Average Error: 26.2 → 26.2
Time: 20.6s
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 r4173148 = a;
        double r4173149 = c;
        double r4173150 = r4173148 * r4173149;
        double r4173151 = b;
        double r4173152 = d;
        double r4173153 = r4173151 * r4173152;
        double r4173154 = r4173150 + r4173153;
        double r4173155 = r4173149 * r4173149;
        double r4173156 = r4173152 * r4173152;
        double r4173157 = r4173155 + r4173156;
        double r4173158 = r4173154 / r4173157;
        return r4173158;
}
↓
double f(double a, double b, double c, double d) {
        double r4173159 = b;
        double r4173160 = d;
        double r4173161 = r4173159 * r4173160;
        double r4173162 = a;
        double r4173163 = c;
        double r4173164 = r4173162 * r4173163;
        double r4173165 = r4173161 + r4173164;
        double r4173166 = r4173163 * r4173163;
        double r4173167 = r4173160 * r4173160;
        double r4173168 = r4173166 + r4173167;
        double r4173169 = r4173165 / r4173168;
        return r4173169;
}

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

Original26.2
Target0.4
Herbie26.2
\[\begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array}\]

Derivation

  1. Initial program 26.2

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

  2. Final simplification26.2

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

Reproduce

herbie shell --seed 2019146 
(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))))