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

Percentage Accurate: 97.8% → 99.3%

Time: 13.9s

Alternatives: 17

Speedup: 0.5×

• 33.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + z \cdot \left(t \cdot 0.0625\right)\right) - a \cdot \frac{b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625 + a \cdot \frac{b \cdot -0.25}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) INFINITY)
   (+ c (- (+ (* x y) (* z (* t 0.0625))) (* a (/ b 4.0))))
   (* t (+ (* z 0.0625) (* a (/ (* b -0.25) t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= ((double) INFINITY)) {
		tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)));
	} else {
		tmp = t * ((z * 0.0625) + (a * ((b * -0.25) / t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= Double.POSITIVE_INFINITY) {
		tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)));
	} else {
		tmp = t * ((z * 0.0625) + (a * ((b * -0.25) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= math.inf:
		tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)))
	else:
		tmp = t * ((z * 0.0625) + (a * ((b * -0.25) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) <= Inf)
		tmp = Float64(c + Float64(Float64(Float64(x * y) + Float64(z * Float64(t * 0.0625))) - Float64(a * Float64(b / 4.0))));
	else
		tmp = Float64(t * Float64(Float64(z * 0.0625) + Float64(a * Float64(Float64(b * -0.25) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= Inf)
		tmp = c + (((x * y) + (z * (t * 0.0625))) - (a * (b / 4.0)));
	else
		tmp = t * ((z * 0.0625) + (a * ((b * -0.25) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(c + N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(b / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z * 0.0625), $MachinePrecision] + N[(a * N[(N[(b * -0.25), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. +-commutative 99.6%

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

      5. associate-+l- 99.6%

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

      6. fma-define 99.6%

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

      7. *-commutative 99.6%

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

      8. associate-/l* 100.0%

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

      9. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-*r/ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-*r/ 100.0%

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

      5. div-inv 100.0%

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

      6. metadata-eval 100.0%

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

   6. Applied egg-rr 100.0%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   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 x around 0 50.0%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.0%

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

      2. +-commutative 50.0%

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

      3. metadata-eval 50.0%

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

      4. div-inv 50.0%

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

      5. associate-*r/ 50.0%

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

      6. associate--l+ 50.0%

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

      7. *-commutative 50.0%

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

      8. *-commutative 50.0%

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

      9. associate-*r* 50.0%

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

      10. div-inv 50.0%

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

      11. metadata-eval 50.0%

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

   5. Applied egg-rr 50.0%

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

   6. Taylor expanded in t around inf 62.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 62.5%

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

      2. associate-*r/ 62.5%

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

      3. div-sub 62.5%

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

      4. cancel-sign-sub-inv 62.5%

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

      5. metadata-eval 62.5%

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

      6. +-commutative 62.5%

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

      7. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in a around inf 62.5%

      \[\leadsto t \cdot \left(0.0625 \cdot z + \color{blue}{-0.25 \cdot \frac{a \cdot b}{t}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 62.5%

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

       2. *-commutative 62.5%

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

       3. associate-*r* 62.5%

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

       4. associate-*r/ 87.5%

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

       5. *-commutative 87.5%

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

   11. Simplified 87.5%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + z \cdot \left(t \cdot 0.0625\right)\right) - a \cdot \frac{b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625 + a \cdot \frac{b \cdot -0.25}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

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 96.5%

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

   1. associate--l+ 96.5%

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

   2. fma-define 98.1%

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

   3. associate-/l* 98.4%

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

   4. fmm-def 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 3: 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 96.5%

