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

Percentage Accurate: 97.8% → 98.6%

Time: 12.3s

Alternatives: 15

Speedup: 0.5×

• 32.5% 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: 97.8% 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: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + 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 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + 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[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +inf.0

   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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 42.9%

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

   4. Taylor expanded in c around 0 42.9%

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

      1. *-commutative 42.9%

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

      2. fma-neg 57.1%

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

      3. distribute-lft-neg-in 57.1%

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

      4. associate-*r* 57.1%

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

      5. metadata-eval 57.1%

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

   6. Applied egg-rr 57.1%

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

   7. Taylor expanded in y around inf 57.4%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. associate-+l- 97.2%

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

   2. associate--l+ 97.2%

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

   3. fma-def 97.7%

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

   4. associate-*l/ 97.7%

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

   5. fma-neg 98.0%

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

   6. sub-neg 98.0%

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

   7. distribute-neg-in 98.0%

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

   8. remove-double-neg 98.0%

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

   9. associate-/l* 98.0%

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

   10. distribute-frac-neg 98.0%

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

   11. associate-/r/ 98.0%

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

   12. fma-def 98.0%

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

   13. neg-mul-1 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

   14. *-commutative 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

   15. associate-/l* 98.0%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

   16. metadata-eval 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ c + \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, b \cdot \left(a \cdot -0.25\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (+ (* x y) (fma t (* z 0.0625) (* b (* a -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((x * y) + fma(t, (z * 0.0625), (b * (a * -0.25))));
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(Float64(x * y) + fma(t, Float64(z * 0.0625), Float64(b * Float64(a * -0.25)))))
end

Wolfram

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

Derivation

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. Step-by-step derivation

   1. associate--l+ 97.2%

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

   2. associate-*l/ 97.2%

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

   3. *-commutative 97.2%

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

   4. fma-neg 97.6%

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

   5. div-inv 97.6%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, \color{blue}{z \cdot \frac{1}{16}}, -\frac{a \cdot b}{4}\right)\right) + c \]

   6. metadata-eval 97.6%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot \color{blue}{0.0625}, -\frac{a \cdot b}{4}\right)\right) + c \]

   7. associate-/l* 97.6%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, -\color{blue}{\frac{a}{\frac{4}{b}}}\right)\right) + c \]

   8. distribute-frac-neg 97.6%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{\frac{-a}{\frac{4}{b}}}\right)\right) + c \]

   9. metadata-eval 97.6%

      \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \frac{-a}{\frac{\color{blue}{--4}}{b}}\right)\right) + c \]

   10. distribute-neg-frac 97.6%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \frac{-a}{\color{blue}{-\frac{-4}{b}}}\right)\right) + c \]

   11. frac-2neg 97.6%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{\frac{a}{\frac{-4}{b}}}\right)\right) + c \]

   12. associate-/r/ 97.6%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{\frac{a}{-4} \cdot b}\right)\right) + c \]

   13. div-inv 97.6%

       \[\leadsto \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, \color{blue}{\left(a \cdot \frac{1}{-4}\right)} \cdot b\right)\right) + c \]

   14. metadata-eval 97.6%

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

4. Applied egg-rr 97.6%

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

5. Final simplification 97.6%

   \[\leadsto c + \left(x \cdot y + \mathsf{fma}\left(t, z \cdot 0.0625, b \cdot \left(a \cdot -0.25\right)\right)\right) \]
6. Add Preprocessing

