Average Error: 3.7 → 1.5
Time: 4.1s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z \cdot 3} \cdot \frac{\sqrt[3]{t}}{y}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z \cdot 3} \cdot \frac{\sqrt[3]{t}}{y}
double f(double x, double y, double z, double t) {
        double r716938 = x;
        double r716939 = y;
        double r716940 = z;
        double r716941 = 3.0;
        double r716942 = r716940 * r716941;
        double r716943 = r716939 / r716942;
        double r716944 = r716938 - r716943;
        double r716945 = t;
        double r716946 = r716942 * r716939;
        double r716947 = r716945 / r716946;
        double r716948 = r716944 + r716947;
        return r716948;
}
↓
double f(double x, double y, double z, double t) {
        double r716949 = x;
        double r716950 = y;
        double r716951 = z;
        double r716952 = 3.0;
        double r716953 = r716951 * r716952;
        double r716954 = r716950 / r716953;
        double r716955 = r716949 - r716954;
        double r716956 = t;
        double r716957 = cbrt(r716956);
        double r716958 = r716957 * r716957;
        double r716959 = r716958 / r716953;
        double r716960 = r716957 / r716950;
        double r716961 = r716959 * r716960;
        double r716962 = r716955 + r716961;
        return r716962;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target1.9
Herbie1.5
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.7

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt3.9

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{\left(z \cdot 3\right) \cdot y}\]

  4. Applied times-frac1.5

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z \cdot 3} \cdot \frac{\sqrt[3]{t}}{y}}\]

  5. Final simplification1.5

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z \cdot 3} \cdot \frac{\sqrt[3]{t}}{y}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))