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

   1. associate-+l- 96.5%

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

   2. +-commutative 96.5%

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

   3. *-commutative 96.5%

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

   4. +-commutative 96.5%

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

   5. associate-+l- 96.5%

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

   6. fma-define 97.7%

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

   7. *-commutative 97.7%

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

   8. associate-/l* 98.0%

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

   9. associate-/l* 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 4: 43.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -1.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.08 \cdot 10^{+39}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq -9.6 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-303}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 9.2 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.06 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= (* x y) -1.2e+132)
     (* x y)
     (if (<= (* x y) -1.08e+39)
       c
       (if (<= (* x y) -9.6e-134)
         t_1
         (if (<= (* x y) -5.5e-303)
           c
           (if (<= (* x y) 9.2e-110)
             t_1
             (if (<= (* x y) 3.1e+102)
               c
               (if (<= (* x y) 1.06e+135) t_1 (* 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 tmp;
	if ((x * y) <= -1.2e+132) {
		tmp = x * y;
	} else if ((x * y) <= -1.08e+39) {
		tmp = c;
	} else if ((x * y) <= -9.6e-134) {
		tmp = t_1;
	} else if ((x * y) <= -5.5e-303) {
		tmp = c;
	} else if ((x * y) <= 9.2e-110) {
		tmp = t_1;
	} else if ((x * y) <= 3.1e+102) {
		tmp = c;
	} else if ((x * y) <= 1.06e+135) {
		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 = a * (b * (-0.25d0))
    if ((x * y) <= (-1.2d+132)) then
        tmp = x * y
    else if ((x * y) <= (-1.08d+39)) then
        tmp = c
    else if ((x * y) <= (-9.6d-134)) then
        tmp = t_1
    else if ((x * y) <= (-5.5d-303)) then
        tmp = c
    else if ((x * y) <= 9.2d-110) then
        tmp = t_1
    else if ((x * y) <= 3.1d+102) then
        tmp = c
    else if ((x * y) <= 1.06d+135) 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 = a * (b * -0.25);
	double tmp;
	if ((x * y) <= -1.2e+132) {
		tmp = x * y;
	} else if ((x * y) <= -1.08e+39) {
		tmp = c;
	} else if ((x * y) <= -9.6e-134) {
		tmp = t_1;
	} else if ((x * y) <= -5.5e-303) {
		tmp = c;
	} else if ((x * y) <= 9.2e-110) {
		tmp = t_1;
	} else if ((x * y) <= 3.1e+102) {
		tmp = c;
	} else if ((x * y) <= 1.06e+135) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if (x * y) <= -1.2e+132:
		tmp = x * y
	elif (x * y) <= -1.08e+39:
		tmp = c
	elif (x * y) <= -9.6e-134:
		tmp = t_1
	elif (x * y) <= -5.5e-303:
		tmp = c
	elif (x * y) <= 9.2e-110:
		tmp = t_1
	elif (x * y) <= 3.1e+102:
		tmp = c
	elif (x * y) <= 1.06e+135:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -1.2e+132)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.08e+39)
		tmp = c;
	elseif (Float64(x * y) <= -9.6e-134)
		tmp = t_1;
	elseif (Float64(x * y) <= -5.5e-303)
		tmp = c;
	elseif (Float64(x * y) <= 9.2e-110)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.1e+102)
		tmp = c;
	elseif (Float64(x * y) <= 1.06e+135)
		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 = a * (b * -0.25);
	tmp = 0.0;
	if ((x * y) <= -1.2e+132)
		tmp = x * y;
	elseif ((x * y) <= -1.08e+39)
		tmp = c;
	elseif ((x * y) <= -9.6e-134)
		tmp = t_1;
	elseif ((x * y) <= -5.5e-303)
		tmp = c;
	elseif ((x * y) <= 9.2e-110)
		tmp = t_1;
	elseif ((x * y) <= 3.1e+102)
		tmp = c;
	elseif ((x * y) <= 1.06e+135)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.2e+132], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.08e+39], c, If[LessEqual[N[(x * y), $MachinePrecision], -9.6e-134], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5.5e-303], c, If[LessEqual[N[(x * y), $MachinePrecision], 9.2e-110], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.1e+102], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.06e+135], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.2000000000000001e132 or 1.06e135 < (*.f64 x y)

   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 85.0%

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

   4. Taylor expanded in x around inf 85.3%

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

      1. associate--l+ 85.3%

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

      2. associate-*r/ 85.3%

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

      3. div-sub 85.3%

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

      4. cancel-sign-sub-inv 85.3%

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

      5. metadata-eval 85.3%

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

      6. +-commutative 85.3%

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

      7. *-commutative 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in x around inf 76.6%

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

   if -1.2000000000000001e132 < (*.f64 x y) < -1.07999999999999998e39 or -9.60000000000000038e-134 < (*.f64 x y) < -5.50000000000000018e-303 or 9.2000000000000006e-110 < (*.f64 x y) < 3.09999999999999987e102

   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 c around inf 40.0%

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

   if -1.07999999999999998e39 < (*.f64 x y) < -9.60000000000000038e-134 or -5.50000000000000018e-303 < (*.f64 x y) < 9.2000000000000006e-110 or 3.09999999999999987e102 < (*.f64 x y) < 1.06e135

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0 95.0%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 95.0%

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

      2. +-commutative 95.0%

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

      3. metadata-eval 95.0%

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

      4. div-inv 95.0%

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

      5. associate-*r/ 95.0%

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

      6. associate--l+ 95.0%

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

      7. *-commutative 95.0%

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

      8. *-commutative 95.0%

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

      9. associate-*r* 95.0%

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

      10. div-inv 95.0%

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

      11. metadata-eval 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in t around inf 84.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 84.5%

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

      2. associate-*r/ 84.5%

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

      3. div-sub 84.6%

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

      4. cancel-sign-sub-inv 84.6%

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

      5. metadata-eval 84.6%

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

      6. +-commutative 84.6%

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

      7. *-commutative 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in a around inf 40.3%

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

       1. *-commutative 40.3%

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

       2. associate-*r* 40.3%

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

       3. *-commutative 40.3%

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

   11. Simplified 40.3%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.08 \cdot 10^{+39}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq -9.6 \cdot 10^{-134}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-303}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 9.2 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{+102}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.06 \cdot 10^{+135}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+305}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+206} \lor \neg \left(a \cdot b \leq -4 \cdot 10^{+158}\right) \land a \cdot b \leq 10^{+106}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+305)
   (* a (* b -0.25))
   (if (or (<= (* a b) -4e+206)
           (and (not (<= (* a b) -4e+158)) (<= (* a b) 1e+106)))
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (+ c (* b (* a -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+305) {
		tmp = a * (b * -0.25);
	} else if (((a * b) <= -4e+206) || (!((a * b) <= -4e+158) && ((a * b) <= 1e+106))) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (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 ((a * b) <= (-2d+305)) then
        tmp = a * (b * (-0.25d0))
    else if (((a * b) <= (-4d+206)) .or. (.not. ((a * b) <= (-4d+158))) .and. ((a * b) <= 1d+106)) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + (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 ((a * b) <= -2e+305) {
		tmp = a * (b * -0.25);
	} else if (((a * b) <= -4e+206) || (!((a * b) <= -4e+158) && ((a * b) <= 1e+106))) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+305:
		tmp = a * (b * -0.25)
	elif ((a * b) <= -4e+206) or (not ((a * b) <= -4e+158) and ((a * b) <= 1e+106)):
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+305)
		tmp = Float64(a * Float64(b * -0.25));
	elseif ((Float64(a * b) <= -4e+206) || (!(Float64(a * b) <= -4e+158) && (Float64(a * b) <= 1e+106)))
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + 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 ((a * b) <= -2e+305)
		tmp = a * (b * -0.25);
	elseif (((a * b) <= -4e+206) || (~(((a * b) <= -4e+158)) && ((a * b) <= 1e+106)))
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e+305], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], -4e+206], And[N[Not[LessEqual[N[(a * b), $MachinePrecision], -4e+158]], $MachinePrecision], LessEqual[N[(a * b), $MachinePrecision], 1e+106]]], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.9999999999999999e305

