Average Error: 0.1 → 0.2
Time: 1.5m
Precision: 64
Internal Precision: 384
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(1.0 - \frac{4.0}{y} \cdot \left(z - x\right)\right) + 1.0\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.2
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

Derivation

  1. Initial program 0.1

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Taylor expanded around 0 0.0

    \[\leadsto 1.0 + \color{blue}{\left(\left(1.0 + 4.0 \cdot \frac{x}{y}\right) - 4.0 \cdot \frac{z}{y}\right)}\]

  3. Applied simplify0.2

    \[\leadsto \color{blue}{\left(1.0 - \frac{4.0}{y} \cdot \left(z - x\right)\right) + 1.0}\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 1.5m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"

  :herbie-target
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y))

  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))