Average Error: 3.7 → 1.5
Time: 4.5s
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 r765083 = x;
        double r765084 = y;
        double r765085 = z;
        double r765086 = 3.0;
        double r765087 = r765085 * r765086;
        double r765088 = r765084 / r765087;
        double r765089 = r765083 - r765088;
        double r765090 = t;
        double r765091 = r765087 * r765084;
        double r765092 = r765090 / r765091;
        double r765093 = r765089 + r765092;
        return r765093;
}
↓
double f(double x, double y, double z, double t) {
        double r765094 = x;
        double r765095 = y;
        double r765096 = z;
        double r765097 = 3.0;
        double r765098 = r765096 * r765097;
        double r765099 = r765095 / r765098;
        double r765100 = r765094 - r765099;
        double r765101 = t;
        double r765102 = cbrt(r765101);
        double r765103 = r765102 * r765102;
        double r765104 = r765103 / r765098;
        double r765105 = r765102 / r765095;
        double r765106 = r765104 * r765105;
        double r765107 = r765100 + r765106;
        return r765107;
}

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 +o rules:numerics
(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))))