Average Error: 0.1 → 0.1
Time: 6.2s
Precision: 64
\[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]
↓
\[\frac{\frac{y + x}{t} - \frac{z}{t}}{2.0}\]
\frac{\left(x + y\right) - z}{t \cdot 2.0}
↓
\frac{\frac{y + x}{t} - \frac{z}{t}}{2.0}
double f(double x, double y, double z, double t) {
        double r662476 = x;
        double r662477 = y;
        double r662478 = r662476 + r662477;
        double r662479 = z;
        double r662480 = r662478 - r662479;
        double r662481 = t;
        double r662482 = 2.0;
        double r662483 = r662481 * r662482;
        double r662484 = r662480 / r662483;
        return r662484;
}
↓
double f(double x, double y, double z, double t) {
        double r662485 = y;
        double r662486 = x;
        double r662487 = r662485 + r662486;
        double r662488 = t;
        double r662489 = r662487 / r662488;
        double r662490 = z;
        double r662491 = r662490 / r662488;
        double r662492 = r662489 - r662491;
        double r662493 = 2.0;
        double r662494 = r662492 / r662493;
        return r662494;
}

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

Derivation

  1. Initial program 0.1

    \[\frac{\left(x + y\right) - z}{t \cdot 2.0}\]
  2. Using strategy rm

  3. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{\left(x + y\right) - z}{t}}{2.0}}\]
  4. Using strategy rm

  5. Applied div-sub0.1

    \[\leadsto \frac{\color{blue}{\frac{x + y}{t} - \frac{z}{t}}}{2.0}\]

  6. Final simplification0.1

    \[\leadsto \frac{\frac{y + x}{t} - \frac{z}{t}}{2.0}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  (/ (- (+ x y) z) (* t 2.0)))