Average Error: 25.8 → 25.9
Time: 49.6s
Precision: 64
\[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]
↓
\[\frac{1}{\frac{c \cdot c + d \cdot d}{b \cdot c - a \cdot d}}\]
\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}
↓
\frac{1}{\frac{c \cdot c + d \cdot d}{b \cdot c - a \cdot d}}
double f(double a, double b, double c, double d) {
        double r35216864 = b;
        double r35216865 = c;
        double r35216866 = r35216864 * r35216865;
        double r35216867 = a;
        double r35216868 = d;
        double r35216869 = r35216867 * r35216868;
        double r35216870 = r35216866 - r35216869;
        double r35216871 = r35216865 * r35216865;
        double r35216872 = r35216868 * r35216868;
        double r35216873 = r35216871 + r35216872;
        double r35216874 = r35216870 / r35216873;
        return r35216874;
}
↓
double f(double a, double b, double c, double d) {
        double r35216875 = 1.0;
        double r35216876 = c;
        double r35216877 = r35216876 * r35216876;
        double r35216878 = d;
        double r35216879 = r35216878 * r35216878;
        double r35216880 = r35216877 + r35216879;
        double r35216881 = b;
        double r35216882 = r35216881 * r35216876;
        double r35216883 = a;
        double r35216884 = r35216883 * r35216878;
        double r35216885 = r35216882 - r35216884;
        double r35216886 = r35216880 / r35216885;
        double r35216887 = r35216875 / r35216886;
        return r35216887;
}

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

Original25.8
Target0.4
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 25.8

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

  3. Applied *-un-lft-identity25.8

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

  4. Applied associate-/l*25.9

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

  5. Final simplification25.9

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

Reproduce

herbie shell --seed 2019121 
(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))))