Average Error: 3.1 → 3.0
Time: 14.1s
Precision: binary64
\[[y, z, t]=\mathsf{sort}([y, z, t])\]
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right) + a \cdot \left(27 \cdot b\right)\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\right) + a \cdot \left(27 \cdot b\right)
(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
 (+ (- (* x 2.0) (* (* y 9.0) (* t z))) (* a (* 27.0 b))))
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) {
	return ((x * 2.0) - ((y * 9.0) * (t * z))) + (a * (27.0 * b));
}

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
Target3.4
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Initial program 3.1

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

  3. Applied associate-*l*_binary64_167283.0

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

  4. Simplified3.0

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

  6. Applied associate-*l*_binary64_167283.0

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

  7. Final simplification3.0

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

Reproduce

herbie shell --seed 2021098 
(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)))