Average Error: 25.7 → 25.7
Time: 12.7s
Precision: 64
\[\frac{a \cdot c + b \cdot d}{c \cdot c + d \cdot d}\]
↓
\[\frac{\frac{1}{\frac{\sqrt{c \cdot c + d \cdot d}}{d \cdot b + c \cdot a}}}{\sqrt{c \cdot c + d \cdot d}}\]
\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 + c \cdot a}}}{\sqrt{c \cdot c + d \cdot d}}
double f(double a, double b, double c, double d) {
        double r2894664 = a;
        double r2894665 = c;
        double r2894666 = r2894664 * r2894665;
        double r2894667 = b;
        double r2894668 = d;
        double r2894669 = r2894667 * r2894668;
        double r2894670 = r2894666 + r2894669;
        double r2894671 = r2894665 * r2894665;
        double r2894672 = r2894668 * r2894668;
        double r2894673 = r2894671 + r2894672;
        double r2894674 = r2894670 / r2894673;
        return r2894674;
}
↓
double f(double a, double b, double c, double d) {
        double r2894675 = 1.0;
        double r2894676 = c;
        double r2894677 = r2894676 * r2894676;
        double r2894678 = d;
        double r2894679 = r2894678 * r2894678;
        double r2894680 = r2894677 + r2894679;
        double r2894681 = sqrt(r2894680);
        double r2894682 = b;
        double r2894683 = r2894678 * r2894682;
        double r2894684 = a;
        double r2894685 = r2894676 * r2894684;
        double r2894686 = r2894683 + r2894685;
        double r2894687 = r2894681 / r2894686;
        double r2894688 = r2894675 / r2894687;
        double r2894689 = r2894688 / r2894681;
        return r2894689;
}

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

Original25.7
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 25.7

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

  3. Applied add-sqr-sqrt25.7

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

  4. Applied associate-/r*25.7

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

  6. Applied clear-num25.7

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

  7. Final simplification25.7

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

Reproduce

herbie shell --seed 2019130 
(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))))