Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E

Average Error: 0.3 → 0.2

Time: 1.9s

Precision: binary64

Math

\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]

↓

\[\left(3 \cdot 2 + 3 \cdot \left(-x \cdot 3\right)\right) \cdot x\]

Error

Bits error versus x

Target

Original	0.3
Target	0.2
Herbie	0.2

\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

1. Initial program 0.3

   \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
2. Using strategy rm

3. Applied sub-neg 0.3

   \[\leadsto \left(3 \cdot \color{blue}{\left(2 + \left(-x \cdot 3\right)\right)}\right) \cdot x\]

4. Applied distribute-lft-in 0.2

   \[\leadsto \color{blue}{\left(3 \cdot 2 + 3 \cdot \left(-x \cdot 3\right)\right)} \cdot x\]

5. Final simplification 0.2

   \[\leadsto \left(3 \cdot 2 + 3 \cdot \left(-x \cdot 3\right)\right) \cdot x\]

Reproduce

herbie shell --seed 2020169 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6.0 x) (* 9.0 (* x x)))

  (* (* 3.0 (- 2.0 (* x 3.0))) x))