Alternative 4: 66.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -2.15 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.7 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (+ c (* 0.0625 (* z t))))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -1.4e+37)
     t_3
     (if (<= (* x y) -2.15e-179)
       t_1
       (if (<= (* x y) -2.8e-255)
         t_2
         (if (<= (* x y) 1.45e+79) t_1 (if (<= (* x y) 3.7e+111) 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 + (a * (b * -0.25));
	double t_2 = c + (0.0625 * (z * t));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.4e+37) {
		tmp = t_3;
	} else if ((x * y) <= -2.15e-179) {
		tmp = t_1;
	} else if ((x * y) <= -2.8e-255) {
		tmp = t_2;
	} else if ((x * y) <= 1.45e+79) {
		tmp = t_1;
	} else if ((x * y) <= 3.7e+111) {
		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 + (a * (b * (-0.25d0)))
    t_2 = c + (0.0625d0 * (z * t))
    t_3 = c + (x * y)
    if ((x * y) <= (-1.4d+37)) then
        tmp = t_3
    else if ((x * y) <= (-2.15d-179)) then
        tmp = t_1
    else if ((x * y) <= (-2.8d-255)) then
        tmp = t_2
    else if ((x * y) <= 1.45d+79) then
        tmp = t_1
    else if ((x * y) <= 3.7d+111) 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 + (a * (b * -0.25));
	double t_2 = c + (0.0625 * (z * t));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.4e+37) {
		tmp = t_3;
	} else if ((x * y) <= -2.15e-179) {
		tmp = t_1;
	} else if ((x * y) <= -2.8e-255) {
		tmp = t_2;
	} else if ((x * y) <= 1.45e+79) {
		tmp = t_1;
	} else if ((x * y) <= 3.7e+111) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = c + (0.0625 * (z * t))
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.4e+37:
		tmp = t_3
	elif (x * y) <= -2.15e-179:
		tmp = t_1
	elif (x * y) <= -2.8e-255:
		tmp = t_2
	elif (x * y) <= 1.45e+79:
		tmp = t_1
	elif (x * y) <= 3.7e+111:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(c + Float64(0.0625 * Float64(z * t)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.4e+37)
		tmp = t_3;
	elseif (Float64(x * y) <= -2.15e-179)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.8e-255)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.45e+79)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.7e+111)
		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 + (a * (b * -0.25));
	t_2 = c + (0.0625 * (z * t));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.4e+37)
		tmp = t_3;
	elseif ((x * y) <= -2.15e-179)
		tmp = t_1;
	elseif ((x * y) <= -2.8e-255)
		tmp = t_2;
	elseif ((x * y) <= 1.45e+79)
		tmp = t_1;
	elseif ((x * y) <= 3.7e+111)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.4e+37], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -2.15e-179], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.8e-255], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.45e+79], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.7e+111], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.3999999999999999e37 or 3.7000000000000003e111 < (*.f64 x y)

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 77.9%

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

   if -1.3999999999999999e37 < (*.f64 x y) < -2.15000000000000013e-179 or -2.80000000000000011e-255 < (*.f64 x y) < 1.44999999999999996e79

   1. Initial program 99.2%

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

   3. Taylor expanded in a around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. associate-*r* 66.6%

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

   5. Simplified 66.6%

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

   if -2.15000000000000013e-179 < (*.f64 x y) < -2.80000000000000011e-255 or 1.44999999999999996e79 < (*.f64 x y) < 3.7000000000000003e111

   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 77.5%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.15 \cdot 10^{-179}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -2.8 \cdot 10^{-255}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.45 \cdot 10^{+79}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.7 \cdot 10^{+111}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := x \cdot y + t_2\\ \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-253}:\\ \;\;\;\;c + t_2\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (* 0.0625 (* z t)))
        (t_3 (+ (* x y) t_2)))
   (if (<= (* x y) -1.65e+97)
     t_3
     (if (<= (* x y) -1.5e-179)
       t_1
       (if (<= (* x y) -1.25e-253)
         (+ c t_2)
         (if (<= (* x y) 3.5e+82) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = 0.0625 * (z * t);
	double t_3 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -1.65e+97) {
		tmp = t_3;
	} else if ((x * y) <= -1.5e-179) {
		tmp = t_1;
	} else if ((x * y) <= -1.25e-253) {
		tmp = c + t_2;
	} else if ((x * y) <= 3.5e+82) {
		tmp = t_1;
	} 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 + (a * (b * (-0.25d0)))
    t_2 = 0.0625d0 * (z * t)
    t_3 = (x * y) + t_2
    if ((x * y) <= (-1.65d+97)) then
        tmp = t_3
    else if ((x * y) <= (-1.5d-179)) then
        tmp = t_1
    else if ((x * y) <= (-1.25d-253)) then
        tmp = c + t_2
    else if ((x * y) <= 3.5d+82) then
        tmp = t_1
    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 + (a * (b * -0.25));
	double t_2 = 0.0625 * (z * t);
	double t_3 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -1.65e+97) {
		tmp = t_3;
	} else if ((x * y) <= -1.5e-179) {
		tmp = t_1;
	} else if ((x * y) <= -1.25e-253) {
		tmp = c + t_2;
	} else if ((x * y) <= 3.5e+82) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = 0.0625 * (z * t)
	t_3 = (x * y) + t_2
	tmp = 0
	if (x * y) <= -1.65e+97:
		tmp = t_3
	elif (x * y) <= -1.5e-179:
		tmp = t_1
	elif (x * y) <= -1.25e-253:
		tmp = c + t_2
	elif (x * y) <= 3.5e+82:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(Float64(x * y) + t_2)
	tmp = 0.0
	if (Float64(x * y) <= -1.65e+97)
		tmp = t_3;
	elseif (Float64(x * y) <= -1.5e-179)
		tmp = t_1;
	elseif (Float64(x * y) <= -1.25e-253)
		tmp = Float64(c + t_2);
	elseif (Float64(x * y) <= 3.5e+82)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = 0.0625 * (z * t);
	t_3 = (x * y) + t_2;
	tmp = 0.0;
	if ((x * y) <= -1.65e+97)
		tmp = t_3;
	elseif ((x * y) <= -1.5e-179)
		tmp = t_1;
	elseif ((x * y) <= -1.25e-253)
		tmp = c + t_2;
	elseif ((x * y) <= 3.5e+82)
		tmp = t_1;
	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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.65e+97], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1.5e-179], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1.25e-253], N[(c + t$95$2), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.5e+82], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.6500000000000001e97 or 3.5e82 < (*.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in a around 0 88.1%

