Average Error: 0.1 → 0.0
Time: 17.8s
Precision: 64
Internal Precision: 384
\[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\frac{x}{z} - \frac{y}{z}\right) \cdot 4.0 - 2.0\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.0
Herbie0.0
\[4.0 \cdot \frac{x}{z} - \left(2.0 + 4.0 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Taylor expanded around 0 0.0

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

  3. Applied simplify0.0

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

Runtime

Time bar (total: 17.8s)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, B"

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))