Average Error: 25.8 → 26.0
Time: 29.3s
Precision: 64
Internal precision: 128
\[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
⬇
\[\left(b \cdot c - a \cdot d\right) \cdot \frac{1}{{c}^2 + {d}^2}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original25.8
Comparison0.4
Herbie26.0
\[ \begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-a\right) + b \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array} \]

Derivation

  1. Initial program 25.8

    \[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
  2. Using strategy rm

  3. Applied div-inv 26.0

    \[\leadsto \color{blue}{\left(b \cdot c - a \cdot d\right) \cdot \frac{1}{{c}^2 + {d}^2}}\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 29.3s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(182362469 2341181653 1341613303 3391166573 3395740364 3420272464)'
(FPCore (a b c d)
  :name "Complex division, imag part"

  :target
  (if (< (fabs d) (fabs c)) (/ (- b (* a (/ d c))) (+ c (* d (/ d c)))) (/ (+ (- a) (* b (/ c d))) (+ d (* c (/ c d)))))

  (/ (- (* b c) (* a d)) (+ (sqr c) (sqr d))))