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

   4. Taylor expanded in c around 0 81.1%

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

   if -1.6500000000000001e97 < (*.f64 x y) < -1.50000000000000003e-179 or -1.24999999999999993e-253 < (*.f64 x y) < 3.5e82

   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 a around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-*r* 65.4%

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

   5. Simplified 65.4%

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

   if -1.50000000000000003e-179 < (*.f64 x y) < -1.24999999999999993e-253

   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 76.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.65 \cdot 10^{+97}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1.5 \cdot 10^{-179}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-253}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-262}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-258}:\\ \;\;\;\;c + t_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* a b) -2e+16)
     t_2
     (if (<= (* a b) -5e-262)
       (+ c (* x y))
       (if (<= (* a b) 2e-258)
         (+ c t_1)
         (if (<= (* a b) 5e+75) (+ (* x y) t_1) t_2))))))

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 t_2 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -2e+16) {
		tmp = t_2;
	} else if ((a * b) <= -5e-262) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e-258) {
		tmp = c + t_1;
	} else if ((a * b) <= 5e+75) {
		tmp = (x * y) + 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 = 0.0625d0 * (z * t)
    t_2 = (x * y) - ((a * b) * 0.25d0)
    if ((a * b) <= (-2d+16)) then
        tmp = t_2
    else if ((a * b) <= (-5d-262)) then
        tmp = c + (x * y)
    else if ((a * b) <= 2d-258) then
        tmp = c + t_1
    else if ((a * b) <= 5d+75) then
        tmp = (x * y) + 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 = 0.0625 * (z * t);
	double t_2 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -2e+16) {
		tmp = t_2;
	} else if ((a * b) <= -5e-262) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e-258) {
		tmp = c + t_1;
	} else if ((a * b) <= 5e+75) {
		tmp = (x * y) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (a * b) <= -2e+16:
		tmp = t_2
	elif (a * b) <= -5e-262:
		tmp = c + (x * y)
	elif (a * b) <= 2e-258:
		tmp = c + t_1
	elif (a * b) <= 5e+75:
		tmp = (x * y) + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(a * b) <= -2e+16)
		tmp = t_2;
	elseif (Float64(a * b) <= -5e-262)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 2e-258)
		tmp = Float64(c + t_1);
	elseif (Float64(a * b) <= 5e+75)
		tmp = Float64(Float64(x * y) + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((a * b) <= -2e+16)
		tmp = t_2;
	elseif ((a * b) <= -5e-262)
		tmp = c + (x * y);
	elseif ((a * b) <= 2e-258)
		tmp = c + t_1;
	elseif ((a * b) <= 5e+75)
		tmp = (x * y) + 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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+16], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -5e-262], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e-258], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+75], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2e16 or 5.0000000000000002e75 < (*.f64 a b)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 85.4%

