Average Error: 25.9 → 25.9
Time: 12.7s
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 r104097 = b;
        double r104098 = c;
        double r104099 = r104097 * r104098;
        double r104100 = a;
        double r104101 = d;
        double r104102 = r104100 * r104101;
        double r104103 = r104099 - r104102;
        double r104104 = r104098 * r104098;
        double r104105 = r104101 * r104101;
        double r104106 = r104104 + r104105;
        double r104107 = r104103 / r104106;
        return r104107;
}
↓
double f(double a, double b, double c, double d) {
        double r104108 = b;
        double r104109 = c;
        double r104110 = r104108 * r104109;
        double r104111 = a;
        double r104112 = d;
        double r104113 = r104111 * r104112;
        double r104114 = r104110 - r104113;
        double r104115 = r104109 * r104109;
        double r104116 = r104112 * r104112;
        double r104117 = r104115 + r104116;
        double r104118 = r104114 / r104117;
        return r104118;
}

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

Original25.9
Target0.5
Herbie25.9
\[\begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-a\right) + b \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array}\]

Derivation

  1. Initial program 25.9

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

  2. Final simplification25.9

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

Reproduce

herbie shell --seed 2019326 
(FPCore (a b c d)
  :name "Complex division, imag part"
  :precision binary64

  :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))))