Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, J

Percentage Accurate: 79.5% → 92.1%

Time: 18.4s

Alternatives: 20

Speedup: 0.8×

• 37.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * 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 * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * 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 * 9.0d0) * y) - (((z * 4.0d0) * t) * a)) + b) / (z * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-27} \lor \neg \left(z \leq 9.5 \cdot 10^{-38}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2e-27) (not (<= z 9.5e-38)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 c))
   (/ (/ (+ b (fma x (* 9.0 y) (* a (* z (* -4.0 t))))) c) z)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2e-27) || !(z <= 9.5e-38)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = ((b + fma(x, (9.0 * y), (a * (z * (-4.0 * t))))) / c) / z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2e-27) || !(z <= 9.5e-38))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(a * Float64(z * Float64(-4.0 * t))))) / c) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2e-27], N[Not[LessEqual[z, 9.5e-38]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(z * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-27 or 9.5000000000000009e-38 < z

   1. Initial program 63.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 63.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 63.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 65.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 65.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 65.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 65.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 63.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 63.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 63.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 68.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 67.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 88.9%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   if -2.0000000000000001e-27 < z < 9.5000000000000009e-38

   1. Initial program 95.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 95.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 95.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 95.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 95.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 95.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 95.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 95.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 95.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 95.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 89.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]
   6. Step-by-step derivation

      1. associate-*l/ 96.5%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}}{z}} \]

      2. *-un-lft-identity 96.5%

         \[\leadsto \frac{\color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}}}{z} \]

   7. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-27} \lor \neg \left(z \leq 9.5 \cdot 10^{-38}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b + \mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(-4 \cdot t\right)\right)\right)}{c}}{z}\\ \end{array} \]

Alternative 2: 85.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(a \cdot \left(-4 \cdot t\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 5.5e-26)
   (/ (+ b (fma x (* 9.0 y) (* z (* a (* -4.0 t))))) (* z c))
   (+ (* (/ a c) (/ t -0.25)) (/ (- (/ b c) (/ (* x (* y -9.0)) c)) z))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 5.5e-26) {
		tmp = (b + fma(x, (9.0 * y), (z * (a * (-4.0 * t))))) / (z * c);
	} else {
		tmp = ((a / c) * (t / -0.25)) + (((b / c) - ((x * (y * -9.0)) / c)) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 5.5e-26)
		tmp = Float64(Float64(b + fma(x, Float64(9.0 * y), Float64(z * Float64(a * Float64(-4.0 * t))))) / Float64(z * c));
	else
		tmp = Float64(Float64(Float64(a / c) * Float64(t / -0.25)) + Float64(Float64(Float64(b / c) - Float64(Float64(x * Float64(y * -9.0)) / c)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 5.5e-26], N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision] + N[(z * N[(a * N[(-4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b / c), $MachinePrecision] - N[(N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 5.5000000000000005e-26

   1. Initial program 81.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. +-commutative 81.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z \cdot c} \]

      2. associate-+r- 81.2%

         \[\leadsto \frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z \cdot c} \]

      3. *-commutative 81.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z \cdot c} \]

      4. associate-*r* 82.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t}}{z \cdot c} \]

      5. *-commutative 82.2%

         \[\leadsto \frac{\left(b + \left(x \cdot 9\right) \cdot y\right) - \color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t}{z \cdot c} \]

      6. associate-+r- 82.2%

         \[\leadsto \frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right)}}{z \cdot c} \]

      7. +-commutative 82.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(\left(-4 \cdot t\right) \cdot a\right)\right) + b}{z \cdot c}} \]

   if 5.5000000000000005e-26 < c

   1. Initial program 67.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 67.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 67.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 69.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 69.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 69.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 69.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 67.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 67.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 68.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 63.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 65.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 73.3%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in z around -inf 83.8%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. *-commutative 83.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      2. mul-1-neg 83.8%

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 + \color{blue}{\left(-\frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}\right)} \]

      3. unsub-neg 83.8%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4 - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]

      4. metadata-eval 83.8%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      5. times-frac 83.8%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      6. *-rgt-identity 83.8%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      7. times-frac 91.0%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      8. mul-1-neg 91.0%

         \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{-9 \cdot \frac{x \cdot y}{c} + \color{blue}{\left(-\frac{b}{c}\right)}}{z} \]

      9. unsub-neg 91.0%

         \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\color{blue}{-9 \cdot \frac{x \cdot y}{c} - \frac{b}{c}}}{z} \]

      10. associate-*r/ 89.6%

          \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\color{blue}{\frac{-9 \cdot \left(x \cdot y\right)}{c}} - \frac{b}{c}}{z} \]

      11. *-commutative 89.6%

          \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\frac{\color{blue}{\left(x \cdot y\right) \cdot -9}}{c} - \frac{b}{c}}{z} \]

      12. associate-*l* 89.6%

          \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\frac{\color{blue}{x \cdot \left(y \cdot -9\right)}}{c} - \frac{b}{c}}{z} \]

   9. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\frac{x \cdot \left(y \cdot -9\right)}{c} - \frac{b}{c}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{b + \mathsf{fma}\left(x, 9 \cdot y, z \cdot \left(a \cdot \left(-4 \cdot t\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25} + \frac{\frac{b}{c} - \frac{x \cdot \left(y \cdot -9\right)}{c}}{z}\\ \end{array} \]

Alternative 3: 92.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5000000000000 \lor \neg \left(z \leq 1.2 \cdot 10^{-37}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -5000000000000.0) (not (<= z 1.2e-37)))
   (* (+ (* -4.0 (* a t)) (+ (* 9.0 (/ (* x y) z)) (/ b z))) (/ 1.0 c))
   (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5000000000000.0) || !(z <= 1.2e-37)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * 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 ((z <= (-5000000000000.0d0)) .or. (.not. (z <= 1.2d-37))) then
        tmp = (((-4.0d0) * (a * t)) + ((9.0d0 * ((x * y) / z)) + (b / z))) * (1.0d0 / c)
    else
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * 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 ((z <= -5000000000000.0) || !(z <= 1.2e-37)) {
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	} else {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5000000000000.0) or not (z <= 1.2e-37):
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c)
	else:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5000000000000.0) || !(z <= 1.2e-37))
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(b / z))) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -5000000000000.0) || ~((z <= 1.2e-37)))
		tmp = ((-4.0 * (a * t)) + ((9.0 * ((x * y) / z)) + (b / z))) * (1.0 / c);
	else
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -5000000000000.0], N[Not[LessEqual[z, 1.2e-37]], $MachinePrecision]], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5e12 or 1.19999999999999995e-37 < z

   1. Initial program 61.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 61.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 61.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 63.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 63.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 63.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 63.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 61.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 61.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 60.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 66.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 66.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 66.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 88.1%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   if -5e12 < z < 1.19999999999999995e-37

   1. Initial program 95.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5000000000000 \lor \neg \left(z \leq 1.2 \cdot 10^{-37}\right):\\ \;\;\;\;\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 4: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+145}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t_1 + 9 \cdot \left(y \cdot \frac{x}{z}\right)\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= z -2.4e+145)
     (* (/ 1.0 c) (+ t_1 (* 9.0 (* y (/ x z)))))
     (if (<= z 9.4e+67)
       (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* a t)))) (* z c))
       (/ (+ t_1 (/ b z)) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (z <= -2.4e+145) {
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	} else if (z <= 9.4e+67) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = (t_1 + (b / z)) / 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if (z <= (-2.4d+145)) then
        tmp = (1.0d0 / c) * (t_1 + (9.0d0 * (y * (x / z))))
    else if (z <= 9.4d+67) then
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (a * t)))) / (z * c)
    else
        tmp = (t_1 + (b / z)) / 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 t_1 = -4.0 * (a * t);
	double tmp;
	if (z <= -2.4e+145) {
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	} else if (z <= 9.4e+67) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if z <= -2.4e+145:
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))))
	elif z <= 9.4e+67:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c)
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -2.4e+145)
		tmp = Float64(Float64(1.0 / c) * Float64(t_1 + Float64(9.0 * Float64(y * Float64(x / z)))));
	elseif (z <= 9.4e+67)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(a * t)))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (z <= -2.4e+145)
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	elseif (z <= 9.4e+67)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (a * t)))) / (z * c);
	else
		tmp = (t_1 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+145], N[(N[(1.0 / c), $MachinePrecision] * N[(t$95$1 + N[(9.0 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e+67], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999992e145

   1. Initial program 47.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 47.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 47.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 42.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 42.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 42.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 42.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 47.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 47.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 47.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 51.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 51.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 78.9%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around inf 67.0%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) \cdot \frac{1}{c} \]
   8. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{\color{blue}{y \cdot x}}{z}\right) \cdot \frac{1}{c} \]

      2. associate-*r/ 78.8%

         \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(y \cdot \frac{x}{z}\right)}\right) \cdot \frac{1}{c} \]