   1. Initial program 86.4%

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

   3. Taylor expanded in x around 0 90.9%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 90.9%

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

      2. +-commutative 90.9%

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

      3. metadata-eval 90.9%

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

      4. div-inv 90.9%

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

      5. associate-*r/ 90.9%

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

      6. associate--l+ 90.9%

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

      7. *-commutative 90.9%

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

      8. *-commutative 90.9%

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

      9. associate-*r* 90.9%

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

      10. div-inv 90.9%

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

      11. metadata-eval 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in t around inf 82.4%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 82.4%

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

      2. associate-*r/ 82.4%

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

      3. div-sub 87.0%

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

      4. cancel-sign-sub-inv 87.0%

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

      5. metadata-eval 87.0%

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

      6. +-commutative 87.0%

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

      7. *-commutative 87.0%

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

   8. Simplified 87.0%

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

   9. Taylor expanded in a around inf 90.9%

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

       1. *-commutative 90.9%

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

       2. associate-*r* 90.9%

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

       3. *-commutative 90.9%

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

   11. Simplified 90.9%

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

   if -1.9999999999999999e305 < (*.f64 a b) < -4.0000000000000002e206 or -3.99999999999999981e158 < (*.f64 a b) < 1.00000000000000009e106

   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 a around 0 92.1%

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

   if -4.0000000000000002e206 < (*.f64 a b) < -3.99999999999999981e158 or 1.00000000000000009e106 < (*.f64 a b)

   1. Initial program 91.1%

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

   3. Taylor expanded in a around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*r* 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+305}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+206} \lor \neg \left(a \cdot b \leq -4 \cdot 10^{+158}\right) \land a \cdot b \leq 10^{+106}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + \left(x \cdot y + t\_1\right)\\ t_3 := t\_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+269}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+158}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+217}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t)))
        (t_2 (+ c (+ (* x y) t_1)))
        (t_3 (- t_1 (* (* a b) 0.25))))
   (if (<= (* a b) -4e+269)
     t_3
     (if (<= (* a b) -4e+206)
       t_2
       (if (<= (* a b) -4e+158)
         (+ c (* b (* a -0.25)))
         (if (<= (* a b) 1e+217) t_2 t_3))))))

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 = c + ((x * y) + t_1);
	double t_3 = t_1 - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -4e+269) {
		tmp = t_3;
	} else if ((a * b) <= -4e+206) {
		tmp = t_2;
	} else if ((a * b) <= -4e+158) {
		tmp = c + (b * (a * -0.25));
	} else if ((a * b) <= 1e+217) {
		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 = 0.0625d0 * (z * t)
    t_2 = c + ((x * y) + t_1)
    t_3 = t_1 - ((a * b) * 0.25d0)
    if ((a * b) <= (-4d+269)) then
        tmp = t_3
    else if ((a * b) <= (-4d+206)) then
        tmp = t_2
    else if ((a * b) <= (-4d+158)) then
        tmp = c + (b * (a * (-0.25d0)))
    else if ((a * b) <= 1d+217) 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 = 0.0625 * (z * t);
	double t_2 = c + ((x * y) + t_1);
	double t_3 = t_1 - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -4e+269) {
		tmp = t_3;
	} else if ((a * b) <= -4e+206) {
		tmp = t_2;
	} else if ((a * b) <= -4e+158) {
		tmp = c + (b * (a * -0.25));
	} else if ((a * b) <= 1e+217) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = c + ((x * y) + t_1)
	t_3 = t_1 - ((a * b) * 0.25)
	tmp = 0
	if (a * b) <= -4e+269:
		tmp = t_3
	elif (a * b) <= -4e+206:
		tmp = t_2
	elif (a * b) <= -4e+158:
		tmp = c + (b * (a * -0.25))
	elif (a * b) <= 1e+217:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(c + Float64(Float64(x * y) + t_1))
	t_3 = Float64(t_1 - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(a * b) <= -4e+269)
		tmp = t_3;
	elseif (Float64(a * b) <= -4e+206)
		tmp = t_2;
	elseif (Float64(a * b) <= -4e+158)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (Float64(a * b) <= 1e+217)
		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 = 0.0625 * (z * t);
	t_2 = c + ((x * y) + t_1);
	t_3 = t_1 - ((a * b) * 0.25);
	tmp = 0.0;
	if ((a * b) <= -4e+269)
		tmp = t_3;
	elseif ((a * b) <= -4e+206)
		tmp = t_2;
	elseif ((a * b) <= -4e+158)
		tmp = c + (b * (a * -0.25));
	elseif ((a * b) <= 1e+217)
		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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+269], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -4e+206], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -4e+158], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+217], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.0000000000000002e269 or 9.9999999999999996e216 < (*.f64 a b)

