Average Error: 25.9 → 25.9
Time: 14.6s
Precision: 64
\[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\]
↓
\[\frac{\frac{1}{\frac{\sqrt{c \cdot c + d \cdot d}}{d \cdot b + a \cdot c}}}{\sqrt{c \cdot c + d \cdot d}}\]
\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}
↓
\frac{\frac{1}{\frac{\sqrt{c \cdot c + d \cdot d}}{d \cdot b + a \cdot c}}}{\sqrt{c \cdot c + d \cdot d}}
double f(double a, double b, double c, double d) {
        double r93235 = a;
        double r93236 = c;
        double r93237 = r93235 * r93236;
        double r93238 = b;
        double r93239 = d;
        double r93240 = r93238 * r93239;
        double r93241 = r93237 + r93240;
        double r93242 = r93236 * r93236;
        double r93243 = r93239 * r93239;
        double r93244 = r93242 + r93243;
        double r93245 = r93241 / r93244;
        return r93245;
}
↓
double f(double a, double b, double c, double d) {
        double r93246 = 1.0;
        double r93247 = c;
        double r93248 = r93247 * r93247;
        double r93249 = d;
        double r93250 = r93249 * r93249;
        double r93251 = r93248 + r93250;
        double r93252 = sqrt(r93251);
        double r93253 = b;
        double r93254 = r93249 * r93253;
        double r93255 = a;
        double r93256 = r93255 * r93247;
        double r93257 = r93254 + r93256;
        double r93258 = r93252 / r93257;
        double r93259 = r93246 / r93258;
        double r93260 = r93259 / r93252;
        return r93260;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt25.9

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

  4. Applied associate-/r*25.8

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

  5. Simplified25.8

    \[\leadsto \frac{\color{blue}{\frac{a \cdot c + d \cdot b}{\sqrt{c \cdot c + d \cdot d}}}}{\sqrt{c \cdot c + d \cdot d}}\]
  6. Using strategy rm

  7. Applied clear-num25.9

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

  8. Simplified25.9

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

  9. Final simplification25.9

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

Reproduce

herbie shell --seed 2019198 
(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))))