   9. Simplified 78.8%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{9 \cdot \left(y \cdot \frac{x}{z}\right)}\right) \cdot \frac{1}{c} \]

   if -2.39999999999999992e145 < z < 9.40000000000000035e67

   1. Initial program 91.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 91.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 91.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 91.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 91.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 91.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 91.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 91.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 91.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 91.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 87.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   if 9.40000000000000035e67 < z

   1. Initial program 52.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 52.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 52.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 61.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 61.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 61.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 61.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 52.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 52.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 52.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 62.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 62.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 90.8%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around 0 81.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+145}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(y \cdot \frac{x}{z}\right)\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(a \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 5: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+144}:\\ \;\;\;\;\frac{1}{c} \cdot \left(t_1 + 9 \cdot \left(y \cdot \frac{x}{z}\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= z -1.55e+144)
     (* (/ 1.0 c) (+ t_1 (* 9.0 (* y (/ x z)))))
     (if (<= z 1.85e+67)
       (/ (+ b (- (* y (* 9.0 x)) (* a (* t (* z 4.0))))) (* z c))
       (/ (+ t_1 (/ b z)) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (z <= -1.55e+144) {
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	} else if (z <= 1.85e+67) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + (b / z)) / 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if (z <= (-1.55d+144)) then
        tmp = (1.0d0 / c) * (t_1 + (9.0d0 * (y * (x / z))))
    else if (z <= 1.85d+67) then
        tmp = (b + ((y * (9.0d0 * x)) - (a * (t * (z * 4.0d0))))) / (z * c)
    else
        tmp = (t_1 + (b / z)) / 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 t_1 = -4.0 * (a * t);
	double tmp;
	if (z <= -1.55e+144) {
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	} else if (z <= 1.85e+67) {
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if z <= -1.55e+144:
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))))
	elif z <= 1.85e+67:
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c)
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (z <= -1.55e+144)
		tmp = Float64(Float64(1.0 / c) * Float64(t_1 + Float64(9.0 * Float64(y * Float64(x / z)))));
	elseif (z <= 1.85e+67)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (z <= -1.55e+144)
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	elseif (z <= 1.85e+67)
		tmp = (b + ((y * (9.0 * x)) - (a * (t * (z * 4.0))))) / (z * c);
	else
		tmp = (t_1 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+144], N[(N[(1.0 / c), $MachinePrecision] * N[(t$95$1 + N[(9.0 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+67], N[(N[(b + N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5500000000000001e144

   1. Initial program 47.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 47.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 47.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 42.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 42.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 42.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 42.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 47.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 47.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 47.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 51.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 51.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 78.9%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around inf 67.0%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) \cdot \frac{1}{c} \]
   8. Step-by-step derivation

      1. *-commutative 67.0%

         \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{\color{blue}{y \cdot x}}{z}\right) \cdot \frac{1}{c} \]

      2. associate-*r/ 78.8%

         \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(y \cdot \frac{x}{z}\right)}\right) \cdot \frac{1}{c} \]

   9. Simplified 78.8%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{9 \cdot \left(y \cdot \frac{x}{z}\right)}\right) \cdot \frac{1}{c} \]

   if -1.5500000000000001e144 < z < 1.8499999999999999e67

   1. Initial program 91.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   if 1.8499999999999999e67 < z

   1. Initial program 52.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 52.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 52.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 61.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 61.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 61.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 61.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 52.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 52.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 52.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 62.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 62.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 62.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 90.8%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around 0 81.0%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+144}:\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(y \cdot \frac{x}{z}\right)\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+67}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 6: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-246}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-282}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{a \cdot t}{\frac{c}{-4}}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-168}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 1600000000000:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ x z) (/ y c)))))
   (if (<= x -2.5e+79)
     t_1
     (if (<= x -2.05e-246)
       (* (/ t c) (/ a -0.25))
       (if (<= x -6e-282)
         (/ (/ b z) c)
         (if (<= x 5.5e-284)
           (/ (* a t) (/ c -4.0))
           (if (<= x 2.9e-168)
             (/ b (* z c))
             (if (<= x 1600000000000.0) (* (/ a c) (/ t -0.25)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (x <= -2.5e+79) {
		tmp = t_1;
	} else if (x <= -2.05e-246) {
		tmp = (t / c) * (a / -0.25);
	} else if (x <= -6e-282) {
		tmp = (b / z) / c;
	} else if (x <= 5.5e-284) {
		tmp = (a * t) / (c / -4.0);
	} else if (x <= 2.9e-168) {
		tmp = b / (z * c);
	} else if (x <= 1600000000000.0) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 9.0d0 * ((x / z) * (y / c))
    if (x <= (-2.5d+79)) then
        tmp = t_1
    else if (x <= (-2.05d-246)) then
        tmp = (t / c) * (a / (-0.25d0))
    else if (x <= (-6d-282)) then
        tmp = (b / z) / c
    else if (x <= 5.5d-284) then
        tmp = (a * t) / (c / (-4.0d0))
    else if (x <= 2.9d-168) then
        tmp = b / (z * c)
    else if (x <= 1600000000000.0d0) then
        tmp = (a / c) * (t / (-0.25d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((x / z) * (y / c));
	double tmp;
	if (x <= -2.5e+79) {
		tmp = t_1;
	} else if (x <= -2.05e-246) {
		tmp = (t / c) * (a / -0.25);
	} else if (x <= -6e-282) {
		tmp = (b / z) / c;
	} else if (x <= 5.5e-284) {
		tmp = (a * t) / (c / -4.0);
	} else if (x <= 2.9e-168) {
		tmp = b / (z * c);
	} else if (x <= 1600000000000.0) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 9.0 * ((x / z) * (y / c))
	tmp = 0
	if x <= -2.5e+79:
		tmp = t_1
	elif x <= -2.05e-246:
		tmp = (t / c) * (a / -0.25)
	elif x <= -6e-282:
		tmp = (b / z) / c
	elif x <= 5.5e-284:
		tmp = (a * t) / (c / -4.0)
	elif x <= 2.9e-168:
		tmp = b / (z * c)
	elif x <= 1600000000000.0:
		tmp = (a / c) * (t / -0.25)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)))
	tmp = 0.0
	if (x <= -2.5e+79)
		tmp = t_1;
	elseif (x <= -2.05e-246)
		tmp = Float64(Float64(t / c) * Float64(a / -0.25));
	elseif (x <= -6e-282)
		tmp = Float64(Float64(b / z) / c);
	elseif (x <= 5.5e-284)
		tmp = Float64(Float64(a * t) / Float64(c / -4.0));
	elseif (x <= 2.9e-168)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 1600000000000.0)
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 9.0 * ((x / z) * (y / c));
	tmp = 0.0;
	if (x <= -2.5e+79)
		tmp = t_1;
	elseif (x <= -2.05e-246)
		tmp = (t / c) * (a / -0.25);
	elseif (x <= -6e-282)
		tmp = (b / z) / c;
	elseif (x <= 5.5e-284)
		tmp = (a * t) / (c / -4.0);
	elseif (x <= 2.9e-168)
		tmp = b / (z * c);
	elseif (x <= 1600000000000.0)
		tmp = (a / c) * (t / -0.25);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+79], t$95$1, If[LessEqual[x, -2.05e-246], N[(N[(t / c), $MachinePrecision] * N[(a / -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-282], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[x, 5.5e-284], N[(N[(a * t), $MachinePrecision] / N[(c / -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e-168], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1600000000000.0], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -2.5e79 or 1.6e12 < x

   1. Initial program 80.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 54.1%

         \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

   6. Simplified 54.1%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{z \cdot c}} \]
   7. Step-by-step derivation

      1. *-commutative 54.1%

         \[\leadsto 9 \cdot \frac{\color{blue}{y \cdot x}}{z \cdot c} \]

      2. *-commutative 54.1%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{c \cdot z}} \]

      3. times-frac 55.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]

   8. Applied egg-rr 55.2%

      \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]

   if -2.5e79 < x < -2.04999999999999993e-246

   1. Initial program 74.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 74.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 47.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 47.7%

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

      3. *-commutative 47.7%

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

      4. associate-/l* 47.7%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 47.7%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 47.7%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]
   7. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{\frac{c}{-4}} \]

      2. div-inv 47.7%

         \[\leadsto \frac{t \cdot a}{\color{blue}{c \cdot \frac{1}{-4}}} \]

      3. times-frac 55.8%

         \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{\frac{1}{-4}}} \]

      4. metadata-eval 55.8%

         \[\leadsto \frac{t}{c} \cdot \frac{a}{\color{blue}{-0.25}} \]

   8. Applied egg-rr 55.8%

      \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{-0.25}} \]

   if -2.04999999999999993e-246 < x < -6.0000000000000001e-282

   1. Initial program 100.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 99.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 99.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 99.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in b around inf 52.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 52.1%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 52.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if -6.0000000000000001e-282 < x < 5.4999999999999995e-284

