Average Error: 25.9 → 25.9
Time: 12.1s
Precision: 64
\[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\]
↓
\[\frac{b \cdot d + a \cdot c}{c \cdot c + d \cdot d}\]
\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}
↓
\frac{b \cdot d + a \cdot c}{c \cdot c + d \cdot d}
double f(double a, double b, double c, double d) {
        double r4151088 = a;
        double r4151089 = c;
        double r4151090 = r4151088 * r4151089;
        double r4151091 = b;
        double r4151092 = d;
        double r4151093 = r4151091 * r4151092;
        double r4151094 = r4151090 + r4151093;
        double r4151095 = r4151089 * r4151089;
        double r4151096 = r4151092 * r4151092;
        double r4151097 = r4151095 + r4151096;
        double r4151098 = r4151094 / r4151097;
        return r4151098;
}
↓
double f(double a, double b, double c, double d) {
        double r4151099 = b;
        double r4151100 = d;
        double r4151101 = r4151099 * r4151100;
        double r4151102 = a;
        double r4151103 = c;
        double r4151104 = r4151102 * r4151103;
        double r4151105 = r4151101 + r4151104;
        double r4151106 = r4151103 * r4151103;
        double r4151107 = r4151100 * r4151100;
        double r4151108 = r4151106 + r4151107;
        double r4151109 = r4151105 / r4151108;
        return r4151109;
}

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
Target0.4
Herbie25.9
\[\begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array}\]

Derivation

  1. Initial program 25.9

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

  2. Final simplification25.9

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

Reproduce

herbie shell --seed 2019129 
(FPCore (a b c d)
  :name "Complex division, real part"

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