Average Error: 3.5 → 1.6
Time: 15.9s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\frac{\frac{\frac{t}{z}}{3}}{y} + \left(x - \frac{\frac{y}{3}}{z}\right)\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\frac{\frac{\frac{t}{z}}{3}}{y} + \left(x - \frac{\frac{y}{3}}{z}\right)
double f(double x, double y, double z, double t) {
        double r595003 = x;
        double r595004 = y;
        double r595005 = z;
        double r595006 = 3.0;
        double r595007 = r595005 * r595006;
        double r595008 = r595004 / r595007;
        double r595009 = r595003 - r595008;
        double r595010 = t;
        double r595011 = r595007 * r595004;
        double r595012 = r595010 / r595011;
        double r595013 = r595009 + r595012;
        return r595013;
}
↓
double f(double x, double y, double z, double t) {
        double r595014 = t;
        double r595015 = z;
        double r595016 = r595014 / r595015;
        double r595017 = 3.0;
        double r595018 = r595016 / r595017;
        double r595019 = y;
        double r595020 = r595018 / r595019;
        double r595021 = x;
        double r595022 = r595019 / r595017;
        double r595023 = r595022 / r595015;
        double r595024 = r595021 - r595023;
        double r595025 = r595020 + r595024;
        return r595025;
}

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

Original3.5
Target1.7
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.5

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

  3. Applied associate-/r*1.7

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

  4. Simplified1.6

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

  6. Applied *-un-lft-identity1.6

    \[\leadsto \left(x - \frac{\color{blue}{1 \cdot y}}{z \cdot 3}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}\]

  7. Applied times-frac1.7

    \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}\]
  8. Using strategy rm

  9. Applied associate-*l/1.6

    \[\leadsto \left(x - \color{blue}{\frac{1 \cdot \frac{y}{3}}{z}}\right) + \frac{\frac{\frac{t}{z}}{3}}{y}\]

  10. Simplified1.6

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

  11. Final simplification1.6

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))