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 79.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 46.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 46.3%

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

      3. *-commutative 46.3%

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

      4. associate-/l* 46.3%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 46.3%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]

   if 5.4999999999999995e-284 < x < 2.8999999999999998e-168

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 72.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 46.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 46.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 2.8999999999999998e-168 < x < 1.6e12

   1. Initial program 74.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 74.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 69.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 48.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 48.0%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 48.0%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 48.0%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 52.5%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 52.5%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+79}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{-246}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-282}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-284}:\\ \;\;\;\;\frac{a \cdot t}{\frac{c}{-4}}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-168}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 1600000000000:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 7: 50.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-242}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-287}:\\ \;\;\;\;\frac{a \cdot t}{\frac{c}{-4}}\\ \mathbf{elif}\;x \leq 6.7 \cdot 10^{-168}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 10500000:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -8.2e+77)
   (* 9.0 (* (/ y z) (/ x c)))
   (if (<= x -6.2e-242)
     (* (/ t c) (/ a -0.25))
     (if (<= x -2e-281)
       (/ (/ b z) c)
       (if (<= x 8e-287)
         (/ (* a t) (/ c -4.0))
         (if (<= x 6.7e-168)
           (/ b (* z c))
           (if (<= x 10500000.0)
             (* (/ a c) (/ t -0.25))
             (* 9.0 (* (/ x z) (/ y c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -8.2e+77) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -6.2e-242) {
		tmp = (t / c) * (a / -0.25);
	} else if (x <= -2e-281) {
		tmp = (b / z) / c;
	} else if (x <= 8e-287) {
		tmp = (a * t) / (c / -4.0);
	} else if (x <= 6.7e-168) {
		tmp = b / (z * c);
	} else if (x <= 10500000.0) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = 9.0 * ((x / z) * (y / 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 <= (-8.2d+77)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= (-6.2d-242)) then
        tmp = (t / c) * (a / (-0.25d0))
    else if (x <= (-2d-281)) then
        tmp = (b / z) / c
    else if (x <= 8d-287) then
        tmp = (a * t) / (c / (-4.0d0))
    else if (x <= 6.7d-168) then
        tmp = b / (z * c)
    else if (x <= 10500000.0d0) then
        tmp = (a / c) * (t / (-0.25d0))
    else
        tmp = 9.0d0 * ((x / z) * (y / 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 <= -8.2e+77) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -6.2e-242) {
		tmp = (t / c) * (a / -0.25);
	} else if (x <= -2e-281) {
		tmp = (b / z) / c;
	} else if (x <= 8e-287) {
		tmp = (a * t) / (c / -4.0);
	} else if (x <= 6.7e-168) {
		tmp = b / (z * c);
	} else if (x <= 10500000.0) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = 9.0 * ((x / z) * (y / c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -8.2e+77:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= -6.2e-242:
		tmp = (t / c) * (a / -0.25)
	elif x <= -2e-281:
		tmp = (b / z) / c
	elif x <= 8e-287:
		tmp = (a * t) / (c / -4.0)
	elif x <= 6.7e-168:
		tmp = b / (z * c)
	elif x <= 10500000.0:
		tmp = (a / c) * (t / -0.25)
	else:
		tmp = 9.0 * ((x / z) * (y / c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -8.2e+77)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= -6.2e-242)
		tmp = Float64(Float64(t / c) * Float64(a / -0.25));
	elseif (x <= -2e-281)
		tmp = Float64(Float64(b / z) / c);
	elseif (x <= 8e-287)
		tmp = Float64(Float64(a * t) / Float64(c / -4.0));
	elseif (x <= 6.7e-168)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 10500000.0)
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	else
		tmp = Float64(9.0 * Float64(Float64(x / z) * Float64(y / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -8.2e+77)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= -6.2e-242)
		tmp = (t / c) * (a / -0.25);
	elseif (x <= -2e-281)
		tmp = (b / z) / c;
	elseif (x <= 8e-287)
		tmp = (a * t) / (c / -4.0);
	elseif (x <= 6.7e-168)
		tmp = b / (z * c);
	elseif (x <= 10500000.0)
		tmp = (a / c) * (t / -0.25);
	else
		tmp = 9.0 * ((x / z) * (y / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -8.2e+77], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e-242], N[(N[(t / c), $MachinePrecision] * N[(a / -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2e-281], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[x, 8e-287], N[(N[(a * t), $MachinePrecision] / N[(c / -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.7e-168], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 10500000.0], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(x / z), $MachinePrecision] * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -8.2000000000000002e77

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 78.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 62.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 62.4%

         \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

   6. Simplified 62.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{z \cdot c}} \]
   7. Step-by-step derivation

      1. *-commutative 62.4%

         \[\leadsto 9 \cdot \frac{\color{blue}{y \cdot x}}{z \cdot c} \]

      2. times-frac 68.8%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   8. Applied egg-rr 68.8%

      \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   if -8.2000000000000002e77 < x < -6.20000000000000031e-242

   1. Initial program 73.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.1%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 73.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 73.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 74.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 49.1%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 49.1%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 49.1%

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

      3. *-commutative 49.1%

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

      4. associate-/l* 49.1%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 49.1%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 49.1%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]
   7. Step-by-step derivation

      1. *-commutative 49.1%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{\frac{c}{-4}} \]

      2. div-inv 49.1%

         \[\leadsto \frac{t \cdot a}{\color{blue}{c \cdot \frac{1}{-4}}} \]

      3. times-frac 57.4%

         \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{\frac{1}{-4}}} \]

      4. metadata-eval 57.4%

         \[\leadsto \frac{t}{c} \cdot \frac{a}{\color{blue}{-0.25}} \]

   8. Applied egg-rr 57.4%

      \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{-0.25}} \]

   if -6.20000000000000031e-242 < x < -2e-281

   1. Initial program 100.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 99.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 99.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 99.5%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in b around inf 68.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 68.1%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 68.1%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 68.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if -2e-281 < x < 8.00000000000000017e-287

   1. Initial program 76.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 76.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 76.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 52.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 52.0%

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

      3. *-commutative 52.0%

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

      4. associate-/l* 52.0%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 52.0%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 52.0%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]

   if 8.00000000000000017e-287 < x < 6.69999999999999988e-168

   1. Initial program 81.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 81.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 81.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 81.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 81.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 81.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 73.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 48.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 6.69999999999999988e-168 < x < 1.05e7

   1. Initial program 74.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 74.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 74.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 71.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 87.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 49.2%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 49.2%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 49.2%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 49.2%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 49.2%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 53.8%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 53.8%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   if 1.05e7 < x

   1. Initial program 80.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 82.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 82.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 82.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 82.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 44.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 44.3%

         \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

   6. Simplified 44.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{z \cdot c}} \]
   7. Step-by-step derivation

      1. *-commutative 44.3%

         \[\leadsto 9 \cdot \frac{\color{blue}{y \cdot x}}{z \cdot c} \]

      2. *-commutative 44.3%

         \[\leadsto 9 \cdot \frac{y \cdot x}{\color{blue}{c \cdot z}} \]

      3. times-frac 48.4%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]

   8. Applied egg-rr 48.4%

      \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-242}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-287}:\\ \;\;\;\;\frac{a \cdot t}{\frac{c}{-4}}\\ \mathbf{elif}\;x \leq 6.7 \cdot 10^{-168}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 10500000:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\\ \end{array} \]

