Error

Try it out

Target

Derivation

1. Split input into 2 regimes

2. if (/ (- (* b c) (* a d)) (+ (* c c) (* d d))) < 2.4669126810910664e+285

   1. Initial program 14.3

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]

   2. Initial simplification14.3

      \[\leadsto \frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]

   3. Taylor expanded around inf 14.3

      \[\leadsto \frac{\color{blue}{b \cdot c - a \cdot d}}{c \cdot c + d \cdot d}\]

   if 2.4669126810910664e+285 < (/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

   1. Initial program 61.0

      \[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]

   2. Initial simplification61.0

      \[\leadsto \frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]

   3. Taylor expanded around inf 61.0

      \[\leadsto \frac{\color{blue}{b \cdot c - a \cdot d}}{c \cdot c + d \cdot d}\]
   4. Using strategy rm

   5. Applied add-sqr-sqrt61.0

      \[\leadsto \frac{b \cdot c - a \cdot d}{\color{blue}{\sqrt{c \cdot c + d \cdot d} \cdot \sqrt{c \cdot c + d \cdot d}}}\]

   6. Applied *-un-lft-identity61.0

      \[\leadsto \frac{\color{blue}{1 \cdot \left(b \cdot c - a \cdot d\right)}}{\sqrt{c \cdot c + d \cdot d} \cdot \sqrt{c \cdot c + d \cdot d}}\]

   7. Applied times-frac61.0

      \[\leadsto \color{blue}{\frac{1}{\sqrt{c \cdot c + d \cdot d}} \cdot \frac{b \cdot c - a \cdot d}{\sqrt{c \cdot c + d \cdot d}}}\]

   8. Taylor expanded around -inf 59.9

      \[\leadsto \frac{1}{\sqrt{c \cdot c + d \cdot d}} \cdot \color{blue}{\left(-1 \cdot b\right)}\]

   9. Simplified59.9

      \[\leadsto \frac{1}{\sqrt{c \cdot c + d \cdot d}} \cdot \color{blue}{\left(-b\right)}\]
3. Recombined 2 regimes into one program.

4. Final simplification25.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \le 2.4669126810910664 \cdot 10^{+285}:\\ \;\;\;\;\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\sqrt{c \cdot c + d \cdot d}} \cdot b\\ \end{array}\]

Runtime

Time bar (total: 20.8s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (a b c d)
  :name "Complex division, imag part"

  :herbie-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)) (+ (* c c) (* d d))))