Average Error: 0.1 → 0.0
Time: 34.2s
Precision: 64
Internal Precision: 384
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2.0 - \left(\frac{z}{y} - \frac{x}{y}\right) \cdot 4.0\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.0
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

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

    \[\leadsto \color{blue}{\left(2.0 + 4.0 \cdot \frac{x}{y}\right) - 4.0 \cdot \frac{z}{y}}\]

  3. Applied simplify0.2

    \[\leadsto \color{blue}{2.0 - \frac{4.0}{y} \cdot \left(z - x\right)}\]

  4. Taylor expanded around 0 0.0

    \[\leadsto 2.0 - \color{blue}{\left(4.0 \cdot \frac{z}{y} - 4.0 \cdot \frac{x}{y}\right)}\]

  5. Applied simplify0.0

    \[\leadsto \color{blue}{2.0 - \left(\frac{z}{y} - \frac{x}{y}\right) \cdot 4.0}\]
  6. Removed slow pow expressions.

Runtime

Time bar (total: 34.2s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(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)))