Alternative 8: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-248}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-283}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-286}:\\ \;\;\;\;\frac{a \cdot t}{\frac{c}{-4}}\\ \mathbf{elif}\;x \leq 2.02 \cdot 10^{-168}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -6e+77)
   (* 9.0 (* (/ y z) (/ x c)))
   (if (<= x -1.7e-248)
     (* (/ t c) (/ a -0.25))
     (if (<= x -7.5e-283)
       (/ (/ b z) c)
       (if (<= x 2.6e-286)
         (/ (* a t) (/ c -4.0))
         (if (<= x 2.02e-168)
           (/ b (* z c))
           (if (<= x 7.8e-9)
             (* (/ a c) (/ t -0.25))
             (* x (* 9.0 (/ y (* z c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -6e+77) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -1.7e-248) {
		tmp = (t / c) * (a / -0.25);
	} else if (x <= -7.5e-283) {
		tmp = (b / z) / c;
	} else if (x <= 2.6e-286) {
		tmp = (a * t) / (c / -4.0);
	} else if (x <= 2.02e-168) {
		tmp = b / (z * c);
	} else if (x <= 7.8e-9) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = x * (9.0 * (y / (z * 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 <= (-6d+77)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= (-1.7d-248)) then
        tmp = (t / c) * (a / (-0.25d0))
    else if (x <= (-7.5d-283)) then
        tmp = (b / z) / c
    else if (x <= 2.6d-286) then
        tmp = (a * t) / (c / (-4.0d0))
    else if (x <= 2.02d-168) then
        tmp = b / (z * c)
    else if (x <= 7.8d-9) then
        tmp = (a / c) * (t / (-0.25d0))
    else
        tmp = x * (9.0d0 * (y / (z * 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 <= -6e+77) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -1.7e-248) {
		tmp = (t / c) * (a / -0.25);
	} else if (x <= -7.5e-283) {
		tmp = (b / z) / c;
	} else if (x <= 2.6e-286) {
		tmp = (a * t) / (c / -4.0);
	} else if (x <= 2.02e-168) {
		tmp = b / (z * c);
	} else if (x <= 7.8e-9) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = x * (9.0 * (y / (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -6e+77:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= -1.7e-248:
		tmp = (t / c) * (a / -0.25)
	elif x <= -7.5e-283:
		tmp = (b / z) / c
	elif x <= 2.6e-286:
		tmp = (a * t) / (c / -4.0)
	elif x <= 2.02e-168:
		tmp = b / (z * c)
	elif x <= 7.8e-9:
		tmp = (a / c) * (t / -0.25)
	else:
		tmp = x * (9.0 * (y / (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -6e+77)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= -1.7e-248)
		tmp = Float64(Float64(t / c) * Float64(a / -0.25));
	elseif (x <= -7.5e-283)
		tmp = Float64(Float64(b / z) / c);
	elseif (x <= 2.6e-286)
		tmp = Float64(Float64(a * t) / Float64(c / -4.0));
	elseif (x <= 2.02e-168)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 7.8e-9)
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	else
		tmp = Float64(x * Float64(9.0 * Float64(y / Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -6e+77)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= -1.7e-248)
		tmp = (t / c) * (a / -0.25);
	elseif (x <= -7.5e-283)
		tmp = (b / z) / c;
	elseif (x <= 2.6e-286)
		tmp = (a * t) / (c / -4.0);
	elseif (x <= 2.02e-168)
		tmp = b / (z * c);
	elseif (x <= 7.8e-9)
		tmp = (a / c) * (t / -0.25);
	else
		tmp = x * (9.0 * (y / (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -6e+77], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.7e-248], N[(N[(t / c), $MachinePrecision] * N[(a / -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-283], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[x, 2.6e-286], N[(N[(a * t), $MachinePrecision] / N[(c / -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.02e-168], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-9], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision], N[(x * N[(9.0 * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -5.9999999999999996e77

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 78.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 62.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 62.4%

         \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

   6. Simplified 62.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{z \cdot c}} \]
   7. Step-by-step derivation

      1. *-commutative 62.4%

         \[\leadsto 9 \cdot \frac{\color{blue}{y \cdot x}}{z \cdot c} \]

      2. times-frac 68.8%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   8. Applied egg-rr 68.8%

      \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   if -5.9999999999999996e77 < x < -1.6999999999999999e-248

   1. Initial program 73.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 48.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-/l* 48.4%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 48.4%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 48.4%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{\frac{c}{-4}} \]

      2. div-inv 48.4%

         \[\leadsto \frac{t \cdot a}{\color{blue}{c \cdot \frac{1}{-4}}} \]

      3. times-frac 56.6%

         \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{\frac{1}{-4}}} \]

      4. metadata-eval 56.6%

         \[\leadsto \frac{t}{c} \cdot \frac{a}{\color{blue}{-0.25}} \]

   8. Applied egg-rr 56.6%

      \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{-0.25}} \]

   if -1.6999999999999999e-248 < x < -7.5000000000000001e-283

   1. Initial program 100.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 99.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 99.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 99.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in b around inf 52.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 52.1%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 52.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if -7.5000000000000001e-283 < x < 2.6e-286

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 79.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 46.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 46.3%

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

      3. *-commutative 46.3%

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

      4. associate-/l* 46.3%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 46.3%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]

   if 2.6e-286 < x < 2.0199999999999999e-168

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 72.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 46.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 46.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 2.0199999999999999e-168 < x < 7.8000000000000004e-9

   1. Initial program 72.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 78.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 78.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 71.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 88.3%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 51.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 51.7%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 51.7%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 51.7%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 51.7%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 57.2%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 57.2%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   if 7.8000000000000004e-9 < x

   1. Initial program 80.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 80.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 79.5%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]

   6. Taylor expanded in x around inf 41.6%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 41.6%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. *-commutative 41.6%

         \[\leadsto \frac{x \cdot y}{\color{blue}{z \cdot c}} \cdot 9 \]

      3. associate-*r/ 45.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{z \cdot c}\right)} \cdot 9 \]

      4. associate-*l* 45.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z \cdot c} \cdot 9\right)} \]

      5. *-commutative 45.2%

         \[\leadsto x \cdot \left(\frac{y}{\color{blue}{c \cdot z}} \cdot 9\right) \]

   8. Simplified 45.2%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{c \cdot z} \cdot 9\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-248}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-283}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-286}:\\ \;\;\;\;\frac{a \cdot t}{\frac{c}{-4}}\\ \mathbf{elif}\;x \leq 2.02 \cdot 10^{-168}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{y}{z \cdot c}\right)\\ \end{array} \]

Alternative 9: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-244}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-279}:\\ \;\;\;\;\frac{a \cdot t}{\frac{c}{-4}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-167}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 62000000000000:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -6e+77)
   (* 9.0 (* (/ y z) (/ x c)))
   (if (<= x -9.2e-244)
     (* (/ t c) (/ a -0.25))
     (if (<= x -1.05e-281)
       (/ (/ b z) c)
       (if (<= x 1.6e-279)
         (/ (* a t) (/ c -4.0))
         (if (<= x 1.3e-167)
           (/ b (* z c))
           (if (<= x 62000000000000.0)
             (* (/ a c) (/ t -0.25))
             (* x (* 9.0 (/ (/ y c) z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -6e+77) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -9.2e-244) {
		tmp = (t / c) * (a / -0.25);
	} else if (x <= -1.05e-281) {
		tmp = (b / z) / c;
	} else if (x <= 1.6e-279) {
		tmp = (a * t) / (c / -4.0);
	} else if (x <= 1.3e-167) {
		tmp = b / (z * c);
	} else if (x <= 62000000000000.0) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = x * (9.0 * ((y / c) / z));
	}
	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 <= (-6d+77)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= (-9.2d-244)) then
        tmp = (t / c) * (a / (-0.25d0))
    else if (x <= (-1.05d-281)) then
        tmp = (b / z) / c
    else if (x <= 1.6d-279) then
        tmp = (a * t) / (c / (-4.0d0))
    else if (x <= 1.3d-167) then
        tmp = b / (z * c)
    else if (x <= 62000000000000.0d0) then
        tmp = (a / c) * (t / (-0.25d0))
    else
        tmp = x * (9.0d0 * ((y / c) / z))
    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 <= -6e+77) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= -9.2e-244) {
		tmp = (t / c) * (a / -0.25);
	} else if (x <= -1.05e-281) {
		tmp = (b / z) / c;
	} else if (x <= 1.6e-279) {
		tmp = (a * t) / (c / -4.0);
	} else if (x <= 1.3e-167) {
		tmp = b / (z * c);
	} else if (x <= 62000000000000.0) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = x * (9.0 * ((y / c) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -6e+77:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= -9.2e-244:
		tmp = (t / c) * (a / -0.25)
	elif x <= -1.05e-281:
		tmp = (b / z) / c
	elif x <= 1.6e-279:
		tmp = (a * t) / (c / -4.0)
	elif x <= 1.3e-167:
		tmp = b / (z * c)
	elif x <= 62000000000000.0:
		tmp = (a / c) * (t / -0.25)
	else:
		tmp = x * (9.0 * ((y / c) / z))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -6e+77)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= -9.2e-244)
		tmp = Float64(Float64(t / c) * Float64(a / -0.25));
	elseif (x <= -1.05e-281)
		tmp = Float64(Float64(b / z) / c);
	elseif (x <= 1.6e-279)
		tmp = Float64(Float64(a * t) / Float64(c / -4.0));
	elseif (x <= 1.3e-167)
		tmp = Float64(b / Float64(z * c));
	elseif (x <= 62000000000000.0)
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	else
		tmp = Float64(x * Float64(9.0 * Float64(Float64(y / c) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -6e+77)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= -9.2e-244)
		tmp = (t / c) * (a / -0.25);
	elseif (x <= -1.05e-281)
		tmp = (b / z) / c;
	elseif (x <= 1.6e-279)
		tmp = (a * t) / (c / -4.0);
	elseif (x <= 1.3e-167)
		tmp = b / (z * c);
	elseif (x <= 62000000000000.0)
		tmp = (a / c) * (t / -0.25);
	else
		tmp = x * (9.0 * ((y / c) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -6e+77], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.2e-244], N[(N[(t / c), $MachinePrecision] * N[(a / -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.05e-281], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[x, 1.6e-279], N[(N[(a * t), $MachinePrecision] / N[(c / -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-167], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 62000000000000.0], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision], N[(x * N[(9.0 * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if x < -5.9999999999999996e77

