Average Error: 3.8 → 1.7
Time: 8.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{\frac{y}{3}}{z}\right) + \frac{\frac{t}{3 \cdot z}}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{\frac{y}{3}}{z}\right) + \frac{\frac{t}{3 \cdot z}}{y}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - ((double) (y / ((double) (z * 3.0)))))) + ((double) (t / ((double) (((double) (z * 3.0)) * y))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - ((double) (((double) (y / 3.0)) / z)))) + ((double) (((double) (t / ((double) (3.0 * z)))) / y))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.8
Target1.7
Herbie1.7
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.8

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-*l*3.7

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}}\]

  4. Applied associate-/r*1.7

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}}\]
  5. Using strategy rm

  6. Applied *-commutative1.7

    \[\leadsto \left(x - \frac{y}{\color{blue}{3 \cdot z}}\right) + \frac{\frac{t}{z}}{3 \cdot y}\]

  7. Applied associate-/r*1.7

    \[\leadsto \left(x - \color{blue}{\frac{\frac{y}{3}}{z}}\right) + \frac{\frac{t}{z}}{3 \cdot y}\]
  8. Using strategy rm

  9. Applied associate-/r*1.7

    \[\leadsto \left(x - \frac{\frac{y}{3}}{z}\right) + \color{blue}{\frac{\frac{\frac{t}{z}}{3}}{y}}\]

  10. Simplified1.7

    \[\leadsto \left(x - \frac{\frac{y}{3}}{z}\right) + \frac{\color{blue}{\frac{t}{3 \cdot z}}}{y}\]

  11. Final simplification1.7

    \[\leadsto \left(x - \frac{\frac{y}{3}}{z}\right) + \frac{\frac{t}{3 \cdot z}}{y}\]

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))