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

   4. Taylor expanded in c around 0 78.6%

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

   if -2e16 < (*.f64 a b) < -4.99999999999999992e-262

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 80.5%

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

   if -4.99999999999999992e-262 < (*.f64 a b) < 1.99999999999999991e-258

   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 76.9%

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

   if 1.99999999999999991e-258 < (*.f64 a b) < 5.0000000000000002e75

   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 a around 0 88.4%

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

   4. Taylor expanded in c around 0 68.6%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+16}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-262}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-258}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+41} \lor \neg \left(x \cdot y \leq 3.9 \cdot 10^{+121}\right):\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* x y) -1.35e+41) (not (<= (* x y) 3.9e+121)))
     (+ c (+ (* x y) t_1))
     (- (+ c t_1) (* (* a b) 0.25)))))

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) <= -1.35e+41) || !((x * y) <= 3.9e+121)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	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) <= (-1.35d+41)) .or. (.not. ((x * y) <= 3.9d+121))) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + t_1) - ((a * b) * 0.25d0)
    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) <= -1.35e+41) || !((x * y) <= 3.9e+121)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((x * y) <= -1.35e+41) or not ((x * y) <= 3.9e+121):
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + t_1) - ((a * b) * 0.25)
	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) <= -1.35e+41) || !(Float64(x * y) <= 3.9e+121))
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	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) <= -1.35e+41) || ~(((x * y) <= 3.9e+121)))
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + t_1) - ((a * b) * 0.25);
	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[Or[LessEqual[N[(x * y), $MachinePrecision], -1.35e+41], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.9e+121]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.35e41 or 3.89999999999999984e121 < (*.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in a around 0 88.8%

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

   if -1.35e41 < (*.f64 x y) < 3.89999999999999984e121

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 93.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+41} \lor \neg \left(x \cdot y \leq 3.9 \cdot 10^{+121}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -1.4e+37)
   (* x y)
   (if (<= (* x y) 6.5e+76)
     (* b (* a -0.25))
     (if (<= (* x y) 2.5e+111) (* z (* t 0.0625)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -1.4e+37) {
		tmp = x * y;
	} else if ((x * y) <= 6.5e+76) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 2.5e+111) {
		tmp = z * (t * 0.0625);
	} 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) :: tmp
    if ((x * y) <= (-1.4d+37)) then
        tmp = x * y
    else if ((x * y) <= 6.5d+76) then
        tmp = b * (a * (-0.25d0))
    else if ((x * y) <= 2.5d+111) then
        tmp = z * (t * 0.0625d0)
    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 tmp;
	if ((x * y) <= -1.4e+37) {
		tmp = x * y;
	} else if ((x * y) <= 6.5e+76) {
		tmp = b * (a * -0.25);
	} else if ((x * y) <= 2.5e+111) {
		tmp = z * (t * 0.0625);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -1.4e+37:
		tmp = x * y
	elif (x * y) <= 6.5e+76:
		tmp = b * (a * -0.25)
	elif (x * y) <= 2.5e+111:
		tmp = z * (t * 0.0625)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1.4e+37)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 6.5e+76)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (Float64(x * y) <= 2.5e+111)
		tmp = Float64(z * Float64(t * 0.0625));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -1.4e+37)
		tmp = x * y;
	elseif ((x * y) <= 6.5e+76)
		tmp = b * (a * -0.25);
	elseif ((x * y) <= 2.5e+111)
		tmp = z * (t * 0.0625);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -1.4e+37], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.5e+76], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+111], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.3999999999999999e37 or 2.4999999999999998e111 < (*.f64 x y)

