Average Error: 32.4 → 0.0
Time: 725.0ms
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(1 \cdot \mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(1 \cdot \mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r29965 = re;
        double r29966 = r29965 * r29965;
        double r29967 = im;
        double r29968 = r29967 * r29967;
        double r29969 = r29966 + r29968;
        double r29970 = sqrt(r29969);
        double r29971 = log(r29970);
        return r29971;
}
↓
double f(double re, double im) {
        double r29972 = 1.0;
        double r29973 = re;
        double r29974 = im;
        double r29975 = hypot(r29973, r29974);
        double r29976 = r29972 * r29975;
        double r29977 = log(r29976);
        return r29977;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.4

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied *-un-lft-identity32.4

    \[\leadsto \log \left(\sqrt{\color{blue}{1 \cdot \left(re \cdot re + im \cdot im\right)}}\right)\]

  4. Applied sqrt-prod32.4

    \[\leadsto \log \color{blue}{\left(\sqrt{1} \cdot \sqrt{re \cdot re + im \cdot im}\right)}\]

  5. Simplified32.4

    \[\leadsto \log \left(\color{blue}{1} \cdot \sqrt{re \cdot re + im \cdot im}\right)\]

  6. Simplified0.0

    \[\leadsto \log \left(1 \cdot \color{blue}{\mathsf{hypot}\left(re, im\right)}\right)\]

  7. Final simplification0.0

    \[\leadsto \log \left(1 \cdot \mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))