Average Error: 3.6 → 1.8
Time: 4.4s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - 1 \cdot \frac{\frac{y}{3}}{z}\right) + \frac{\frac{1}{z} \cdot \frac{t}{3}}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - 1 \cdot \frac{\frac{y}{3}}{z}\right) + \frac{\frac{1}{z} \cdot \frac{t}{3}}{y}
double code(double x, double y, double z, double t) {
	return ((x - (y / (z * 3.0))) + (t / ((z * 3.0) * y)));
}
↓
double code(double x, double y, double z, double t) {
	return ((x - (1.0 * ((y / 3.0) / z))) + (((1.0 / z) * (t / 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

Original3.6
Target1.8
Herbie1.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.6

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

  3. Applied associate-/r*1.8

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

  5. Applied *-un-lft-identity1.8

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

  6. Applied times-frac1.8

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

  8. Applied *-un-lft-identity1.8

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

  9. Applied times-frac1.8

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

  11. Applied *-un-lft-identity1.8

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

  12. Applied *-un-lft-identity1.8

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

  13. Applied times-frac1.8

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

  14. Applied associate-*l*1.8

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

  15. Simplified1.8

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

  16. Final simplification1.8

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

Reproduce

herbie shell --seed 2020058 +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))))