Average Error: 0.0 → 0.1
Time: 14.0s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{\sqrt[3]{-\left(n + f\right)} \cdot \sqrt[3]{-\left(n + f\right)}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{-\left(n + f\right)}}{\sqrt[3]{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{\sqrt[3]{-\left(n + f\right)} \cdot \sqrt[3]{-\left(n + f\right)}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{-\left(n + f\right)}}{\sqrt[3]{f - n}}
double f(double f, double n) {
        double r888386 = f;
        double r888387 = n;
        double r888388 = r888386 + r888387;
        double r888389 = -r888388;
        double r888390 = r888386 - r888387;
        double r888391 = r888389 / r888390;
        return r888391;
}
↓
double f(double f, double n) {
        double r888392 = n;
        double r888393 = f;
        double r888394 = r888392 + r888393;
        double r888395 = -r888394;
        double r888396 = cbrt(r888395);
        double r888397 = r888396 * r888396;
        double r888398 = r888393 - r888392;
        double r888399 = cbrt(r888398);
        double r888400 = r888399 * r888399;
        double r888401 = r888397 / r888400;
        double r888402 = r888396 / r888399;
        double r888403 = r888401 * r888402;
        return r888403;
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.4

    \[\leadsto \frac{-\left(f + n\right)}{\color{blue}{\left(\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}\right) \cdot \sqrt[3]{f - n}}}\]

  4. Applied add-cube-cbrt0.1

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{-\left(f + n\right)} \cdot \sqrt[3]{-\left(f + n\right)}\right) \cdot \sqrt[3]{-\left(f + n\right)}}}{\left(\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}\right) \cdot \sqrt[3]{f - n}}\]

  5. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{-\left(f + n\right)} \cdot \sqrt[3]{-\left(f + n\right)}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{-\left(f + n\right)}}{\sqrt[3]{f - n}}}\]

  6. Final simplification0.1

    \[\leadsto \frac{\sqrt[3]{-\left(n + f\right)} \cdot \sqrt[3]{-\left(n + f\right)}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{-\left(n + f\right)}}{\sqrt[3]{f - n}}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))