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 78.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 62.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 62.4%

         \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

   6. Simplified 62.4%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{z \cdot c}} \]
   7. Step-by-step derivation

      1. *-commutative 62.4%

         \[\leadsto 9 \cdot \frac{\color{blue}{y \cdot x}}{z \cdot c} \]

      2. times-frac 68.8%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   8. Applied egg-rr 68.8%

      \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   if -5.9999999999999996e77 < x < -9.2e-244

   1. Initial program 73.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 73.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 73.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 73.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.3%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 48.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-/l* 48.4%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 48.4%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 48.4%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]
   7. Step-by-step derivation

      1. *-commutative 48.4%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{\frac{c}{-4}} \]

      2. div-inv 48.4%

         \[\leadsto \frac{t \cdot a}{\color{blue}{c \cdot \frac{1}{-4}}} \]

      3. times-frac 56.6%

         \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{\frac{1}{-4}}} \]

      4. metadata-eval 56.6%

         \[\leadsto \frac{t}{c} \cdot \frac{a}{\color{blue}{-0.25}} \]

   8. Applied egg-rr 56.6%

      \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{-0.25}} \]

   if -9.2e-244 < x < -1.0499999999999999e-281

   1. Initial program 100.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 100.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 100.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 99.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 99.2%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 99.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in b around inf 52.1%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 52.1%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 52.1%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if -1.0499999999999999e-281 < x < 1.5999999999999999e-279

   1. Initial program 79.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.3%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.4%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 79.3%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 46.3%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 46.3%

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

      3. *-commutative 46.3%

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

      4. associate-/l* 46.3%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 46.3%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 46.3%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]

   if 1.5999999999999999e-279 < x < 1.2999999999999999e-167

   1. Initial program 80.5%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.5%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 72.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 46.0%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 46.0%

      \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

   if 1.2999999999999999e-167 < x < 6.2e13

   1. Initial program 74.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 74.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 74.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 74.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 74.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 79.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 69.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 85.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 48.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 48.0%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 48.0%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 48.0%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 52.5%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 52.5%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   if 6.2e13 < x

   1. Initial program 80.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 78.6%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]

   6. Taylor expanded in x around inf 43.1%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. *-commutative 43.1%

         \[\leadsto \frac{x \cdot y}{\color{blue}{z \cdot c}} \cdot 9 \]

      3. associate-*r/ 47.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{z \cdot c}\right)} \cdot 9 \]

      4. associate-*l* 47.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z \cdot c} \cdot 9\right)} \]

      5. *-commutative 47.2%

         \[\leadsto x \cdot \left(\frac{y}{\color{blue}{c \cdot z}} \cdot 9\right) \]

   8. Simplified 47.2%

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

      1. expm1-log1p-u 34.8%

         \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)\right)} \cdot 9\right) \]

      2. expm1-udef 23.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)} - 1\right)} \cdot 9\right) \]

   10. Applied egg-rr 23.0%

       \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)} - 1\right)} \cdot 9\right) \]
   11. Step-by-step derivation

       1. expm1-def 34.8%

          \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)\right)} \cdot 9\right) \]

       2. expm1-log1p 47.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{y}{c \cdot z}} \cdot 9\right) \]

       3. associate-/r* 51.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{y}{c}}{z}} \cdot 9\right) \]

   12. Simplified 51.2%

       \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{y}{c}}{z}} \cdot 9\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-244}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-279}:\\ \;\;\;\;\frac{a \cdot t}{\frac{c}{-4}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-167}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 62000000000000:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]

Alternative 10: 73.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+46} \lor \neg \left(x \leq 2.05 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(t_1 + 9 \cdot \left(y \cdot \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))))
   (if (or (<= x -4.5e+46) (not (<= x 2.05e-89)))
     (* (/ 1.0 c) (+ t_1 (* 9.0 (* y (/ x z)))))
     (/ (+ t_1 (/ b z)) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if ((x <= -4.5e+46) || !(x <= 2.05e-89)) {
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	} else {
		tmp = (t_1 + (b / z)) / 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) :: t_1
    real(8) :: tmp
    t_1 = (-4.0d0) * (a * t)
    if ((x <= (-4.5d+46)) .or. (.not. (x <= 2.05d-89))) then
        tmp = (1.0d0 / c) * (t_1 + (9.0d0 * (y * (x / z))))
    else
        tmp = (t_1 + (b / z)) / 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 t_1 = -4.0 * (a * t);
	double tmp;
	if ((x <= -4.5e+46) || !(x <= 2.05e-89)) {
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if (x <= -4.5e+46) or not (x <= 2.05e-89):
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))))
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if ((x <= -4.5e+46) || !(x <= 2.05e-89))
		tmp = Float64(Float64(1.0 / c) * Float64(t_1 + Float64(9.0 * Float64(y * Float64(x / z)))));
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if ((x <= -4.5e+46) || ~((x <= 2.05e-89)))
		tmp = (1.0 / c) * (t_1 + (9.0 * (y * (x / z))));
	else
		tmp = (t_1 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -4.5e+46], N[Not[LessEqual[x, 2.05e-89]], $MachinePrecision]], N[(N[(1.0 / c), $MachinePrecision] * N[(t$95$1 + N[(9.0 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000001e46 or 2.0499999999999999e-89 < x

   1. Initial program 79.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 78.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 79.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 79.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 78.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 72.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 74.3%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around inf 67.2%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{9 \cdot \frac{x \cdot y}{z}}\right) \cdot \frac{1}{c} \]
   8. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{\color{blue}{y \cdot x}}{z}\right) \cdot \frac{1}{c} \]

      2. associate-*r/ 71.2%

         \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \color{blue}{\left(y \cdot \frac{x}{z}\right)}\right) \cdot \frac{1}{c} \]

   9. Simplified 71.2%

      \[\leadsto \left(-4 \cdot \left(a \cdot t\right) + \color{blue}{9 \cdot \left(y \cdot \frac{x}{z}\right)}\right) \cdot \frac{1}{c} \]

   if -4.5000000000000001e46 < x < 2.0499999999999999e-89

   1. Initial program 75.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 75.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 75.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 75.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 75.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.0%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.7%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 90.5%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around 0 80.7%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+46} \lor \neg \left(x \leq 2.05 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{1}{c} \cdot \left(-4 \cdot \left(a \cdot t\right) + 9 \cdot \left(y \cdot \frac{x}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 11: 69.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+46}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;x \leq 18000000000:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -4.0 (* a t))))
   (if (<= x -1.7e+46)
     (/ (+ t_1 (* 9.0 (/ (* x y) z))) c)
     (if (<= x 18000000000.0)
       (/ (+ t_1 (/ b z)) c)
       (* x (* 9.0 (/ (/ y c) z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -4.0 * (a * t);
	double tmp;
	if (x <= -1.7e+46) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else if (x <= 18000000000.0) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = x * (9.0 * ((y / c) / z));
	}
	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 = (-4.0d0) * (a * t)
    if (x <= (-1.7d+46)) then
        tmp = (t_1 + (9.0d0 * ((x * y) / z))) / c
    else if (x <= 18000000000.0d0) then
        tmp = (t_1 + (b / z)) / c
    else
        tmp = x * (9.0d0 * ((y / c) / z))
    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 = -4.0 * (a * t);
	double tmp;
	if (x <= -1.7e+46) {
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	} else if (x <= 18000000000.0) {
		tmp = (t_1 + (b / z)) / c;
	} else {
		tmp = x * (9.0 * ((y / c) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -4.0 * (a * t)
	tmp = 0
	if x <= -1.7e+46:
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c
	elif x <= 18000000000.0:
		tmp = (t_1 + (b / z)) / c
	else:
		tmp = x * (9.0 * ((y / c) / z))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-4.0 * Float64(a * t))
	tmp = 0.0
	if (x <= -1.7e+46)
		tmp = Float64(Float64(t_1 + Float64(9.0 * Float64(Float64(x * y) / z))) / c);
	elseif (x <= 18000000000.0)
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	else
		tmp = Float64(x * Float64(9.0 * Float64(Float64(y / c) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -4.0 * (a * t);
	tmp = 0.0;
	if (x <= -1.7e+46)
		tmp = (t_1 + (9.0 * ((x * y) / z))) / c;
	elseif (x <= 18000000000.0)
		tmp = (t_1 + (b / z)) / c;
	else
		tmp = x * (9.0 * ((y / c) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+46], N[(N[(t$95$1 + N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[x, 18000000000.0], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(x * N[(9.0 * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6999999999999999e46

