Average Error: 3.8 → 0.6
Time: 5.9s
Precision: binary64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq -\infty:\\ \;\;\;\;\left(x \cdot 2 + y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \leq 5.185698389749829 \cdot 10^{+236}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \end{array}\]
\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}\;\left(y \cdot 9\right) \cdot z \leq -\infty:\\
\;\;\;\;\left(x \cdot 2 + y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \leq 5.185698389749829 \cdot 10^{+236}:\\
\;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\

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

\end{array}
(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))
↓
(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (* y 9.0) z) (- INFINITY))
   (+ (+ (* x 2.0) (* y (* (* z -9.0) t))) (* a (* 27.0 b)))
   (if (<= (* (* y 9.0) z) 5.185698389749829e+236)
     (+ (- (* x 2.0) (* t (* y (* 9.0 z)))) (* b (* a 27.0)))
     (+ (* b (* a 27.0)) (- (* x 2.0) (* (* y 9.0) (* z t)))))))
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 tmp;
	if (((y * 9.0) * z) <= -((double) INFINITY)) {
		tmp = ((x * 2.0) + (y * ((z * -9.0) * t))) + (a * (27.0 * b));
	} else if (((y * 9.0) * z) <= 5.185698389749829e+236) {
		tmp = ((x * 2.0) - (t * (y * (9.0 * z)))) + (b * (a * 27.0));
	} else {
		tmp = (b * (a * 27.0)) + ((x * 2.0) - ((y * 9.0) * (z * t)));
	}
	return tmp;
}

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

Original3.8
Target2.7
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 (*.f64 y 9) z) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-*l*_binary6464.0

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

    5. Applied sub-neg_binary6464.0

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

    6. Simplified1.1

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

    if -inf.0 < (*.f64 (*.f64 y 9) z) < 5.1856983897498286e236

    1. Initial program 0.4

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

    3. Applied associate-*l*_binary640.5

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

    if 5.1856983897498286e236 < (*.f64 (*.f64 y 9) z)

    1. Initial program 34.4

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

    3. Applied associate-*l*_binary641.2

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq -\infty:\\ \;\;\;\;\left(x \cdot 2 + y \cdot \left(\left(z \cdot -9\right) \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \leq 5.185698389749829 \cdot 10^{+236}:\\ \;\;\;\;\left(x \cdot 2 - t \cdot \left(y \cdot \left(9 \cdot z\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020224 
(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 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))