   1. Initial program 84.3%

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

   3. Taylor expanded in x around 0 88.5%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 88.5%

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

      2. +-commutative 88.5%

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

      3. metadata-eval 88.5%

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

      4. div-inv 88.5%

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

      5. associate-*r/ 88.5%

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

      6. associate--l+ 88.5%

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

      7. *-commutative 88.5%

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

      8. *-commutative 88.5%

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

      9. associate-*r* 90.2%

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

      10. div-inv 90.2%

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

      11. metadata-eval 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in c around 0 86.5%

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

   if -4.0000000000000002e269 < (*.f64 a b) < -4.0000000000000002e206 or -3.99999999999999981e158 < (*.f64 a b) < 9.9999999999999996e216

   1. Initial program 99.5%

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

   3. Taylor expanded in a around 0 91.0%

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

   if -4.0000000000000002e206 < (*.f64 a b) < -3.99999999999999981e158

   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 88.9%

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

      1. *-commutative 88.9%

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

      2. *-commutative 88.9%

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

      3. associate-*r* 88.9%

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

   5. Simplified 88.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+269}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+206}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+158}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+217}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625 + a \cdot \frac{b \cdot -0.25}{t}\right)\\ \end{array} \end{array} \]

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)
     (* t (+ (* z 0.0625) (* a (/ (* b -0.25) t)))))))

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 = t * ((z * 0.0625) + (a * ((b * -0.25) / t)));
	}
	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 = t * ((z * 0.0625) + (a * ((b * -0.25) / t)));
	}
	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 = t * ((z * 0.0625) + (a * ((b * -0.25) / t)))
	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(t * Float64(Float64(z * 0.0625) + Float64(a * Float64(Float64(b * -0.25) / t))));
	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 = t * ((z * 0.0625) + (a * ((b * -0.25) / t)));
	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[(t * N[(N[(z * 0.0625), $MachinePrecision] + N[(a * N[(N[(b * -0.25), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 99.6%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   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 x around 0 50.0%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.0%

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

      2. +-commutative 50.0%

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

      3. metadata-eval 50.0%

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

      4. div-inv 50.0%

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

      5. associate-*r/ 50.0%

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

      6. associate--l+ 50.0%

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

      7. *-commutative 50.0%

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

      8. *-commutative 50.0%

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

      9. associate-*r* 50.0%

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

      10. div-inv 50.0%

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

      11. metadata-eval 50.0%

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

   5. Applied egg-rr 50.0%

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

   6. Taylor expanded in t around inf 62.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 62.5%

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

      2. associate-*r/ 62.5%

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

      3. div-sub 62.5%

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

      4. cancel-sign-sub-inv 62.5%

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

      5. metadata-eval 62.5%

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

      6. +-commutative 62.5%

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

      7. *-commutative 62.5%

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

   8. Simplified 62.5%

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

   9. Taylor expanded in a around inf 62.5%

      \[\leadsto t \cdot \left(0.0625 \cdot z + \color{blue}{-0.25 \cdot \frac{a \cdot b}{t}}\right) \]
   10. Step-by-step derivation

       1. associate-*r/ 62.5%

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

       2. *-commutative 62.5%

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

       3. associate-*r* 62.5%

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

       4. associate-*r/ 87.5%

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

       5. *-commutative 87.5%

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

   11. Simplified 87.5%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625 + a \cdot \frac{b \cdot -0.25}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+45}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.06 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -7e+45)
     t_2
     (if (<= (* x y) 6e+25)
       t_1
       (if (<= (* x y) 8e+62)
         (* z (* t 0.0625))
         (if (<= (* x y) 1.06e+135) 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 + (b * (a * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -7e+45) {
		tmp = t_2;
	} else if ((x * y) <= 6e+25) {
		tmp = t_1;
	} else if ((x * y) <= 8e+62) {
		tmp = z * (t * 0.0625);
	} else if ((x * y) <= 1.06e+135) {
		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 + (b * (a * (-0.25d0)))
    t_2 = c + (x * y)
    if ((x * y) <= (-7d+45)) then
        tmp = t_2
    else if ((x * y) <= 6d+25) then
        tmp = t_1
    else if ((x * y) <= 8d+62) then
        tmp = z * (t * 0.0625d0)
    else if ((x * y) <= 1.06d+135) 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 + (b * (a * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -7e+45) {
		tmp = t_2;
	} else if ((x * y) <= 6e+25) {
		tmp = t_1;
	} else if ((x * y) <= 8e+62) {
		tmp = z * (t * 0.0625);
	} else if ((x * y) <= 1.06e+135) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -7e+45:
		tmp = t_2
	elif (x * y) <= 6e+25:
		tmp = t_1
	elif (x * y) <= 8e+62:
		tmp = z * (t * 0.0625)
	elif (x * y) <= 1.06e+135:
		tmp = t_1
	else:
		tmp = t_2
	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(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -7e+45)
		tmp = t_2;
	elseif (Float64(x * y) <= 6e+25)
		tmp = t_1;
	elseif (Float64(x * y) <= 8e+62)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (Float64(x * y) <= 1.06e+135)
		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 + (b * (a * -0.25));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -7e+45)
		tmp = t_2;
	elseif ((x * y) <= 6e+25)
		tmp = t_1;
	elseif ((x * y) <= 8e+62)
		tmp = z * (t * 0.0625);
	elseif ((x * y) <= 1.06e+135)
		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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -7e+45], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 6e+25], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 8e+62], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.06e+135], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.00000000000000046e45 or 1.06e135 < (*.f64 x y)