   1. Initial program 79.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 79.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 79.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 79.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 79.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 79.6%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 78.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 79.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 76.2%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in b around 0 74.4%

      \[\leadsto \color{blue}{\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}} \]

   if -1.6999999999999999e46 < x < 1.8e10

   1. Initial program 76.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 78.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 76.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 88.6%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around 0 79.1%

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

   if 1.8e10 < x

   1. Initial program 80.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 78.6%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]

   6. Taylor expanded in x around inf 43.1%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. *-commutative 43.1%

         \[\leadsto \frac{x \cdot y}{\color{blue}{z \cdot c}} \cdot 9 \]

      3. associate-*r/ 47.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{z \cdot c}\right)} \cdot 9 \]

      4. associate-*l* 47.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z \cdot c} \cdot 9\right)} \]

      5. *-commutative 47.2%

         \[\leadsto x \cdot \left(\frac{y}{\color{blue}{c \cdot z}} \cdot 9\right) \]

   8. Simplified 47.2%

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

      1. expm1-log1p-u 34.8%

         \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)\right)} \cdot 9\right) \]

      2. expm1-udef 23.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)} - 1\right)} \cdot 9\right) \]

   10. Applied egg-rr 23.0%

       \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)} - 1\right)} \cdot 9\right) \]
   11. Step-by-step derivation

       1. expm1-def 34.8%

          \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)\right)} \cdot 9\right) \]

       2. expm1-log1p 47.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{y}{c \cdot z}} \cdot 9\right) \]

       3. associate-/r* 51.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{y}{c}}{z}} \cdot 9\right) \]

   12. Simplified 51.2%

       \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{y}{c}}{z}} \cdot 9\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+46}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;x \leq 18000000000:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]

Alternative 12: 68.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+141}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -2.3e+141)
   (* 9.0 (* (/ y z) (/ x c)))
   (if (<= x 1.1e+15)
     (/ (+ (* -4.0 (* a t)) (/ b z)) c)
     (* x (* 9.0 (/ (/ y c) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -2.3e+141) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= 1.1e+15) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = x * (9.0 * ((y / c) / z));
	}
	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 <= (-2.3d+141)) then
        tmp = 9.0d0 * ((y / z) * (x / c))
    else if (x <= 1.1d+15) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = x * (9.0d0 * ((y / c) / z))
    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 <= -2.3e+141) {
		tmp = 9.0 * ((y / z) * (x / c));
	} else if (x <= 1.1e+15) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = x * (9.0 * ((y / c) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -2.3e+141:
		tmp = 9.0 * ((y / z) * (x / c))
	elif x <= 1.1e+15:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = x * (9.0 * ((y / c) / z))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -2.3e+141)
		tmp = Float64(9.0 * Float64(Float64(y / z) * Float64(x / c)));
	elseif (x <= 1.1e+15)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(x * Float64(9.0 * Float64(Float64(y / c) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -2.3e+141)
		tmp = 9.0 * ((y / z) * (x / c));
	elseif (x <= 1.1e+15)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = x * (9.0 * ((y / c) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -2.3e+141], N[(9.0 * N[(N[(y / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+15], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(x * N[(9.0 * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3000000000000002e141

   1. Initial program 77.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 75.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 75.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 75.7%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 75.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 77.7%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 75.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 65.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 65.3%

         \[\leadsto 9 \cdot \frac{x \cdot y}{\color{blue}{z \cdot c}} \]

   6. Simplified 65.3%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{z \cdot c}} \]
   7. Step-by-step derivation

      1. *-commutative 65.3%

         \[\leadsto 9 \cdot \frac{\color{blue}{y \cdot x}}{z \cdot c} \]

      2. times-frac 75.2%

         \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   8. Applied egg-rr 75.2%

      \[\leadsto 9 \cdot \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{c}\right)} \]

   if -2.3000000000000002e141 < x < 1.1e15

   1. Initial program 77.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 76.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 77.8%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 76.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 88.0%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around 0 76.1%

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

   if 1.1e15 < x

   1. Initial program 80.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 78.6%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]

   6. Taylor expanded in x around inf 43.1%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. *-commutative 43.1%

         \[\leadsto \frac{x \cdot y}{\color{blue}{z \cdot c}} \cdot 9 \]

      3. associate-*r/ 47.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{z \cdot c}\right)} \cdot 9 \]

      4. associate-*l* 47.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z \cdot c} \cdot 9\right)} \]

      5. *-commutative 47.2%

         \[\leadsto x \cdot \left(\frac{y}{\color{blue}{c \cdot z}} \cdot 9\right) \]

   8. Simplified 47.2%

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

      1. expm1-log1p-u 34.8%

         \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)\right)} \cdot 9\right) \]

      2. expm1-udef 23.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)} - 1\right)} \cdot 9\right) \]

   10. Applied egg-rr 23.0%

       \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)} - 1\right)} \cdot 9\right) \]
   11. Step-by-step derivation

       1. expm1-def 34.8%

          \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)\right)} \cdot 9\right) \]

       2. expm1-log1p 47.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{y}{c \cdot z}} \cdot 9\right) \]

       3. associate-/r* 51.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{y}{c}}{z}} \cdot 9\right) \]

   12. Simplified 51.2%

       \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{y}{c}}{z}} \cdot 9\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+141}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]

Alternative 13: 69.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -3.6e+78)
   (/ (+ b (* 9.0 (* x y))) (* z c))
   (if (<= x 5.2e+14)
     (/ (+ (* -4.0 (* a t)) (/ b z)) c)
     (* x (* 9.0 (/ (/ y c) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -3.6e+78) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (x <= 5.2e+14) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = x * (9.0 * ((y / c) / z));
	}
	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 <= (-3.6d+78)) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else if (x <= 5.2d+14) then
        tmp = (((-4.0d0) * (a * t)) + (b / z)) / c
    else
        tmp = x * (9.0d0 * ((y / c) / z))
    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 <= -3.6e+78) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else if (x <= 5.2e+14) {
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	} else {
		tmp = x * (9.0 * ((y / c) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -3.6e+78:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	elif x <= 5.2e+14:
		tmp = ((-4.0 * (a * t)) + (b / z)) / c
	else:
		tmp = x * (9.0 * ((y / c) / z))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -3.6e+78)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	elseif (x <= 5.2e+14)
		tmp = Float64(Float64(Float64(-4.0 * Float64(a * t)) + Float64(b / z)) / c);
	else
		tmp = Float64(x * Float64(9.0 * Float64(Float64(y / c) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -3.6e+78)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	elseif (x <= 5.2e+14)
		tmp = ((-4.0 * (a * t)) + (b / z)) / c;
	else
		tmp = x * (9.0 * ((y / c) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -3.6e+78], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+14], N[(N[(N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(x * N[(9.0 * N[(N[(y / c), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.6000000000000002e78

   1. Initial program 80.2%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.2%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 78.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 78.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in x around inf 70.0%

      \[\leadsto \frac{\color{blue}{9 \cdot \left(x \cdot y\right)} + b}{z \cdot c} \]

   if -3.6000000000000002e78 < x < 5.2e14

   1. Initial program 76.1%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 76.1%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 76.1%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 78.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 78.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 78.8%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 78.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 76.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 76.1%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 75.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 76.9%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 75.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 87.8%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in x around 0 77.7%

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

   if 5.2e14 < x

   1. Initial program 80.0%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 80.1%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.1%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 78.6%

      \[\leadsto \color{blue}{\frac{1}{z} \cdot \frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{c}} \]

   6. Taylor expanded in x around inf 43.1%

      \[\leadsto \color{blue}{9 \cdot \frac{x \cdot y}{c \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{c \cdot z} \cdot 9} \]

      2. *-commutative 43.1%

         \[\leadsto \frac{x \cdot y}{\color{blue}{z \cdot c}} \cdot 9 \]

      3. associate-*r/ 47.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{z \cdot c}\right)} \cdot 9 \]

      4. associate-*l* 47.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z \cdot c} \cdot 9\right)} \]

      5. *-commutative 47.2%

         \[\leadsto x \cdot \left(\frac{y}{\color{blue}{c \cdot z}} \cdot 9\right) \]

   8. Simplified 47.2%

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

      1. expm1-log1p-u 34.8%

         \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)\right)} \cdot 9\right) \]

      2. expm1-udef 23.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)} - 1\right)} \cdot 9\right) \]

   10. Applied egg-rr 23.0%

       \[\leadsto x \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)} - 1\right)} \cdot 9\right) \]
   11. Step-by-step derivation

       1. expm1-def 34.8%

          \[\leadsto x \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{c \cdot z}\right)\right)} \cdot 9\right) \]

       2. expm1-log1p 47.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{y}{c \cdot z}} \cdot 9\right) \]

       3. associate-/r* 51.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{y}{c}}{z}} \cdot 9\right) \]

   12. Simplified 51.2%

       \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{y}{c}}{z}} \cdot 9\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \end{array} \]

