Average Error: 25.7 → 25.7
Time: 11.1s
Precision: 64
\[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]
↓
\[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]
\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}
↓
\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}
double f(double a, double b, double c, double d) {
        double r4312599 = b;
        double r4312600 = c;
        double r4312601 = r4312599 * r4312600;
        double r4312602 = a;
        double r4312603 = d;
        double r4312604 = r4312602 * r4312603;
        double r4312605 = r4312601 - r4312604;
        double r4312606 = r4312600 * r4312600;
        double r4312607 = r4312603 * r4312603;
        double r4312608 = r4312606 + r4312607;
        double r4312609 = r4312605 / r4312608;
        return r4312609;
}
↓
double f(double a, double b, double c, double d) {
        double r4312610 = b;
        double r4312611 = c;
        double r4312612 = r4312610 * r4312611;
        double r4312613 = a;
        double r4312614 = d;
        double r4312615 = r4312613 * r4312614;
        double r4312616 = r4312612 - r4312615;
        double r4312617 = r4312611 * r4312611;
        double r4312618 = r4312614 * r4312614;
        double r4312619 = r4312617 + r4312618;
        double r4312620 = r4312616 / r4312619;
        return r4312620;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original25.7
Target0.4
Herbie25.7
\[\begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-a\right) + b \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array}\]

Derivation

  1. Initial program 25.7

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

  2. Final simplification25.7

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

Reproduce

herbie shell --seed 2019142 
(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))))