   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 x around inf 76.6%

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

   if -7.00000000000000046e45 < (*.f64 x y) < 6.00000000000000011e25 or 8.00000000000000028e62 < (*.f64 x y) < 1.06e135

   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 a around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. *-commutative 63.4%

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

      3. associate-*r* 63.4%

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

   5. Simplified 63.4%

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

   if 6.00000000000000011e25 < (*.f64 x y) < 8.00000000000000028e62

   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 92.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 92.8%

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

      2. +-commutative 92.8%

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

      3. metadata-eval 92.8%

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

      4. div-inv 92.8%

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

      5. associate-*r/ 92.8%

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

      6. associate--l+ 92.8%

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

      7. *-commutative 92.8%

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

      8. *-commutative 92.8%

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

      9. associate-*r* 92.8%

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

      10. div-inv 92.8%

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

      11. metadata-eval 92.8%

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

   5. Applied egg-rr 92.8%

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

   6. Taylor expanded in t around inf 92.6%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 92.6%

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

      2. associate-*r/ 92.6%

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

      3. div-sub 92.6%

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

      4. cancel-sign-sub-inv 92.6%

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

      5. metadata-eval 92.6%

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

      6. +-commutative 92.6%

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

      7. *-commutative 92.6%

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

   8. Simplified 92.6%

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

   9. Taylor expanded in t around inf 78.8%

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

       1. associate-*r* 78.8%

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

   11. Simplified 78.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7 \cdot 10^{+45}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+25}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.06 \cdot 10^{+135}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.6 \cdot 10^{+38}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq -1.65 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -2.2e+132)
   (* x y)
   (if (<= (* x y) -5.6e+38)
     c
     (if (<= (* x y) -1.65e-12)
       (* a (* b -0.25))
       (if (<= (* x y) 6.6e+134) (* 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) <= -2.2e+132) {
		tmp = x * y;
	} else if ((x * y) <= -5.6e+38) {
		tmp = c;
	} else if ((x * y) <= -1.65e-12) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 6.6e+134) {
		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) <= (-2.2d+132)) then
        tmp = x * y
    else if ((x * y) <= (-5.6d+38)) then
        tmp = c
    else if ((x * y) <= (-1.65d-12)) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 6.6d+134) 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) <= -2.2e+132) {
		tmp = x * y;
	} else if ((x * y) <= -5.6e+38) {
		tmp = c;
	} else if ((x * y) <= -1.65e-12) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 6.6e+134) {
		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) <= -2.2e+132:
		tmp = x * y
	elif (x * y) <= -5.6e+38:
		tmp = c
	elif (x * y) <= -1.65e-12:
		tmp = a * (b * -0.25)
	elif (x * y) <= 6.6e+134:
		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) <= -2.2e+132)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.6e+38)
		tmp = c;
	elseif (Float64(x * y) <= -1.65e-12)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 6.6e+134)
		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) <= -2.2e+132)
		tmp = x * y;
	elseif ((x * y) <= -5.6e+38)
		tmp = c;
	elseif ((x * y) <= -1.65e-12)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 6.6e+134)
		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], -2.2e+132], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.6e+38], c, If[LessEqual[N[(x * y), $MachinePrecision], -1.65e-12], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.6e+134], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.19999999999999989e132 or 6.6e134 < (*.f64 x y)

   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 85.0%

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

   4. Taylor expanded in x around inf 85.3%

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

      1. associate--l+ 85.3%

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

      2. associate-*r/ 85.3%

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

      3. div-sub 85.3%

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

      4. cancel-sign-sub-inv 85.3%

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

      5. metadata-eval 85.3%

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

      6. +-commutative 85.3%

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

      7. *-commutative 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in x around inf 76.6%

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

   if -2.19999999999999989e132 < (*.f64 x y) < -5.6e38

   1. Initial program 94.7%

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

   3. Taylor expanded in c around inf 40.4%

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

   if -5.6e38 < (*.f64 x y) < -1.65e-12

   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 83.5%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 83.5%

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

      2. +-commutative 83.5%

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

      3. metadata-eval 83.5%

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

      4. div-inv 83.5%

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

      5. associate-*r/ 83.5%

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

      6. associate--l+ 83.5%

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

      7. *-commutative 83.5%

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

      8. *-commutative 83.5%

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

      9. associate-*r* 83.5%

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

      10. div-inv 83.5%

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

      11. metadata-eval 83.5%

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

   5. Applied egg-rr 83.5%

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

   6. Taylor expanded in t around inf 75.1%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 75.1%

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

      2. associate-*r/ 75.1%

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

      3. div-sub 75.1%

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

      4. cancel-sign-sub-inv 75.1%

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

      5. metadata-eval 75.1%

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

      6. +-commutative 75.1%

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

      7. *-commutative 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in a around inf 47.2%

