Average Error: 3.5 → 0.7
Time: 6.1s
Precision: binary64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \leq -\infty:\\ \;\;\;\;x \cdot 2 + \left(\sqrt[3]{a \cdot \left(27 \cdot b\right)} \cdot \left(\sqrt[3]{a \cdot \left(27 \cdot b\right)} \cdot \sqrt[3]{a \cdot \left(27 \cdot b\right)}\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \leq 1.837175409797796 \cdot 10^{+271}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(y \cdot \sqrt{9}\right) \cdot \left(z \cdot \left(t \cdot \sqrt{9}\right)\right)\right)\\ \end{array}\]
\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(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \leq -\infty:\\
\;\;\;\;x \cdot 2 + \left(\sqrt[3]{a \cdot \left(27 \cdot b\right)} \cdot \left(\sqrt[3]{a \cdot \left(27 \cdot b\right)} \cdot \sqrt[3]{a \cdot \left(27 \cdot b\right)}\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\

\mathbf{elif}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \leq 1.837175409797796 \cdot 10^{+271}:\\
\;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(y \cdot \sqrt{9}\right) \cdot \left(z \cdot \left(t \cdot \sqrt{9}\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 (<= (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)) (- INFINITY))
   (+
    (* x 2.0)
    (-
     (*
      (cbrt (* a (* 27.0 b)))
      (* (cbrt (* a (* 27.0 b))) (cbrt (* a (* 27.0 b)))))
     (* y (* 9.0 (* z t)))))
   (if (<=
        (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b))
        1.837175409797796e+271)
     (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b))
     (+
      (* x 2.0)
      (- (* a (* 27.0 b)) (* (* y (sqrt 9.0)) (* z (* t (sqrt 9.0)))))))))
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) (((double) (x * 2.0)) - ((double) (((double) (((double) (y * 9.0)) * z)) * t)))) + ((double) (((double) (a * 27.0)) * b)))) <= ((double) -(((double) INFINITY))))) {
		tmp = ((double) (((double) (x * 2.0)) + ((double) (((double) (((double) cbrt(((double) (a * ((double) (27.0 * b)))))) * ((double) (((double) cbrt(((double) (a * ((double) (27.0 * b)))))) * ((double) cbrt(((double) (a * ((double) (27.0 * b)))))))))) - ((double) (y * ((double) (9.0 * ((double) (z * t))))))))));
	} else {
		double tmp_1;
		if ((((double) (((double) (((double) (x * 2.0)) - ((double) (((double) (((double) (y * 9.0)) * z)) * t)))) + ((double) (((double) (a * 27.0)) * b)))) <= 1.837175409797796e+271)) {
			tmp_1 = ((double) (((double) (((double) (x * 2.0)) - ((double) (((double) (((double) (y * 9.0)) * z)) * t)))) + ((double) (((double) (a * 27.0)) * b))));
		} else {
			tmp_1 = ((double) (((double) (x * 2.0)) + ((double) (((double) (a * ((double) (27.0 * b)))) - ((double) (((double) (y * ((double) sqrt(9.0)))) * ((double) (z * ((double) (t * ((double) sqrt(9.0))))))))))));
		}
		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

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

Derivation

  1. Split input into 3 regimes

  2. if (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)) < -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: 0.6 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: 0.8 bits

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

    if -inf.0 < (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)) < 1.83717540979779605e271

    1. Initial program Error: 0.3 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 1.83717540979779605e271 < (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b))

    1. Initial program Error: 18.8 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: 4.8 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-sqr-sqrtError: 4.8 bits

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

    5. Applied associate-*l*Error: 4.9 bits

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

    6. SimplifiedError: 4.9 bits

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

    8. Applied associate-*r*Error: 5.1 bits

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

  4. Final simplificationError: 0.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \leq -\infty:\\ \;\;\;\;x \cdot 2 + \left(\sqrt[3]{a \cdot \left(27 \cdot b\right)} \cdot \left(\sqrt[3]{a \cdot \left(27 \cdot b\right)} \cdot \sqrt[3]{a \cdot \left(27 \cdot b\right)}\right) - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \leq 1.837175409797796 \cdot 10^{+271}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \left(y \cdot \sqrt{9}\right) \cdot \left(z \cdot \left(t \cdot \sqrt{9}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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)))