Average Error: 3.6 → 1.8
Time: 12.5s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{1}{z} \cdot t}{y \cdot 3}\]
\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{\frac{1}{z} \cdot t}{y \cdot 3}
double f(double x, double y, double z, double t) {
        double r492137 = x;
        double r492138 = y;
        double r492139 = z;
        double r492140 = 3.0;
        double r492141 = r492139 * r492140;
        double r492142 = r492138 / r492141;
        double r492143 = r492137 - r492142;
        double r492144 = t;
        double r492145 = r492141 * r492138;
        double r492146 = r492144 / r492145;
        double r492147 = r492143 + r492146;
        return r492147;
}
↓
double f(double x, double y, double z, double t) {
        double r492148 = x;
        double r492149 = y;
        double r492150 = z;
        double r492151 = 3.0;
        double r492152 = r492150 * r492151;
        double r492153 = r492149 / r492152;
        double r492154 = r492148 - r492153;
        double r492155 = 1.0;
        double r492156 = r492155 / r492150;
        double r492157 = t;
        double r492158 = r492156 * r492157;
        double r492159 = r492149 * r492151;
        double r492160 = r492158 / r492159;
        double r492161 = r492154 + r492160;
        return r492161;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.6
Target1.8
Herbie1.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.6

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

  3. Applied associate-/r*1.8

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

  5. Applied *-un-lft-identity1.8

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

  6. Applied times-frac1.8

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

  8. Applied associate-*r/1.8

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

  9. Applied associate-/l/1.8

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

  10. Final simplification1.8

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

Reproduce

herbie shell --seed 2019306 
(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))))