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

       1. *-commutative 47.2%

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

       2. associate-*r* 47.2%

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

       3. *-commutative 47.2%

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

   11. Simplified 47.2%

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

   if -1.65e-12 < (*.f64 x y) < 6.6e134

   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 0 96.2%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 96.2%

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

      2. +-commutative 96.2%

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

      3. metadata-eval 96.2%

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

      4. div-inv 96.2%

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

      5. associate-*r/ 96.2%

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

      6. associate--l+ 96.2%

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

      7. *-commutative 96.2%

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

      8. *-commutative 96.2%

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

      9. associate-*r* 96.7%

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

      10. div-inv 96.7%

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

      11. metadata-eval 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in t around inf 84.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 84.8%

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

      2. associate-*r/ 84.8%

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

      3. div-sub 84.9%

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

      4. cancel-sign-sub-inv 84.9%

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

      5. metadata-eval 84.9%

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

      6. +-commutative 84.9%

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

      7. *-commutative 84.9%

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

   8. Simplified 84.9%

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

   9. Taylor expanded in t around inf 38.5%

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

       1. associate-*r* 38.9%

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

   11. Simplified 38.9%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.6 \cdot 10^{+38}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq -1.65 \cdot 10^{-12}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.6 \cdot 10^{+134}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+242}:\\ \;\;\;\;b \cdot \left(0.0625 \cdot \frac{z \cdot t}{b} - a \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+158} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{-23}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -1e+242)
   (* b (- (* 0.0625 (/ (* z t) b)) (* a 0.25)))
   (if (or (<= (* a b) -4e+158) (not (<= (* a b) 2e-23)))
     (- (+ 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+242) {
		tmp = b * ((0.0625 * ((z * t) / b)) - (a * 0.25));
	} else if (((a * b) <= -4e+158) || !((a * b) <= 2e-23)) {
		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+242)) then
        tmp = b * ((0.0625d0 * ((z * t) / b)) - (a * 0.25d0))
    else if (((a * b) <= (-4d+158)) .or. (.not. ((a * b) <= 2d-23))) 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+242) {
		tmp = b * ((0.0625 * ((z * t) / b)) - (a * 0.25));
	} else if (((a * b) <= -4e+158) || !((a * b) <= 2e-23)) {
		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+242:
		tmp = b * ((0.0625 * ((z * t) / b)) - (a * 0.25))
	elif ((a * b) <= -4e+158) or not ((a * b) <= 2e-23):
		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+242)
		tmp = Float64(b * Float64(Float64(0.0625 * Float64(Float64(z * t) / b)) - Float64(a * 0.25)));
	elseif ((Float64(a * b) <= -4e+158) || !(Float64(a * b) <= 2e-23))
		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+242)
		tmp = b * ((0.0625 * ((z * t) / b)) - (a * 0.25));
	elseif (((a * b) <= -4e+158) || ~(((a * b) <= 2e-23)))
		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[LessEqual[N[(a * b), $MachinePrecision], -1e+242], N[(b * N[(N[(0.0625 * N[(N[(z * t), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * b), $MachinePrecision], -4e+158], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e-23]], $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 3 regimes

2. if (*.f64 a b) < -1.00000000000000005e242

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0 86.1%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 86.1%

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

      2. +-commutative 86.1%

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

      3. metadata-eval 86.1%

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

      4. div-inv 86.1%

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

      5. associate-*r/ 86.1%

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

      6. associate--l+ 86.1%

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

      7. *-commutative 86.1%

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

      8. *-commutative 86.1%

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

      9. associate-*r* 88.5%

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

      10. div-inv 88.5%

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

      11. metadata-eval 88.5%

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

   5. Applied egg-rr 88.5%

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

   6. Taylor expanded in c around 0 83.1%

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

   7. Taylor expanded in b around inf 89.0%

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

   if -1.00000000000000005e242 < (*.f64 a b) < -3.99999999999999981e158 or 1.99999999999999992e-23 < (*.f64 a b)

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 85.1%

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

   if -3.99999999999999981e158 < (*.f64 a b) < 1.99999999999999992e-23

   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 95.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+242}:\\ \;\;\;\;b \cdot \left(0.0625 \cdot \frac{z \cdot t}{b} - a \cdot 0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{+158} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{-23}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+46} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right) + \left(c - a \cdot \left(b \cdot 0.25\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -5e+46) (not (<= (* x y) 5e+134)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))
   (+ (* z (* t 0.0625)) (- c (* a (* b 0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -5e+46) || !((x * y) <= 5e+134)) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (z * (t * 0.0625)) + (c - (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) :: tmp
    if (((x * y) <= (-5d+46)) .or. (.not. ((x * y) <= 5d+134))) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (z * (t * 0.0625d0)) + (c - (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 tmp;
	if (((x * y) <= -5e+46) || !((x * y) <= 5e+134)) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (z * (t * 0.0625)) + (c - (a * (b * 0.25)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -5e+46) or not ((x * y) <= 5e+134):
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (z * (t * 0.0625)) + (c - (a * (b * 0.25)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+46) || !(Float64(x * y) <= 5e+134))
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(z * Float64(t * 0.0625)) + Float64(c - Float64(a * Float64(b * 0.25))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -5e+46) || ~(((x * y) <= 5e+134)))
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (z * (t * 0.0625)) + (c - (a * (b * 0.25)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+46], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+134]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision] + N[(c - N[(a * N[(b * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.0000000000000002e46 or 4.99999999999999981e134 < (*.f64 x y)

