Average Error: 0.2 → 0.0
Time: 47.8s
Precision: 64
Internal Precision: 384
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1.0 + 3.0\right) - \left(\frac{z}{y} - \frac{x}{y}\right) \cdot 4.0\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.2
Target0.2
Herbie0.0
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

Derivation

  1. Initial program 0.2

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Taylor expanded around 0 0.0

    \[\leadsto 1.0 + \color{blue}{\left(\left(3.0 + 4.0 \cdot \frac{x}{y}\right) - 4.0 \cdot \frac{z}{y}\right)}\]

  3. Applied simplify0.2

    \[\leadsto \color{blue}{\left(3.0 + 1.0\right) - \frac{4.0}{y} \cdot \left(z - x\right)}\]

  4. Taylor expanded around 0 0.0

    \[\leadsto \left(3.0 + 1.0\right) - \color{blue}{\left(4.0 \cdot \frac{z}{y} - 4.0 \cdot \frac{x}{y}\right)}\]

  5. Applied simplify0.0

    \[\leadsto \color{blue}{\left(1.0 + 3.0\right) - \left(\frac{z}{y} - \frac{x}{y}\right) \cdot 4.0}\]
  6. Removed slow pow expressions.

Runtime

Time bar (total: 47.8s)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, A"

  :herbie-target
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y))

  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))