Alternative 14: 48.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-57} \lor \neg \left(t \leq 2.5 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.5e-57) (not (<= t 2.5e-101)))
   (* (/ a c) (/ t -0.25))
   (/ (/ b z) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.5e-57) || !(t <= 2.5e-101)) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = (b / z) / 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 ((t <= (-1.5d-57)) .or. (.not. (t <= 2.5d-101))) then
        tmp = (a / c) * (t / (-0.25d0))
    else
        tmp = (b / z) / 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 ((t <= -1.5e-57) || !(t <= 2.5e-101)) {
		tmp = (a / c) * (t / -0.25);
	} else {
		tmp = (b / z) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.5e-57) or not (t <= 2.5e-101):
		tmp = (a / c) * (t / -0.25)
	else:
		tmp = (b / z) / c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.5e-57) || !(t <= 2.5e-101))
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	else
		tmp = Float64(Float64(b / z) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.5e-57) || ~((t <= 2.5e-101)))
		tmp = (a / c) * (t / -0.25);
	else
		tmp = (b / z) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.5e-57], N[Not[LessEqual[t, 2.5e-101]], $MachinePrecision]], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e-57 or 2.5e-101 < t

   1. Initial program 72.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 77.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 77.3%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 77.3%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 77.3%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 72.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 72.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 71.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 72.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 68.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 80.6%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 55.4%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 55.4%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 55.4%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 55.4%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 55.4%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 58.5%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 58.5%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   if -1.5e-57 < t < 2.5e-101

   1. Initial program 84.4%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.4%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.4%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 84.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.4%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 84.4%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 83.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 82.9%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in b around inf 41.7%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 41.7%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 42.8%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 42.8%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-57} \lor \neg \left(t \leq 2.5 \cdot 10^{-101}\right):\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 15: 49.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-48}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -7e-48)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 4e-102) (/ (/ b z) c) (* (/ a c) (/ t -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -7e-48) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 4e-102) {
		tmp = (b / z) / c;
	} else {
		tmp = (a / c) * (t / -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 (t <= (-7d-48)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 4d-102) then
        tmp = (b / z) / c
    else
        tmp = (a / c) * (t / (-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 (t <= -7e-48) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 4e-102) {
		tmp = (b / z) / c;
	} else {
		tmp = (a / c) * (t / -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -7e-48:
		tmp = -4.0 * (a / (c / t))
	elif t <= 4e-102:
		tmp = (b / z) / c
	else:
		tmp = (a / c) * (t / -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -7e-48)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 4e-102)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -7e-48)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 4e-102)
		tmp = (b / z) / c;
	else
		tmp = (a / c) * (t / -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -7e-48], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-102], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.99999999999999982e-48

   1. Initial program 72.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 64.8%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if -6.99999999999999982e-48 < t < 3.99999999999999973e-102

   1. Initial program 84.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 84.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 84.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 83.0%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in b around inf 41.4%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 41.4%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

      2. associate-/r* 42.5%

         \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   9. Simplified 42.5%

      \[\leadsto \color{blue}{\frac{\frac{b}{z}}{c}} \]

   if 3.99999999999999973e-102 < t

   1. Initial program 71.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 74.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 70.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 73.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 70.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 53.0%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 53.0%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 53.0%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 54.8%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-48}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \]

Alternative 16: 49.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-48}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.8e-48)
   (* -4.0 (/ a (/ c t)))
   (if (<= t 8.8e-102) (* (/ b z) (/ 1.0 c)) (* (/ a c) (/ t -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.8e-48) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 8.8e-102) {
		tmp = (b / z) * (1.0 / c);
	} else {
		tmp = (a / c) * (t / -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 (t <= (-3.8d-48)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (t <= 8.8d-102) then
        tmp = (b / z) * (1.0d0 / c)
    else
        tmp = (a / c) * (t / (-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 (t <= -3.8e-48) {
		tmp = -4.0 * (a / (c / t));
	} else if (t <= 8.8e-102) {
		tmp = (b / z) * (1.0 / c);
	} else {
		tmp = (a / c) * (t / -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.8e-48:
		tmp = -4.0 * (a / (c / t))
	elif t <= 8.8e-102:
		tmp = (b / z) * (1.0 / c)
	else:
		tmp = (a / c) * (t / -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.8e-48)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (t <= 8.8e-102)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.8e-48)
		tmp = -4.0 * (a / (c / t));
	elseif (t <= 8.8e-102)
		tmp = (b / z) * (1.0 / c);
	else
		tmp = (a / c) * (t / -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.8e-48], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-102], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.80000000000000002e-48

   1. Initial program 72.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. associate-/l* 64.8%

         \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   6. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{a}{\frac{c}{t}} \cdot -4} \]

   if -3.80000000000000002e-48 < t < 8.80000000000000052e-102

   1. Initial program 84.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 84.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 84.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in b around inf 42.5%

      \[\leadsto \color{blue}{\frac{b}{z}} \cdot \frac{1}{c} \]

   if 8.80000000000000052e-102 < t

   1. Initial program 71.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 74.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 70.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 73.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 70.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 53.0%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 53.0%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 53.0%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 54.8%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-48}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \]

Alternative 17: 49.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-52}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-101}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -8e-52)
   (* (/ t c) (/ a -0.25))
   (if (<= t 1.9e-101) (* (/ b z) (/ 1.0 c)) (* (/ a c) (/ t -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8e-52) {
		tmp = (t / c) * (a / -0.25);
	} else if (t <= 1.9e-101) {
		tmp = (b / z) * (1.0 / c);
	} else {
		tmp = (a / c) * (t / -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 (t <= (-8d-52)) then
        tmp = (t / c) * (a / (-0.25d0))
    else if (t <= 1.9d-101) then
        tmp = (b / z) * (1.0d0 / c)
    else
        tmp = (a / c) * (t / (-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 (t <= -8e-52) {
		tmp = (t / c) * (a / -0.25);
	} else if (t <= 1.9e-101) {
		tmp = (b / z) * (1.0 / c);
	} else {
		tmp = (a / c) * (t / -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -8e-52:
		tmp = (t / c) * (a / -0.25)
	elif t <= 1.9e-101:
		tmp = (b / z) * (1.0 / c)
	else:
		tmp = (a / c) * (t / -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -8e-52)
		tmp = Float64(Float64(t / c) * Float64(a / -0.25));
	elseif (t <= 1.9e-101)
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	else
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -8e-52)
		tmp = (t / c) * (a / -0.25);
	elseif (t <= 1.9e-101)
		tmp = (b / z) * (1.0 / c);
	else
		tmp = (a / c) * (t / -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -8e-52], N[(N[(t / c), $MachinePrecision] * N[(a / -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-101], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.0000000000000001e-52

   1. Initial program 72.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-/l* 58.7%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 58.7%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 58.7%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]
   7. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{\frac{c}{-4}} \]

      2. div-inv 58.7%

         \[\leadsto \frac{t \cdot a}{\color{blue}{c \cdot \frac{1}{-4}}} \]

      3. times-frac 64.8%

         \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{\frac{1}{-4}}} \]

      4. metadata-eval 64.8%

         \[\leadsto \frac{t}{c} \cdot \frac{a}{\color{blue}{-0.25}} \]

   8. Applied egg-rr 64.8%

      \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{-0.25}} \]

   if -8.0000000000000001e-52 < t < 1.90000000000000005e-101

   1. Initial program 84.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 84.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 84.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in b around inf 42.5%

      \[\leadsto \color{blue}{\frac{b}{z}} \cdot \frac{1}{c} \]

   if 1.90000000000000005e-101 < t

   1. Initial program 71.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 74.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 70.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 73.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 70.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 53.0%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 53.0%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 53.0%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 54.8%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-52}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-101}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \]

Alternative 18: 49.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{-52}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -6.1e-52)
   (* (/ t c) (/ a -0.25))
   (if (<= t 2.5e-101) (/ 1.0 (* c (/ z b))) (* (/ a c) (/ t -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -6.1e-52) {
		tmp = (t / c) * (a / -0.25);
	} else if (t <= 2.5e-101) {
		tmp = 1.0 / (c * (z / b));
	} else {
		tmp = (a / c) * (t / -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 (t <= (-6.1d-52)) then
        tmp = (t / c) * (a / (-0.25d0))
    else if (t <= 2.5d-101) then
        tmp = 1.0d0 / (c * (z / b))
    else
        tmp = (a / c) * (t / (-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 (t <= -6.1e-52) {
		tmp = (t / c) * (a / -0.25);
	} else if (t <= 2.5e-101) {
		tmp = 1.0 / (c * (z / b));
	} else {
		tmp = (a / c) * (t / -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -6.1e-52:
		tmp = (t / c) * (a / -0.25)
	elif t <= 2.5e-101:
		tmp = 1.0 / (c * (z / b))
	else:
		tmp = (a / c) * (t / -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -6.1e-52)
		tmp = Float64(Float64(t / c) * Float64(a / -0.25));
	elseif (t <= 2.5e-101)
		tmp = Float64(1.0 / Float64(c * Float64(z / b)));
	else
		tmp = Float64(Float64(a / c) * Float64(t / -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -6.1e-52)
		tmp = (t / c) * (a / -0.25);
	elseif (t <= 2.5e-101)
		tmp = 1.0 / (c * (z / b));
	else
		tmp = (a / c) * (t / -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -6.1e-52], N[(N[(t / c), $MachinePrecision] * N[(a / -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-101], N[(1.0 / N[(c * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a / c), $MachinePrecision] * N[(t / -0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.0999999999999999e-52