   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 a around 0 86.5%

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

   if -5.0000000000000002e46 < (*.f64 x y) < 4.99999999999999981e134

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 95.3%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 95.3%

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

      2. +-commutative 95.3%

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

      3. metadata-eval 95.3%

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

      4. div-inv 95.3%

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

      5. associate-*r/ 95.3%

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

      6. associate--l+ 95.3%

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

      7. *-commutative 95.3%

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

      8. *-commutative 95.3%

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

      9. associate-*r* 95.8%

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

      10. div-inv 95.8%

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

      11. metadata-eval 95.8%

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

   5. Applied egg-rr 95.8%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+46} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right) + \left(c - a \cdot \left(b \cdot 0.25\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -380:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* a (* b -0.25))))
   (if (<= a -1.7e+188)
     t_2
     (if (<= a -380.0)
       t_1
       (if (<= a -1.6e-12) (* z (* t 0.0625)) (if (<= a 4.5e+23) 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 = a * (b * -0.25);
	double tmp;
	if (a <= -1.7e+188) {
		tmp = t_2;
	} else if (a <= -380.0) {
		tmp = t_1;
	} else if (a <= -1.6e-12) {
		tmp = z * (t * 0.0625);
	} else if (a <= 4.5e+23) {
		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 = a * (b * (-0.25d0))
    if (a <= (-1.7d+188)) then
        tmp = t_2
    else if (a <= (-380.0d0)) then
        tmp = t_1
    else if (a <= (-1.6d-12)) then
        tmp = z * (t * 0.0625d0)
    else if (a <= 4.5d+23) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = a * (b * -0.25);
	double tmp;
	if (a <= -1.7e+188) {
		tmp = t_2;
	} else if (a <= -380.0) {
		tmp = t_1;
	} else if (a <= -1.6e-12) {
		tmp = z * (t * 0.0625);
	} else if (a <= 4.5e+23) {
		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 = a * (b * -0.25)
	tmp = 0
	if a <= -1.7e+188:
		tmp = t_2
	elif a <= -380.0:
		tmp = t_1
	elif a <= -1.6e-12:
		tmp = z * (t * 0.0625)
	elif a <= 4.5e+23:
		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(a * Float64(b * -0.25))
	tmp = 0.0
	if (a <= -1.7e+188)
		tmp = t_2;
	elseif (a <= -380.0)
		tmp = t_1;
	elseif (a <= -1.6e-12)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (a <= 4.5e+23)
		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 = a * (b * -0.25);
	tmp = 0.0;
	if (a <= -1.7e+188)
		tmp = t_2;
	elseif (a <= -380.0)
		tmp = t_1;
	elseif (a <= -1.6e-12)
		tmp = z * (t * 0.0625);
	elseif (a <= 4.5e+23)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+188], t$95$2, If[LessEqual[a, -380.0], t$95$1, If[LessEqual[a, -1.6e-12], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+23], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999998e188 or 4.49999999999999979e23 < a

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0 80.4%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 80.4%

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

      2. +-commutative 80.4%

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

      3. metadata-eval 80.4%

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

      4. div-inv 80.4%

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

      5. associate-*r/ 80.4%

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

      6. associate--l+ 80.4%

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

      7. *-commutative 80.4%

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

      8. *-commutative 80.4%

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

      9. associate-*r* 80.4%

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

      10. div-inv 80.4%

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

      11. metadata-eval 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in t around inf 71.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 71.0%

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

      2. associate-*r/ 71.0%

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

      3. div-sub 72.2%

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

      4. cancel-sign-sub-inv 72.2%

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

      5. metadata-eval 72.2%

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

      6. +-commutative 72.2%

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

      7. *-commutative 72.2%

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

   8. Simplified 72.2%

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

   9. Taylor expanded in a around inf 50.6%

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

       1. *-commutative 50.6%

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

       2. associate-*r* 50.6%

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

       3. *-commutative 50.6%

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

   11. Simplified 50.6%

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

   if -1.69999999999999998e188 < a < -380 or -1.6e-12 < a < 4.49999999999999979e23

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 59.2%

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

   if -380 < a < -1.6e-12

   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 0 100.0%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. metadata-eval 100.0%

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

      4. div-inv 100.0%

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

      5. associate-*r/ 100.0%

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

      6. associate--l+ 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-*r* 100.0%

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

      10. div-inv 100.0%

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

      11. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(0.0625 \cdot z + \frac{c}{t}\right) - 0.25 \cdot \frac{a \cdot b}{t}\right)} \]
   7. Step-by-step derivation

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. div-sub 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. metadata-eval 100.0%

