Average Error: 7.8 → 5.7
Time: 8.8s
Precision: 64
\[x0 = 1.855 \land x1 = 0.000209 \lor x0 = 2.985 \land x1 = 0.0186\]
\[\frac{x0}{1 - x1} - x0\]
↓
\[\frac{\left(\frac{1}{1 - x1} \cdot x0\right) \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right)}\]
\frac{x0}{1 - x1} - x0
↓
\frac{\left(\frac{1}{1 - x1} \cdot x0\right) \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right)}
double f(double x0, double x1) {
        double r6219949 = x0;
        double r6219950 = 1.0;
        double r6219951 = x1;
        double r6219952 = r6219950 - r6219951;
        double r6219953 = r6219949 / r6219952;
        double r6219954 = r6219953 - r6219949;
        return r6219954;
}
↓
double f(double x0, double x1) {
        double r6219955 = 1.0;
        double r6219956 = x1;
        double r6219957 = r6219955 - r6219956;
        double r6219958 = r6219955 / r6219957;
        double r6219959 = x0;
        double r6219960 = r6219958 * r6219959;
        double r6219961 = r6219959 / r6219957;
        double r6219962 = r6219960 * r6219961;
        double r6219963 = r6219959 * r6219959;
        double r6219964 = r6219962 - r6219963;
        double r6219965 = r6219959 + r6219961;
        double r6219966 = cbrt(r6219965);
        double r6219967 = r6219966 * r6219966;
        double r6219968 = r6219966 * r6219967;
        double r6219969 = r6219964 / r6219968;
        return r6219969;
}

Error

Bits error versus x0

Bits error versus x1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.8
Target0.3
Herbie5.7
\[\frac{x0 \cdot x1}{1 - x1}\]

Derivation

  1. Initial program 7.8

    \[\frac{x0}{1 - x1} - x0\]
  2. Using strategy rm

  3. Applied flip--7.2

    \[\leadsto \color{blue}{\frac{\frac{x0}{1 - x1} \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}}\]
  4. Using strategy rm

  5. Applied div-inv5.6

    \[\leadsto \frac{\frac{x0}{1 - x1} \cdot \color{blue}{\left(x0 \cdot \frac{1}{1 - x1}\right)} - x0 \cdot x0}{\frac{x0}{1 - x1} + x0}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt5.7

    \[\leadsto \frac{\frac{x0}{1 - x1} \cdot \left(x0 \cdot \frac{1}{1 - x1}\right) - x0 \cdot x0}{\color{blue}{\left(\sqrt[3]{\frac{x0}{1 - x1} + x0} \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}\right) \cdot \sqrt[3]{\frac{x0}{1 - x1} + x0}}}\]

  8. Final simplification5.7

    \[\leadsto \frac{\left(\frac{1}{1 - x1} \cdot x0\right) \cdot \frac{x0}{1 - x1} - x0 \cdot x0}{\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \left(\sqrt[3]{x0 + \frac{x0}{1 - x1}} \cdot \sqrt[3]{x0 + \frac{x0}{1 - x1}}\right)}\]

Reproduce

herbie shell --seed 2019134 
(FPCore (x0 x1)
  :name "(- (/ x0 (- 1 x1)) x0)"
  :pre (or (and (== x0 1.855) (== x1 0.000209)) (and (== x0 2.985) (== x1 0.0186)))

  :herbie-target
  (/ (* x0 x1) (- 1 x1))

  (- (/ x0 (- 1 x1)) x0))