Average Error: 3.9 → 1.5
Time: 9.6s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{3 \cdot y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{3 \cdot 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) (y / ((double) (z * 3.0)))))) + ((double) (((double) (t / z)) / ((double) (3.0 * 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

Original3.9
Target1.6
Herbie1.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.9

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

  3. Applied associate-/r*1.6

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

  5. Applied associate-/r*1.6

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

  7. Applied div-inv1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{t}{z} \cdot \frac{1}{3}}}{y}\]

  8. Applied associate-/l*1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{\frac{y}{\frac{1}{3}}}}\]

  9. Simplified1.5

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

  10. Final simplification1.5

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

Reproduce

herbie shell --seed 2020148 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))