Average Error: 0.1 → 0.0
Time: 5.5s
Precision: 64
Internal precision: 128
\[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
⬇
\[4.0 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2.0\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Comparison0.0
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. Applied taylor 0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Applied simplify 0.0

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

Runtime

Time bar (total: 5.5s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(813668631 486729202 3692612365 2806844463 113457232 3238271469)'
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"

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

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