Average Error: 0.2 → 0.0
Time: 5.1s
Precision: 64
Internal Precision: 1344
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(30 + d2\right) \cdot d1\]

Error

Bits error versus d1

Bits error versus d2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[d1 \cdot \left(30 + d2\right)\]

Derivation

  1. Initial program 0.2

    \[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]

  2. Initial simplification0.1

    \[\leadsto (d1 \cdot \left(d2 + 20\right) + \left(d1 \cdot 10\right))_*\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{d2 \cdot d1 + 30 \cdot d1}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(30 + d2\right)}\]

  5. Final simplification0.0

    \[\leadsto \left(30 + d2\right) \cdot d1\]

Runtime

Time bar (total: 5.1s)Debug logProfile

herbie shell --seed 2018217 +o rules:numerics
(FPCore (d1 d2)
  :name "FastMath test2"

  :herbie-target
  (* d1 (+ 30 d2))

  (+ (+ (* d1 10) (* d1 d2)) (* d1 20)))