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

      6. +-commutative 100.0%

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

      7. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in t around inf 100.0%

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

       1. associate-*r* 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+188}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -380:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-12}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+23}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+116} \lor \neg \left(x \cdot y \leq 10^{+103}\right):\\ \;\;\;\;x \cdot \left(y + -0.25 \cdot \frac{a \cdot b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -4e+116) (not (<= (* x y) 1e+103)))
   (* x (+ y (* -0.25 (/ (* a b) x))))
   (+ c (* t (* z 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -4e+116) || !((x * y) <= 1e+103)) {
		tmp = x * (y + (-0.25 * ((a * b) / x)));
	} else {
		tmp = c + (t * (z * 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) <= (-4d+116)) .or. (.not. ((x * y) <= 1d+103))) then
        tmp = x * (y + ((-0.25d0) * ((a * b) / x)))
    else
        tmp = c + (t * (z * 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) <= -4e+116) || !((x * y) <= 1e+103)) {
		tmp = x * (y + (-0.25 * ((a * b) / x)));
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -4e+116) or not ((x * y) <= 1e+103):
		tmp = x * (y + (-0.25 * ((a * b) / x)))
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -4e+116) || !(Float64(x * y) <= 1e+103))
		tmp = Float64(x * Float64(y + Float64(-0.25 * Float64(Float64(a * b) / x))));
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -4e+116) || ~(((x * y) <= 1e+103)))
		tmp = x * (y + (-0.25 * ((a * b) / x)));
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4e+116], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+103]], $MachinePrecision]], N[(x * N[(y + N[(-0.25 * N[(N[(a * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.00000000000000006e116 or 1e103 < (*.f64 x y)

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 85.5%

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

   4. Taylor expanded in x around inf 83.8%

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

      1. associate--l+ 83.8%

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

      2. associate-*r/ 83.8%

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

      3. div-sub 83.8%

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

      4. cancel-sign-sub-inv 83.8%

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

      5. metadata-eval 83.8%

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

      6. +-commutative 83.8%

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

      7. *-commutative 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in c around 0 80.1%

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

   if -4.00000000000000006e116 < (*.f64 x y) < 1e103

   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 67.3%

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

      1. associate-*r* 67.6%

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

      2. *-commutative 67.6%

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

      3. associate-*r* 67.6%

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

   5. Simplified 67.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+116} \lor \neg \left(x \cdot y \leq 10^{+103}\right):\\ \;\;\;\;x \cdot \left(y + -0.25 \cdot \frac{a \cdot b}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+158} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{-23}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -4e+158) (not (<= (* a b) 2e-23)))
   (- (+ 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) <= -4e+158) || !((a * b) <= 2e-23)) {
		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) <= (-4d+158)) .or. (.not. ((a * b) <= 2d-23))) 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) <= -4e+158) || !((a * b) <= 2e-23)) {
		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) <= -4e+158) or not ((a * b) <= 2e-23):
		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) <= -4e+158) || !(Float64(a * b) <= 2e-23))
		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) <= -4e+158) || ~(((a * b) <= 2e-23)))
		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], -4e+158], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e-23]], $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) < -3.99999999999999981e158 or 1.99999999999999992e-23 < (*.f64 a b)

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 81.5%

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

   if -3.99999999999999981e158 < (*.f64 a b) < 1.99999999999999992e-23

   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 95.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+158} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{-23}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+116} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -4e+116) (not (<= (* x y) 5e+134)))
   (+ c (* x y))
   (+ c (* t (* z 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -4e+116) || !((x * y) <= 5e+134)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (t * (z * 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) <= (-4d+116)) .or. (.not. ((x * y) <= 5d+134))) then
        tmp = c + (x * y)
    else
        tmp = c + (t * (z * 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) <= -4e+116) || !((x * y) <= 5e+134)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -4e+116) or not ((x * y) <= 5e+134):
		tmp = c + (x * y)
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -4e+116) || !(Float64(x * y) <= 5e+134))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -4e+116) || ~(((x * y) <= 5e+134)))
		tmp = c + (x * y);
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -4e+116], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+134]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.00000000000000006e116 or 4.99999999999999981e134 < (*.f64 x y)

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 78.6%

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

   if -4.00000000000000006e116 < (*.f64 x y) < 4.99999999999999981e134

   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 66.3%

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

      1. associate-*r* 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.6%

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

   5. Simplified 66.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+116} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+134}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.9 \cdot 10^{+132} \lor \neg \left(x \cdot y \leq 1.45 \cdot 10^{+100}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.9e+132) (not (<= (* x y) 1.45e+100))) (* 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) <= -1.9e+132) || !((x * y) <= 1.45e+100)) {
		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) <= (-1.9d+132)) .or. (.not. ((x * y) <= 1.45d+100))) 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) <= -1.9e+132) || !((x * y) <= 1.45e+100)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.9e+132) or not ((x * y) <= 1.45e+100):
		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) <= -1.9e+132) || !(Float64(x * y) <= 1.45e+100))
		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) <= -1.9e+132) || ~(((x * y) <= 1.45e+100)))
		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], -1.9e+132], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.45e+100]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.90000000000000003e132 or 1.45e100 < (*.f64 x y)

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 83.6%

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

   4. Taylor expanded in x around inf 83.9%

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

      1. associate--l+ 83.9%

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

      2. associate-*r/ 83.9%

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

      3. div-sub 83.9%

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

      4. cancel-sign-sub-inv 83.9%

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

      5. metadata-eval 83.9%

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

      6. +-commutative 83.9%

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

      7. *-commutative 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in x around inf 72.4%

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

   if -1.90000000000000003e132 < (*.f64 x y) < 1.45e100

   1. Initial program 97.7%

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

   3. Taylor expanded in c around inf 32.0%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.9 \cdot 10^{+132} \lor \neg \left(x \cdot y \leq 1.45 \cdot 10^{+100}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.1% 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 96.5%

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

3. Taylor expanded in c around inf 22.3%

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

4. Final simplification 22.3%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(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))