Average Error: 0.0 → 0.1
Time: 14.5s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-\sqrt[3]{n + f} \cdot \sqrt[3]{n + f}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{n + f}}{\sqrt[3]{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-\sqrt[3]{n + f} \cdot \sqrt[3]{n + f}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{n + f}}{\sqrt[3]{f - n}}
double f(double f, double n) {
        double r798105 = f;
        double r798106 = n;
        double r798107 = r798105 + r798106;
        double r798108 = -r798107;
        double r798109 = r798105 - r798106;
        double r798110 = r798108 / r798109;
        return r798110;
}
↓
double f(double f, double n) {
        double r798111 = n;
        double r798112 = f;
        double r798113 = r798111 + r798112;
        double r798114 = cbrt(r798113);
        double r798115 = r798114 * r798114;
        double r798116 = -r798115;
        double r798117 = r798112 - r798111;
        double r798118 = cbrt(r798117);
        double r798119 = r798118 * r798118;
        double r798120 = r798116 / r798119;
        double r798121 = r798114 / r798118;
        double r798122 = r798120 * r798121;
        return r798122;
}

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

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

  5. Applied distribute-lft-neg-in0.1

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

  6. Applied times-frac0.1

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

  7. Final simplification0.1

    \[\leadsto \frac{-\sqrt[3]{n + f} \cdot \sqrt[3]{n + f}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}} \cdot \frac{\sqrt[3]{n + f}}{\sqrt[3]{f - n}}\]

Reproduce

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