Average Error: 0.0 → 0.1
Time: 13.2s
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 r1023395 = f;
        double r1023396 = n;
        double r1023397 = r1023395 + r1023396;
        double r1023398 = -r1023397;
        double r1023399 = r1023395 - r1023396;
        double r1023400 = r1023398 / r1023399;
        return r1023400;
}
↓
double f(double f, double n) {
        double r1023401 = n;
        double r1023402 = f;
        double r1023403 = r1023401 + r1023402;
        double r1023404 = cbrt(r1023403);
        double r1023405 = r1023404 * r1023404;
        double r1023406 = -r1023405;
        double r1023407 = r1023402 - r1023401;
        double r1023408 = cbrt(r1023407);
        double r1023409 = r1023408 * r1023408;
        double r1023410 = r1023406 / r1023409;
        double r1023411 = r1023404 / r1023408;
        double r1023412 = r1023410 * r1023411;
        return r1023412;
}

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 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))