Average Error: 3.1 → 0.6
Time: 24.1s
Precision: binary64
\[[y, z, t]=\mathsf{sort}([y, z, t])\]
\[[a, b]=\mathsf{sort}([a, b])\]
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq 1.7667806396472788 \cdot 10^{-44}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array}\]
\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}\;z \leq 1.7667806396472788 \cdot 10^{-44}:\\
\;\;\;\;\left(x \cdot 2 - \left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\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 (<= z 1.7667806396472788e-44)
   (+ (- (* x 2.0) (* (* 9.0 y) (* z t))) (* a (* 27.0 b)))
   (+ (- (* x 2.0) (* 9.0 (* t (* z y)))) (* b (* a 27.0)))))
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 (z <= 1.7667806396472788e-44) {
		tmp = ((x * 2.0) - ((9.0 * y) * (z * t))) + (a * (27.0 * b));
	} else {
		tmp = ((x * 2.0) - (9.0 * (t * (z * y)))) + (b * (a * 27.0));
	}
	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

Original3.1
Target3.7
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 2 regimes

  2. if z < 1.76678063964727877e-44

    1. Initial program 3.6

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

    3. Applied associate-*l*_binary64_191153.7

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

    5. Applied associate-*l*_binary64_191150.7

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

    6. Simplified0.7

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

    8. Applied associate-*l*_binary64_191150.6

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

    10. Applied associate-*r*_binary64_191140.7

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

    11. Simplified0.7

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

    if 1.76678063964727877e-44 < z

    1. Initial program 0.3

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

    2. Taylor expanded around 0 0.3

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7667806396472788 \cdot 10^{-44}:\\ \;\;\;\;\left(x \cdot 2 - \left(9 \cdot y\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021076 
(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)))