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 86.7%

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

   4. Taylor expanded in c around 0 76.9%

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

      1. *-commutative 76.9%

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

      2. fma-neg 77.9%

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

      3. distribute-lft-neg-in 77.9%

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

      4. associate-*r* 77.9%

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

      5. metadata-eval 77.9%

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

   6. Applied egg-rr 77.9%

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

   7. Taylor expanded in y around inf 68.0%

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

   if -1.3999999999999999e37 < (*.f64 x y) < 6.5000000000000005e76

   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 0 68.6%

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

   4. Taylor expanded in c around 0 43.7%

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

   5. Taylor expanded in x around 0 38.9%

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

      1. associate-*r* 38.9%

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

      2. *-commutative 38.9%

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

   7. Simplified 38.9%

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

   if 6.5000000000000005e76 < (*.f64 x y) < 2.4999999999999998e111

   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 0 84.7%

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

   4. Taylor expanded in c around 0 62.4%

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

   5. Taylor expanded in t around inf 54.7%

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

      1. associate-*r* 54.7%

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

   7. Simplified 54.7%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+76}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+111}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 4 \cdot 10^{+81}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+71) (not (<= (* a b) 4e+81)))
   (- (* x y) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+71) || !((a * b) <= 4e+81)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	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 (((a * b) <= (-5d+71)) .or. (.not. ((a * b) <= 4d+81))) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (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 tmp;
	if (((a * b) <= -5e+71) || !((a * b) <= 4e+81)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+71) or not ((a * b) <= 4e+81):
		tmp = (x * y) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+71) || !(Float64(a * b) <= 4e+81))
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+71) || ~(((a * b) <= 4e+81)))
		tmp = (x * y) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+71], N[Not[LessEqual[N[(a * b), $MachinePrecision], 4e+81]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.99999999999999972e71 or 3.99999999999999969e81 < (*.f64 a b)

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 85.4%

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

   4. Taylor expanded in c around 0 80.9%

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

   if -4.99999999999999972e71 < (*.f64 a b) < 3.99999999999999969e81

   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 a around 0 92.3%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 4 \cdot 10^{+81}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+35} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+75}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+35) (not (<= (* a b) 5e+75)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e+35) || !((a * b) <= 5e+75)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	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 (((a * b) <= (-1d+35)) .or. (.not. ((a * b) <= 5d+75))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (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 tmp;
	if (((a * b) <= -1e+35) || !((a * b) <= 5e+75)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1e+35) or not ((a * b) <= 5e+75):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1e+35) || !(Float64(a * b) <= 5e+75))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1e+35) || ~(((a * b) <= 5e+75)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+35], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+75]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.9999999999999997e34 or 5.0000000000000002e75 < (*.f64 a b)

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 86.1%

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

   if -9.9999999999999997e34 < (*.f64 a b) < 5.0000000000000002e75

   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 a around 0 93.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+35} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+75}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+40} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+114}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2e+40) (not (<= (* x y) 1.35e+114)))
   (+ c (* x y))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2e+40) || !((x * y) <= 1.35e+114)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	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) <= (-2d+40)) .or. (.not. ((x * y) <= 1.35d+114))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (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 tmp;
	if (((x * y) <= -2e+40) || !((x * y) <= 1.35e+114)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2e+40) or not ((x * y) <= 1.35e+114):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+40) || !(Float64(x * y) <= 1.35e+114))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -2e+40) || ~(((x * y) <= 1.35e+114)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+40], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.35e+114]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000006e40 or 1.35e114 < (*.f64 x y)

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 78.6%

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

   if -2.00000000000000006e40 < (*.f64 x y) < 1.35e114

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 59.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+40} \lor \neg \left(x \cdot y \leq 1.35 \cdot 10^{+114}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-167} \lor \neg \left(z \leq -4.5 \cdot 10^{-216}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -1.55e+197)
   (* z (* t 0.0625))
   (if (or (<= z -9.5e-167) (not (<= z -4.5e-216)))
     (+ c (* x y))
     (* b (* a -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -1.55e+197) {
		tmp = z * (t * 0.0625);
	} else if ((z <= -9.5e-167) || !(z <= -4.5e-216)) {
		tmp = c + (x * y);
	} else {
		tmp = b * (a * -0.25);
	}
	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 (z <= (-1.55d+197)) then
        tmp = z * (t * 0.0625d0)
    else if ((z <= (-9.5d-167)) .or. (.not. (z <= (-4.5d-216)))) then
        tmp = c + (x * y)
    else
        tmp = b * (a * (-0.25d0))
    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 (z <= -1.55e+197) {
		tmp = z * (t * 0.0625);
	} else if ((z <= -9.5e-167) || !(z <= -4.5e-216)) {
		tmp = c + (x * y);
	} else {
		tmp = b * (a * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -1.55e+197:
		tmp = z * (t * 0.0625)
	elif (z <= -9.5e-167) or not (z <= -4.5e-216):
		tmp = c + (x * y)
	else:
		tmp = b * (a * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -1.55e+197)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif ((z <= -9.5e-167) || !(z <= -4.5e-216))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(b * Float64(a * -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -1.55e+197)
		tmp = z * (t * 0.0625);
	elseif ((z <= -9.5e-167) || ~((z <= -4.5e-216)))
		tmp = c + (x * y);
	else
		tmp = b * (a * -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -1.55e+197], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -9.5e-167], N[Not[LessEqual[z, -4.5e-216]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e197

