Average Error: 3.6 → 1.8
Time: 3.7s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z} \cdot \frac{\frac{1}{y}}{3}\]
\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{t}{z} \cdot \frac{\frac{1}{y}}{3}
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 - (y / (z * 3.0))) + ((t / z) * ((1.0 / y) / 3.0)));
}

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 add-cube-cbrt3.9

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

  4. Applied times-frac1.7

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

  6. Applied div-inv1.7

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

  7. Applied associate-*r*2.0

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

  8. Simplified1.8

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

  10. Applied associate-/r*1.8

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

  12. Applied div-inv1.8

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

  13. Applied associate-*l*1.8

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

  14. Simplified1.8

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

  15. Final simplification1.8

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

Reproduce

herbie shell --seed 2020075 
(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))))