x y) < 7.50000000000000003e118

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.2%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+145} \lor \neg \left(x \cdot y \leq 7.5 \cdot 10^{+118}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* 0.0625 (* z t))))
   (if (<= t -6.4e+38)
     t_2
     (if (<= t 6.5e-270)
       t_1
       (if (<= t 1.5e-234) (* a (* b -0.25)) (if (<= t 5e+154) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if (t <= -6.4e+38) {
		tmp = t_2;
	} else if (t <= 6.5e-270) {
		tmp = t_1;
	} else if (t <= 1.5e-234) {
		tmp = a * (b * -0.25);
	} else if (t <= 5e+154) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = 0.0625d0 * (z * t)
    if (t <= (-6.4d+38)) then
        tmp = t_2
    else if (t <= 6.5d-270) then
        tmp = t_1
    else if (t <= 1.5d-234) then
        tmp = a * (b * (-0.25d0))
    else if (t <= 5d+154) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if (t <= -6.4e+38) {
		tmp = t_2;
	} else if (t <= 6.5e-270) {
		tmp = t_1;
	} else if (t <= 1.5e-234) {
		tmp = a * (b * -0.25);
	} else if (t <= 5e+154) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if t <= -6.4e+38:
		tmp = t_2
	elif t <= 6.5e-270:
		tmp = t_1
	elif t <= 1.5e-234:
		tmp = a * (b * -0.25)
	elif t <= 5e+154:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (t <= -6.4e+38)
		tmp = t_2;
	elseif (t <= 6.5e-270)
		tmp = t_1;
	elseif (t <= 1.5e-234)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (t <= 5e+154)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if (t <= -6.4e+38)
		tmp = t_2;
	elseif (t <= 6.5e-270)
		tmp = t_1;
	elseif (t <= 1.5e-234)
		tmp = a * (b * -0.25);
	elseif (t <= 5e+154)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.4e+38], t$95$2, If[LessEqual[t, 6.5e-270], t$95$1, If[LessEqual[t, 1.5e-234], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+154], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.3999999999999997e38 or 5.00000000000000004e154 < t

   1. Initial program 97.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.6%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 64.6%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 64.6%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 64.6%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 64.6%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   5. Simplified 64.6%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   6. Taylor expanded in z around inf 53.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]

   if -6.3999999999999997e38 < t < 6.5000000000000001e-270 or 1.49999999999999994e-234 < t < 5.00000000000000004e154

   1. Initial program 98.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 60.4%

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

   if 6.5000000000000001e-270 < t < 1.49999999999999994e-234

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 94.1%

      \[\leadsto \color{blue}{\left(x \cdot y - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fma-neg 94.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -0.25 \cdot \left(a \cdot b\right)\right)} + c \]

      2. distribute-lft-neg-in 94.1%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25\right) \cdot \left(a \cdot b\right)}\right) + c \]

      3. metadata-eval 94.1%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{-0.25} \cdot \left(a \cdot b\right)\right) + c \]

      4. associate-*r* 94.1%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25 \cdot a\right) \cdot b}\right) + c \]

   5. Simplified 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} + c \]
   6. Step-by-step derivation

      1. +-commutative 94.1%

         \[\leadsto \color{blue}{c + \mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} \]

      2. fma-undefine 94.1%

         \[\leadsto c + \color{blue}{\left(x \cdot y + \left(-0.25 \cdot a\right) \cdot b\right)} \]

      3. associate-+r+ 94.1%

         \[\leadsto \color{blue}{\left(c + x \cdot y\right) + \left(-0.25 \cdot a\right) \cdot b} \]

      4. *-commutative 94.1%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      5. associate-*r* 94.1%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

      6. *-commutative 94.1%

         \[\leadsto \left(c + x \cdot y\right) + a \cdot \color{blue}{\left(b \cdot -0.25\right)} \]

      7. +-commutative 94.1%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right) + \left(c + x \cdot y\right)} \]