   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 0 79.8%

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

   4. Taylor expanded in c around 0 69.8%

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

   5. Taylor expanded in t around inf 53.0%

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

      1. associate-*r* 53.0%

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

   7. Simplified 53.0%

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

   if -1.55e197 < z < -9.49999999999999955e-167 or -4.4999999999999999e-216 < z

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 51.4%

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

   if -9.49999999999999955e-167 < z < -4.4999999999999999e-216

   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 z around 0 99.9%

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

   4. Taylor expanded in c around 0 78.3%

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

   5. Taylor expanded in x around 0 51.8%

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

      1. associate-*r* 51.8%

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

      2. *-commutative 51.8%

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

   7. Simplified 51.8%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+197}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-167} \lor \neg \left(z \leq -4.5 \cdot 10^{-216}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+37} \lor \neg \left(x \cdot y \leq 3.8 \cdot 10^{+179}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.6e+37) (not (<= (* x y) 3.8e+179)))
   (* x y)
   (* b (* a -0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.6e+37) || !((x * y) <= 3.8e+179)) {
		tmp = x * y;
	} else {
		tmp = b * (a * -0.25);
	}
	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) <= (-1.6d+37)) .or. (.not. ((x * y) <= 3.8d+179))) then
        tmp = x * y
    else
        tmp = b * (a * (-0.25d0))
    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) <= -1.6e+37) || !((x * y) <= 3.8e+179)) {
		tmp = x * y;
	} else {
		tmp = b * (a * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.6e+37) or not ((x * y) <= 3.8e+179):
		tmp = x * y
	else:
		tmp = b * (a * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.6e+37) || !(Float64(x * y) <= 3.8e+179))
		tmp = Float64(x * y);
	else
		tmp = Float64(b * Float64(a * -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.6e+37) || ~(((x * y) <= 3.8e+179)))
		tmp = x * y;
	else
		tmp = b * (a * -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.6e+37], N[Not[LessEqual[N[(x * y), $MachinePrecision], 3.8e+179]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.60000000000000007e37 or 3.8e179 < (*.f64 x y)

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 87.1%

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

   4. Taylor expanded in c around 0 78.5%

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

      1. *-commutative 78.5%

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

      2. fma-neg 79.7%

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

      3. distribute-lft-neg-in 79.7%

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

      4. associate-*r* 79.7%

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

      5. metadata-eval 79.7%

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

   6. Applied egg-rr 79.7%

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

   7. Taylor expanded in y around inf 73.1%

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

   if -1.60000000000000007e37 < (*.f64 x y) < 3.8e179

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 67.9%

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

   4. Taylor expanded in c around 0 43.5%

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

   5. Taylor expanded in x around 0 36.8%

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

      1. associate-*r* 36.8%

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

      2. *-commutative 36.8%

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

   7. Simplified 36.8%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6 \cdot 10^{+37} \lor \neg \left(x \cdot y \leq 3.8 \cdot 10^{+179}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 41.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+114} \lor \neg \left(x \cdot y \leq 8 \cdot 10^{+128}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -3.4e+114) (not (<= (* x y) 8e+128))) (* 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) <= -3.4e+114) || !((x * y) <= 8e+128)) {
		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) <= (-3.4d+114)) .or. (.not. ((x * y) <= 8d+128))) 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) <= -3.4e+114) || !((x * y) <= 8e+128)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -3.4e+114) or not ((x * y) <= 8e+128):
		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) <= -3.4e+114) || !(Float64(x * y) <= 8e+128))
		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) <= -3.4e+114) || ~(((x * y) <= 8e+128)))
		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], -3.4e+114], N[Not[LessEqual[N[(x * y), $MachinePrecision], 8e+128]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.4000000000000001e114 or 8.0000000000000006e128 < (*.f64 x y)

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 88.7%

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

   4. Taylor expanded in c around 0 84.0%

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

      1. *-commutative 84.0%

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

      2. fma-neg 85.2%

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

      3. distribute-lft-neg-in 85.2%

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

      4. associate-*r* 85.2%

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

      5. metadata-eval 85.2%

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

   6. Applied egg-rr 85.2%

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

   7. Taylor expanded in y around inf 77.3%

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

   if -3.4000000000000001e114 < (*.f64 x y) < 8.0000000000000006e128

   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 c around inf 27.4%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+114} \lor \neg \left(x \cdot y \leq 8 \cdot 10^{+128}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 22.8% 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 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 c around inf 20.6%

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

4. Final simplification 20.6%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024018 
(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))