Average Error: 26.1 → 26.1
Time: 23.9s
Precision: 64
Internal precision: 128
\[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
⬇
\[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original26.1
Comparison0.4
Herbie26.1
\[ \begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array} \]

Derivation

  1. Initial program 26.1

    \[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
  2. Removed slow pow expressions

Runtime

Time bar (total: 23.9s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(979151995 2143678282 3046080362 77161989 1045872106 3296572012)'
(FPCore (a b c d)
  :name "Complex division, real part"

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

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