Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Average Error: 0.0 → 0.4

Time: 24.7s

Precision: binary64

Math

\[x + \left(y - z\right) \cdot \left(t - x\right)\]

↓

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	0.0
Target	0.0
Herbie	0.4

\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)\]

Derivation

1. Initial program 0.0

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

3. Applied sub-neg 0.0

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

4. Applied distribute-lft-in 0.0

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

6. Applied add-cube-cbrt 0.4

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

7. Applied distribute-lft-neg-in 0.4

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

8. Applied associate-*r* 0.4

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

9. Final simplification 0.4

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

Reproduce

herbie shell --seed 2020163 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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