Average Error: 3.6 → 0.5
Time: 6.6s
Precision: binary64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq -\infty:\\ \;\;\;\;x \cdot 2 + \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(27 \cdot \left(b \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)\right)\right)\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \leq 2.3002485405598045 \cdot 10^{+238}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\right)\\ \end{array}\]
\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:\\
\;\;\;\;x \cdot 2 + \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(27 \cdot \left(b \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)\right)\right)\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \leq 2.3002485405598045 \cdot 10^{+238}:\\
\;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + b \cdot \left(a \cdot 27\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - y \cdot \left(t \cdot \left(9 \cdot z\right)\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)
    (-
     (*
      (* (cbrt a) (cbrt a))
      (* 27.0 (* b (* (cbrt (cbrt a)) (* (cbrt (cbrt a)) (cbrt (cbrt a)))))))
     (* y (* 9.0 (* z t)))))
   (if (<= (* (* y 9.0) z) 2.3002485405598045e+238)
     (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* b (* a 27.0)))
     (+ (* x 2.0) (- (* a (* 27.0 b)) (* y (* t (* 9.0 z))))))))
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 tmp;
	if ((((double) (((double) (y * 9.0)) * z)) <= ((double) -(((double) INFINITY))))) {
		tmp = ((double) (((double) (x * 2.0)) + ((double) (((double) (((double) (((double) cbrt(a)) * ((double) cbrt(a)))) * ((double) (27.0 * ((double) (b * ((double) (((double) cbrt(((double) cbrt(a)))) * ((double) (((double) cbrt(((double) cbrt(a)))) * ((double) cbrt(((double) cbrt(a)))))))))))))) - ((double) (y * ((double) (9.0 * ((double) (z * t))))))))));
	} else {
		double tmp_1;
		if ((((double) (((double) (y * 9.0)) * z)) <= 2.3002485405598045e+238)) {
			tmp_1 = ((double) (((double) (((double) (x * 2.0)) - ((double) (((double) (((double) (y * 9.0)) * z)) * t)))) + ((double) (b * ((double) (a * 27.0))))));
		} else {
			tmp_1 = ((double) (((double) (x * 2.0)) + ((double) (((double) (a * ((double) (27.0 * b)))) - ((double) (y * ((double) (t * ((double) (9.0 * z))))))))));
		}
		tmp = tmp_1;
	}
	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

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

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -inf.0

    1. Initial program Error: 64.0 bits

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

    2. SimplifiedError: 0.3 bits

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

    4. Applied add-cube-cbrtError: 0.3 bits

      \[\leadsto x \cdot 2 + \left(\color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)} \cdot \left(27 \cdot b\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\]

    5. Applied associate-*l*Error: 0.3 bits

      \[\leadsto x \cdot 2 + \left(\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(\sqrt[3]{a} \cdot \left(27 \cdot b\right)\right)} - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\]

    6. SimplifiedError: 0.3 bits

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

    8. Applied add-cube-cbrtError: 0.4 bits

      \[\leadsto x \cdot 2 + \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(27 \cdot \left(b \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right) \cdot \sqrt[3]{\sqrt[3]{a}}\right)}\right)\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\]

    if -inf.0 < (* (* y 9.0) z) < 2.3002485405598045e238

    1. Initial program Error: 0.5 bits

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

    if 2.3002485405598045e238 < (* (* y 9.0) z)

    1. Initial program Error: 34.2 bits

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

    2. SimplifiedError: 0.4 bits

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

    4. Applied associate-*r*Error: 0.8 bits

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

  4. Final simplificationError: 0.5 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq -\infty:\\ \;\;\;\;x \cdot 2 + \left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \left(27 \cdot \left(b \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \left(\sqrt[3]{\sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)\right)\right)\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \leq 2.3002485405598045 \cdot 10^{+238}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - y \cdot \left(t \cdot \left(9 \cdot z\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020204 
(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)))