Average Error: 26.1 → 26.1
Time: 3.3s
Precision: 64
\[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\]
↓
\[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\]
\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}
↓
\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}
double f(double a, double b, double c, double d) {
        double r115674 = a;
        double r115675 = c;
        double r115676 = r115674 * r115675;
        double r115677 = b;
        double r115678 = d;
        double r115679 = r115677 * r115678;
        double r115680 = r115676 + r115679;
        double r115681 = r115675 * r115675;
        double r115682 = r115678 * r115678;
        double r115683 = r115681 + r115682;
        double r115684 = r115680 / r115683;
        return r115684;
}
↓
double f(double a, double b, double c, double d) {
        double r115685 = a;
        double r115686 = c;
        double r115687 = r115685 * r115686;
        double r115688 = b;
        double r115689 = d;
        double r115690 = r115688 * r115689;
        double r115691 = r115687 + r115690;
        double r115692 = r115686 * r115686;
        double r115693 = r115689 * r115689;
        double r115694 = r115692 + r115693;
        double r115695 = r115691 / r115694;
        return r115695;
}

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

Original26.1
Target0.5
Herbie26.1
\[\begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array}\]

Derivation

  1. Initial program 26.1

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

  2. Final simplification26.1

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

Reproduce

herbie shell --seed 2020059 
(FPCore (a b c d)
  :name "Complex division, real part"
  :precision binary64

  :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))))