Average Error: 25.6 → 25.7
Time: 14.7s
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 r6570499 = a;
        double r6570500 = c;
        double r6570501 = r6570499 * r6570500;
        double r6570502 = b;
        double r6570503 = d;
        double r6570504 = r6570502 * r6570503;
        double r6570505 = r6570501 + r6570504;
        double r6570506 = r6570500 * r6570500;
        double r6570507 = r6570503 * r6570503;
        double r6570508 = r6570506 + r6570507;
        double r6570509 = r6570505 / r6570508;
        return r6570509;
}
↓
double f(double a, double b, double c, double d) {
        double r6570510 = 1.0;
        double r6570511 = c;
        double r6570512 = r6570511 * r6570511;
        double r6570513 = d;
        double r6570514 = r6570513 * r6570513;
        double r6570515 = r6570512 + r6570514;
        double r6570516 = r6570510 / r6570515;
        double r6570517 = b;
        double r6570518 = r6570517 * r6570513;
        double r6570519 = a;
        double r6570520 = r6570519 * r6570511;
        double r6570521 = r6570518 + r6570520;
        double r6570522 = r6570516 * r6570521;
        return r6570522;
}

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

Original25.6
Target0.4
Herbie25.7
\[\begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{a + b \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + a \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array}\]

Derivation

  1. Initial program 25.6

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

  3. Applied div-inv25.7

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

  4. Final simplification25.7

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

Reproduce

herbie shell --seed 2019162 
(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))))