Average Error: 3.7 → 0.9
Time: 9.4s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -2.50676067528363454 \cdot 10^{-6} \lor \neg \left(y \cdot 9 \le 2.7809908210998818 \cdot 10^{95}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right)\\ \end{array}\]
\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}\;y \cdot 9 \le -2.50676067528363454 \cdot 10^{-6} \lor \neg \left(y \cdot 9 \le 2.7809908210998818 \cdot 10^{95}\right):\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;1 \cdot \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right)\\

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (x * 2.0)) - ((double) (((double) (((double) (y * 9.0)) * z)) * t)))) + ((double) (((double) (a * 27.0)) * b))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double VAR;
	if (((((double) (y * 9.0)) <= -2.5067606752836345e-06) || !(((double) (y * 9.0)) <= 2.780990821099882e+95))) {
		VAR = ((double) (((double) (((double) (x * 2.0)) - ((double) (y * ((double) (((double) (9.0 * z)) * t)))))) + ((double) (((double) (a * 27.0)) * b))));
	} else {
		VAR = ((double) (1.0 * ((double) fma(a, ((double) (27.0 * b)), ((double) (((double) (x * 2.0)) - ((double) (z * ((double) (((double) (y * 9.0)) * t))))))))));
	}
	return VAR;
}

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

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

Derivation

  1. Split input into 2 regimes

  2. if (* y 9.0) < -2.5067606752836345e-06 or 2.780990821099882e+95 < (* y 9.0)

    1. Initial program 9.1

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

    3. Applied associate-*l*9.0

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

    4. Applied associate-*l*1.0

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

    if -2.5067606752836345e-06 < (* y 9.0) < 2.780990821099882e+95

    1. Initial program 0.8

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

    3. Applied *-commutative0.8

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

    4. Applied associate-*l*0.8

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

    6. Applied *-un-lft-identity0.8

      \[\leadsto \left(x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right) + \color{blue}{1 \cdot \left(\left(a \cdot 27\right) \cdot b\right)}\]

    7. Applied *-un-lft-identity0.8

      \[\leadsto \color{blue}{1 \cdot \left(x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right)} + 1 \cdot \left(\left(a \cdot 27\right) \cdot b\right)\]

    8. Applied distribute-lft-out0.8

      \[\leadsto \color{blue}{1 \cdot \left(\left(x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\right)}\]

    9. Simplified0.8

      \[\leadsto 1 \cdot \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -2.50676067528363454 \cdot 10^{-6} \lor \neg \left(y \cdot 9 \le 2.7809908210998818 \cdot 10^{95}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - z \cdot \left(\left(y \cdot 9\right) \cdot t\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020113 +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)))