      8. *-commutative 94.1%

         \[\leadsto \color{blue}{\left(b \cdot -0.25\right) \cdot a} + \left(c + x \cdot y\right) \]

      9. fma-define 94.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot -0.25, a, c + x \cdot y\right)} \]

      10. *-commutative 94.1%

          \[\leadsto \mathsf{fma}\left(\color{blue}{-0.25 \cdot b}, a, c + x \cdot y\right) \]

      11. +-commutative 94.1%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{x \cdot y + c}\right) \]

      12. fma-undefine 94.1%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{\mathsf{fma}\left(x, y, c\right)}\right) \]

   7. Applied egg-rr 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.25 \cdot b, a, \mathsf{fma}\left(x, y, c\right)\right)} \]

   8. Taylor expanded in b around inf 65.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   9. Step-by-step derivation

      1. *-commutative 65.9%

         \[\leadsto -0.25 \cdot \color{blue}{\left(b \cdot a\right)} \]

      2. associate-*r* 65.9%

         \[\leadsto \color{blue}{\left(-0.25 \cdot b\right) \cdot a} \]

      3. *-commutative 65.9%

         \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

   10. Simplified 65.9%

       \[\leadsto \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+38}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-270}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+154}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+135} \lor \neg \left(x \cdot y \leq 4.8 \cdot 10^{+117}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.45e+135) (not (<= (* x y) 4.8e+117)))
   (+ c (* x y))
   (+ c (* z (* t 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.45e+135) || !((x * y) <= 4.8e+117)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (((x * y) <= (-1.45d+135)) .or. (.not. ((x * y) <= 4.8d+117))) then
        tmp = c + (x * y)
    else
        tmp = c + (z * (t * 0.0625d0))
    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 tmp;
	if (((x * y) <= -1.45e+135) || !((x * y) <= 4.8e+117)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.45e+135) or not ((x * y) <= 4.8e+117):
		tmp = c + (x * y)
	else:
		tmp = c + (z * (t * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.45e+135) || !(Float64(x * y) <= 4.8e+117))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.45e+135) || ~(((x * y) <= 4.8e+117)))
		tmp = c + (x * y);
	else
		tmp = c + (z * (t * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.45e+135], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.8e+117]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.4499999999999999e135 or 4.7999999999999998e117 < (*.f64 x y)

   1. Initial program 97.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 85.2%

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

   if -1.4499999999999999e135 < (*.f64 x y) < 4.7999999999999998e117

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 61.8%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 61.8%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 61.8%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 61.8%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   5. Simplified 61.8%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+135} \lor \neg \left(x \cdot y \leq 4.8 \cdot 10^{+117}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+38}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+174}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -6.4e+38)
   (* 0.0625 (* z t))
   (if (<= t 1.95e+174)
     (- (+ c (* x y)) (* (* a b) 0.25))
     (+ c (* z (* t 0.0625))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -6.4e+38) {
		tmp = 0.0625 * (z * t);
	} else if (t <= 1.95e+174) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (t <= (-6.4d+38)) then
        tmp = 0.0625d0 * (z * t)
    else if (t <= 1.95d+174) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + (z * (t * 0.0625d0))
    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 tmp;
	if (t <= -6.4e+38) {
		tmp = 0.0625 * (z * t);
	} else if (t <= 1.95e+174) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -6.4e+38:
		tmp = 0.0625 * (z * t)
	elif t <= 1.95e+174:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + (z * (t * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -6.4e+38)
		tmp = Float64(0.0625 * Float64(z * t));
	elseif (t <= 1.95e+174)
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -6.4e+38)
		tmp = 0.0625 * (z * t);
	elseif (t <= 1.95e+174)
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + (z * (t * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -6.4e+38], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+174], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.3999999999999997e38

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 57.8%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 57.8%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 57.8%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 57.8%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 57.8%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   5. Simplified 57.8%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   6. Taylor expanded in z around inf 43.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]

   if -6.3999999999999997e38 < t < 1.9499999999999999e174

   1. Initial program 98.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.3%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if 1.9499999999999999e174 < t

