Average Error: 9.9 → 0.2
Time: 1.3m
Precision: 64
Internal Precision: 384
\[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z} \le -1.293154407109218 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1.0\right) - x\\ \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z} \le 4.04716974457547 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1.0\right) - x\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original9.9
Target0.5
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x \lt 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1.0\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ (- y z) 1.0)) z) < -1.293154407109218e+92 or 4.04716974457547e-37 < (/ (* x (+ (- y z) 1.0)) z)

    1. Initial program 17.5

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

    2. Taylor expanded around 0 6.0

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

    3. Applied simplify0.1

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

    if -1.293154407109218e+92 < (/ (* x (+ (- y z) 1.0)) z) < 4.04716974457547e-37

    1. Initial program 0.1

      \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.4

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}}\]
  3. Recombined 2 regimes into one program.
  4. Removed slow pow expressions.

Runtime

Time bar (total: 1.3m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

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