Average Error: 3.5 → 0.7
Time: 8.7s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b = -\infty \lor \neg \left(\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \le 3.7125537497480025 \cdot 10^{275}\right):\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b = -\infty \lor \neg \left(\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \le 3.7125537497480025 \cdot 10^{275}\right):\\
\;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return (((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double temp;
	if ((((((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)) <= -inf.0) || !((((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)) <= 3.7125537497480025e+275))) {
		temp = fma(a, (27.0 * b), ((x * 2.0) - (9.0 * ((t * y) * z))));
	} else {
		temp = (((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b));
	}
	return temp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.5
Target2.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)) < -inf.0 or 3.7125537497480025e+275 < (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b))

    1. Initial program 31.9

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

    2. Simplified31.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)}\]
    3. Using strategy rm

    4. Applied *-commutative31.0

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\color{blue}{\left(9 \cdot y\right)} \cdot z\right) \cdot t\right)\]

    5. Applied associate-*l*30.5

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(9 \cdot \left(y \cdot z\right)\right)} \cdot t\right)\]

    6. Applied associate-*l*30.2

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{9 \cdot \left(\left(y \cdot z\right) \cdot t\right)}\right)\]

    7. Simplified30.2

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \color{blue}{\left(t \cdot \left(z \cdot y\right)\right)}\right)\]
    8. Using strategy rm

    9. Applied *-commutative30.2

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right)\]

    10. Applied associate-*r*3.0

      \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \color{blue}{\left(\left(t \cdot y\right) \cdot z\right)}\right)\]

    if -inf.0 < (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)) < 3.7125537497480025e+275

    1. Initial program 0.4

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b = -\infty \lor \neg \left(\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \le 3.7125537497480025 \cdot 10^{275}\right):\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(\left(t \cdot y\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b)))

  (+ (- (* x 2) (* (* (* y 9) z) t)) (* (* a 27) b)))