Average Error: 3.6 → 0.5
Time: 8.8s
Precision: binary64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq -1.4503248697000447 \cdot 10^{+170} \lor \neg \left(\left(y \cdot 9\right) \cdot z \leq 2.6660413148695774 \cdot 10^{+221}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array}\]
\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 -1.4503248697000447 \cdot 10^{+170} \lor \neg \left(\left(y \cdot 9\right) \cdot z \leq 2.6660413148695774 \cdot 10^{+221}\right):\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\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 (or (<= (* (* y 9.0) z) -1.4503248697000447e+170)
         (not (<= (* (* y 9.0) z) 2.6660413148695774e+221)))
   (+ (- (* x 2.0) (* (* y t) (* 9.0 z))) (* (* a 27.0) b))
   (+ (* (* a 27.0) b) (- (* 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) <= -1.4503248697000447e+170) || !(((y * 9.0) * z) <= 2.6660413148695774e+221)) {
		tmp = ((x * 2.0) - ((y * t) * (9.0 * z))) + ((a * 27.0) * b);
	} else {
		tmp = ((a * 27.0) * b) + ((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

Original3.6
Target2.7
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 2 regimes

  2. if (*.f64 (*.f64 y 9) z) < -1.4503248697000447e170 or 2.66604131486957738e221 < (*.f64 (*.f64 y 9) z)

    1. Initial program 25.5

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

    3. Applied add-cube-cbrt_binary64_2091425.9

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

    4. Applied associate-*r*_binary64_2081925.9

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

    5. Taylor expanded around -inf 24.8

      \[\leadsto \left(x \cdot 2 - \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot \left(z \cdot {\left(\sqrt[3]{-1}\right)}^{3}\right)\right)\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    6. Simplified1.5

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

    if -1.4503248697000447e170 < (*.f64 (*.f64 y 9) z) < 2.66604131486957738e221

    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 simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq -1.4503248697000447 \cdot 10^{+170} \lor \neg \left(\left(y \cdot 9\right) \cdot z \leq 2.6660413148695774 \cdot 10^{+221}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot t\right) \cdot \left(9 \cdot z\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020342 
(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)))