Average Error: 25.4 → 25.5
Time: 35.6s
Precision: 64
\[\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\]
↓
\[\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot c - a \cdot d\right)\]
\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}
↓
\frac{1}{c \cdot c + d \cdot d} \cdot \left(b \cdot c - a \cdot d\right)
double f(double a, double b, double c, double d) {
        double r29583942 = b;
        double r29583943 = c;
        double r29583944 = r29583942 * r29583943;
        double r29583945 = a;
        double r29583946 = d;
        double r29583947 = r29583945 * r29583946;
        double r29583948 = r29583944 - r29583947;
        double r29583949 = r29583943 * r29583943;
        double r29583950 = r29583946 * r29583946;
        double r29583951 = r29583949 + r29583950;
        double r29583952 = r29583948 / r29583951;
        return r29583952;
}
↓
double f(double a, double b, double c, double d) {
        double r29583953 = 1.0;
        double r29583954 = c;
        double r29583955 = r29583954 * r29583954;
        double r29583956 = d;
        double r29583957 = r29583956 * r29583956;
        double r29583958 = r29583955 + r29583957;
        double r29583959 = r29583953 / r29583958;
        double r29583960 = b;
        double r29583961 = r29583960 * r29583954;
        double r29583962 = a;
        double r29583963 = r29583962 * r29583956;
        double r29583964 = r29583961 - r29583963;
        double r29583965 = r29583959 * r29583964;
        return r29583965;
}

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

Original25.4
Target0.4
Herbie25.5
\[\begin{array}{l} \mathbf{if}\;\left|d\right| \lt \left|c\right|:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-a\right) + b \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array}\]

Derivation

  1. Initial program 25.4

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

  3. Applied div-inv25.5

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

  4. Final simplification25.5

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

Reproduce

herbie shell --seed 2019125 
(FPCore (a b c d)
  :name "Complex division, imag part"

  :herbie-target
  (if (< (fabs d) (fabs c)) (/ (- b (* a (/ d c))) (+ c (* d (/ d c)))) (/ (+ (- a) (* b (/ c d))) (+ d (* c (/ c d)))))

  (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))