   1. Initial program 91.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 87.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 87.3%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 87.3%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 87.3%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 87.3%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   5. Simplified 87.3%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+38}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+174}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.7 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 1.28 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -3.7e+90) (not (<= (* x y) 1.28e+138))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -3.7e+90) || !((x * y) <= 1.28e+138)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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) :: tmp
    if (((x * y) <= (-3.7d+90)) .or. (.not. ((x * y) <= 1.28d+138))) then
        tmp = x * y
    else
        tmp = c
    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 tmp;
	if (((x * y) <= -3.7e+90) || !((x * y) <= 1.28e+138)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -3.7e+90) or not ((x * y) <= 1.28e+138):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -3.7e+90) || !(Float64(x * y) <= 1.28e+138))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -3.7e+90) || ~(((x * y) <= 1.28e+138)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.7e+90], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.28e+138]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.7e90 or 1.28000000000000008e138 < (*.f64 x y)

   1. Initial program 97.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.6%

      \[\leadsto \color{blue}{\left(x \cdot y - 0.25 \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fma-neg 89.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -0.25 \cdot \left(a \cdot b\right)\right)} + c \]

      2. distribute-lft-neg-in 89.6%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25\right) \cdot \left(a \cdot b\right)}\right) + c \]

      3. metadata-eval 89.6%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{-0.25} \cdot \left(a \cdot b\right)\right) + c \]

      4. associate-*r* 89.6%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-0.25 \cdot a\right) \cdot b}\right) + c \]

   5. Simplified 89.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} + c \]
   6. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \color{blue}{c + \mathsf{fma}\left(x, y, \left(-0.25 \cdot a\right) \cdot b\right)} \]

      2. fma-undefine 89.6%

         \[\leadsto c + \color{blue}{\left(x \cdot y + \left(-0.25 \cdot a\right) \cdot b\right)} \]

      3. associate-+r+ 89.6%

         \[\leadsto \color{blue}{\left(c + x \cdot y\right) + \left(-0.25 \cdot a\right) \cdot b} \]

      4. *-commutative 89.6%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      5. associate-*r* 89.6%

         \[\leadsto \left(c + x \cdot y\right) + \color{blue}{a \cdot \left(-0.25 \cdot b\right)} \]

      6. *-commutative 89.6%

         \[\leadsto \left(c + x \cdot y\right) + a \cdot \color{blue}{\left(b \cdot -0.25\right)} \]

      7. +-commutative 89.6%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right) + \left(c + x \cdot y\right)} \]

      8. *-commutative 89.6%

         \[\leadsto \color{blue}{\left(b \cdot -0.25\right) \cdot a} + \left(c + x \cdot y\right) \]

      9. fma-define 90.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot -0.25, a, c + x \cdot y\right)} \]

      10. *-commutative 90.5%

          \[\leadsto \mathsf{fma}\left(\color{blue}{-0.25 \cdot b}, a, c + x \cdot y\right) \]

      11. +-commutative 90.5%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{x \cdot y + c}\right) \]

      12. fma-undefine 90.5%

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \color{blue}{\mathsf{fma}\left(x, y, c\right)}\right) \]

   7. Applied egg-rr 90.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.25 \cdot b, a, \mathsf{fma}\left(x, y, c\right)\right)} \]

   8. Taylor expanded in x around inf 72.4%

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

   if -3.7e90 < (*.f64 x y) < 1.28000000000000008e138

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 30.0%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.7 \cdot 10^{+90} \lor \neg \left(x \cdot y \leq 1.28 \cdot 10^{+138}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = c + (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0));
}

Python

def code(x, y, z, t, a, b, c):
	return c + (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Add Preprocessing

3. Final simplification 98.4%

   \[\leadsto c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) \]
4. Add Preprocessing

Alternative 13: 22.9% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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
    code = c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Add Preprocessing

3. Taylor expanded in c around inf 21.6%

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

4. Final simplification 21.6%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))