Average Error: 3.8 → 1.6
Time: 4.8s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{0.333333333333333315 \cdot \frac{t}{z}}{y}\]
\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{0.333333333333333315 \cdot \frac{t}{z}}{y}
double f(double x, double y, double z, double t) {
        double r857114 = x;
        double r857115 = y;
        double r857116 = z;
        double r857117 = 3.0;
        double r857118 = r857116 * r857117;
        double r857119 = r857115 / r857118;
        double r857120 = r857114 - r857119;
        double r857121 = t;
        double r857122 = r857118 * r857115;
        double r857123 = r857121 / r857122;
        double r857124 = r857120 + r857123;
        return r857124;
}
↓
double f(double x, double y, double z, double t) {
        double r857125 = x;
        double r857126 = y;
        double r857127 = z;
        double r857128 = 3.0;
        double r857129 = r857127 * r857128;
        double r857130 = r857126 / r857129;
        double r857131 = r857125 - r857130;
        double r857132 = 0.3333333333333333;
        double r857133 = t;
        double r857134 = r857133 / r857127;
        double r857135 = r857132 * r857134;
        double r857136 = r857135 / r857126;
        double r857137 = r857131 + r857136;
        return r857137;
}

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

Original3.8
Target1.5
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.8

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

  3. Applied associate-/r*1.5

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

  4. Taylor expanded around 0 1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{0.333333333333333315 \cdot \frac{t}{z}}}{y}\]

  5. Final simplification1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{0.333333333333333315 \cdot \frac{t}{z}}{y}\]

Reproduce

herbie shell --seed 2020100 +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))))