Average Error: 0.0 → 0.1
Time: 13.2s
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 r858259 = f;
        double r858260 = n;
        double r858261 = r858259 + r858260;
        double r858262 = -r858261;
        double r858263 = r858259 - r858260;
        double r858264 = r858262 / r858263;
        return r858264;
}
↓
double f(double f, double n) {
        double r858265 = n;
        double r858266 = f;
        double r858267 = r858265 + r858266;
        double r858268 = -r858267;
        double r858269 = cbrt(r858268);
        double r858270 = r858269 * r858269;
        double r858271 = r858266 - r858265;
        double r858272 = cbrt(r858271);
        double r858273 = r858272 * r858272;
        double r858274 = r858270 / r858273;
        double r858275 = r858269 / r858272;
        double r858276 = r858274 * r858275;
        return r858276;
}

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)))