   1. Initial program 72.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 72.8%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 72.8%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 79.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 79.9%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 79.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 72.8%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 72.8%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in z around inf 58.7%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   5. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]

      2. associate-*r/ 58.7%

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

      3. *-commutative 58.7%

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

      4. associate-/l* 58.7%

         \[\leadsto \color{blue}{\frac{t \cdot a}{\frac{c}{-4}}} \]

      5. *-commutative 58.7%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{\frac{c}{-4}} \]

   6. Simplified 58.7%

      \[\leadsto \color{blue}{\frac{a \cdot t}{\frac{c}{-4}}} \]
   7. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto \frac{\color{blue}{t \cdot a}}{\frac{c}{-4}} \]

      2. div-inv 58.7%

         \[\leadsto \frac{t \cdot a}{\color{blue}{c \cdot \frac{1}{-4}}} \]

      3. times-frac 64.8%

         \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{\frac{1}{-4}}} \]

      4. metadata-eval 64.8%

         \[\leadsto \frac{t}{c} \cdot \frac{a}{\color{blue}{-0.25}} \]

   8. Applied egg-rr 64.8%

      \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{-0.25}} \]

   if -6.0999999999999999e-52 < t < 2.5e-101

   1. Initial program 84.6%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 84.6%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 84.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 81.2%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 81.2%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 81.2%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 84.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 84.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 84.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 84.6%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 83.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in b around inf 42.5%

      \[\leadsto \color{blue}{\frac{b}{z}} \cdot \frac{1}{c} \]
   7. Step-by-step derivation

      1. clear-num 42.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{b}}} \cdot \frac{1}{c} \]

      2. frac-times 42.5%

         \[\leadsto \color{blue}{\frac{1 \cdot 1}{\frac{z}{b} \cdot c}} \]

      3. metadata-eval 42.5%

         \[\leadsto \frac{\color{blue}{1}}{\frac{z}{b} \cdot c} \]

   8. Applied egg-rr 42.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{b} \cdot c}} \]

   if 2.5e-101 < t

   1. Initial program 71.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 71.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 71.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 74.6%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 74.6%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 74.6%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 71.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 70.5%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 73.4%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 70.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]
   8. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]

      2. metadata-eval 53.0%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} \]

      3. times-frac 53.0%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} \]

      4. *-rgt-identity 53.0%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} \]

      5. times-frac 54.8%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]

   9. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{-52}:\\ \;\;\;\;\frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c} \cdot \frac{t}{-0.25}\\ \end{array} \]

Alternative 19: 35.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 1.6e-61) (/ (/ b c) z) (/ b (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 1.6e-61) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * 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 (a <= 1.6d-61) then
        tmp = (b / c) / z
    else
        tmp = b / (z * 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 (a <= 1.6e-61) {
		tmp = (b / c) / z;
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 1.6e-61:
		tmp = (b / c) / z
	else:
		tmp = b / (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 1.6e-61)
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 1.6e-61)
		tmp = (b / c) / z;
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 1.6e-61], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.6000000000000001e-61

   1. Initial program 77.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.7%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.7%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 80.0%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 80.0%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 80.0%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.7%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 77.2%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 80.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   5. Applied egg-rr 76.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, a \cdot \left(z \cdot \left(t \cdot -4\right)\right)\right) + b}{z} \cdot \frac{1}{c}} \]

   6. Taylor expanded in x around 0 82.6%

      \[\leadsto \color{blue}{\left(-4 \cdot \left(a \cdot t\right) + \left(9 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)\right)} \cdot \frac{1}{c} \]

   7. Taylor expanded in z around -inf 81.5%

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]
   8. Step-by-step derivation

      1. *-commutative 81.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} + -1 \cdot \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      2. mul-1-neg 81.5%

         \[\leadsto \frac{a \cdot t}{c} \cdot -4 + \color{blue}{\left(-\frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}\right)} \]

      3. unsub-neg 81.5%

         \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4 - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z}} \]

      4. metadata-eval 81.5%

         \[\leadsto \frac{a \cdot t}{c} \cdot \color{blue}{\frac{1}{-0.25}} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      5. times-frac 81.5%

         \[\leadsto \color{blue}{\frac{\left(a \cdot t\right) \cdot 1}{c \cdot -0.25}} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      6. *-rgt-identity 81.5%

         \[\leadsto \frac{\color{blue}{a \cdot t}}{c \cdot -0.25} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      7. times-frac 80.4%

         \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25}} - \frac{-9 \cdot \frac{x \cdot y}{c} + -1 \cdot \frac{b}{c}}{z} \]

      8. mul-1-neg 80.4%

         \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{-9 \cdot \frac{x \cdot y}{c} + \color{blue}{\left(-\frac{b}{c}\right)}}{z} \]

      9. unsub-neg 80.4%

         \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\color{blue}{-9 \cdot \frac{x \cdot y}{c} - \frac{b}{c}}}{z} \]

      10. associate-*r/ 79.9%

          \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\color{blue}{\frac{-9 \cdot \left(x \cdot y\right)}{c}} - \frac{b}{c}}{z} \]

      11. *-commutative 79.9%

          \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\frac{\color{blue}{\left(x \cdot y\right) \cdot -9}}{c} - \frac{b}{c}}{z} \]

      12. associate-*l* 79.4%

          \[\leadsto \frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\frac{\color{blue}{x \cdot \left(y \cdot -9\right)}}{c} - \frac{b}{c}}{z} \]

   9. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \frac{t}{-0.25} - \frac{\frac{x \cdot \left(y \cdot -9\right)}{c} - \frac{b}{c}}{z}} \]

   10. Taylor expanded in b around inf 30.9%

       \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   11. Step-by-step derivation

       1. associate-/r* 31.1%

          \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   12. Simplified 31.1%

       \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z}} \]

   if 1.6000000000000001e-61 < a

   1. Initial program 77.9%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
   2. Step-by-step derivation

      1. associate-+l- 77.9%

         \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

      2. *-commutative 77.9%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

      3. associate-*r* 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

      4. *-commutative 76.5%

         \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

      5. associate-+l- 76.5%

         \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

      6. *-commutative 76.5%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

      7. associate-*r* 77.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

      8. *-commutative 77.9%

         \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

      9. associate-*l* 77.9%

         \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

      10. associate-*l* 71.5%

          \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Simplified 71.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

   4. Taylor expanded in b around inf 27.6%

      \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 27.6%

         \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

   6. Simplified 27.6%

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

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 20: 35.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \frac{b}{z \cdot c} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return b / (z * 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 = b / (z * c)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.8%

   \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
2. Step-by-step derivation

   1. associate-+l- 77.8%

      \[\leadsto \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]

   2. *-commutative 77.8%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)} - b\right)}{z \cdot c} \]

   3. associate-*r* 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(a \cdot \left(z \cdot 4\right)\right) \cdot t} - b\right)}{z \cdot c} \]

   4. *-commutative 79.0%

      \[\leadsto \frac{\left(x \cdot 9\right) \cdot y - \left(\color{blue}{\left(\left(z \cdot 4\right) \cdot a\right)} \cdot t - b\right)}{z \cdot c} \]

   5. associate-+l- 79.0%

      \[\leadsto \frac{\color{blue}{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot a\right) \cdot t\right) + b}}{z \cdot c} \]

   6. *-commutative 79.0%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(a \cdot \left(z \cdot 4\right)\right)} \cdot t\right) + b}{z \cdot c} \]

   7. associate-*r* 77.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + b}{z \cdot c} \]

   8. *-commutative 77.8%

      \[\leadsto \frac{\left(\left(x \cdot 9\right) \cdot y - \color{blue}{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}\right) + b}{z \cdot c} \]

   9. associate-*l* 77.4%

      \[\leadsto \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   10. associate-*l* 77.9%

       \[\leadsto \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

3. Simplified 77.9%

   \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]

4. Taylor expanded in b around inf 29.9%

   \[\leadsto \color{blue}{\frac{b}{c \cdot z}} \]
5. Step-by-step derivation

   1. *-commutative 29.9%

      \[\leadsto \frac{b}{\color{blue}{z \cdot c}} \]

6. Simplified 29.9%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]

7. Final simplification 29.9%

   \[\leadsto \frac{b}{z \cdot c} \]

Developer target: 80.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - 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 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023340 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))