Average Error: 25.3 → 25.5
Time: 36.5s
Precision: 64
\[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\]
↓
\[\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot d + a \cdot c\right)\]
\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}
↓
\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot d + a \cdot c\right)
double f(double a, double b, double c, double d) {
        double r22383420 = a;
        double r22383421 = c;
        double r22383422 = r22383420 * r22383421;
        double r22383423 = b;
        double r22383424 = d;
        double r22383425 = r22383423 * r22383424;
        double r22383426 = r22383422 + r22383425;
        double r22383427 = r22383421 * r22383421;
        double r22383428 = r22383424 * r22383424;
        double r22383429 = r22383427 + r22383428;
        double r22383430 = r22383426 / r22383429;
        return r22383430;
}
↓
double f(double a, double b, double c, double d) {
        double r22383431 = 1.0;
        double r22383432 = c;
        double r22383433 = r22383432 * r22383432;
        double r22383434 = d;
        double r22383435 = r22383434 * r22383434;
        double r22383436 = r22383433 + r22383435;
        double r22383437 = r22383431 / r22383436;
        double r22383438 = b;
        double r22383439 = r22383438 * r22383434;
        double r22383440 = a;
        double r22383441 = r22383440 * r22383432;
        double r22383442 = r22383439 + r22383441;
        double r22383443 = r22383437 * r22383442;
        return r22383443;
}

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

Original25.3
Target0.5
Herbie25.5
\[\begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array}\]

Derivation

  1. Initial program 25.3

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

  3. Applied div-inv25.5

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

  4. Final simplification25.5

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

Reproduce

herbie shell --seed 2019125 
(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))))