Average Error: 7.3 → 0.3
Time: 30.5s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
↓
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{1.0 + x}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}
↓
\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{1.0 + x}
double f(double x, double y, double z, double t) {
        double r31146433 = x;
        double r31146434 = y;
        double r31146435 = z;
        double r31146436 = r31146434 * r31146435;
        double r31146437 = r31146436 - r31146433;
        double r31146438 = t;
        double r31146439 = r31146438 * r31146435;
        double r31146440 = r31146439 - r31146433;
        double r31146441 = r31146437 / r31146440;
        double r31146442 = r31146433 + r31146441;
        double r31146443 = 1.0;
        double r31146444 = r31146433 + r31146443;
        double r31146445 = r31146442 / r31146444;
        return r31146445;
}
↓
double f(double x, double y, double z, double t) {
        double r31146446 = x;
        double r31146447 = y;
        double r31146448 = t;
        double r31146449 = z;
        double r31146450 = r31146446 / r31146449;
        double r31146451 = r31146448 - r31146450;
        double r31146452 = r31146447 / r31146451;
        double r31146453 = r31146448 * r31146449;
        double r31146454 = r31146453 - r31146446;
        double r31146455 = r31146446 / r31146454;
        double r31146456 = r31146452 - r31146455;
        double r31146457 = r31146446 + r31146456;
        double r31146458 = 1.0;
        double r31146459 = r31146458 + r31146446;
        double r31146460 = r31146457 / r31146459;
        return r31146460;
}

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

Original7.3
Target0.3
Herbie0.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

Derivation

  1. Initial program 7.3

    \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
  2. Using strategy rm

  3. Applied div-sub7.3

    \[\leadsto \frac{x + \color{blue}{\left(\frac{y \cdot z}{t \cdot z - x} - \frac{x}{t \cdot z - x}\right)}}{x + 1.0}\]
  4. Using strategy rm

  5. Applied associate-/l*2.3

    \[\leadsto \frac{x + \left(\color{blue}{\frac{y}{\frac{t \cdot z - x}{z}}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]
  6. Using strategy rm

  7. Applied div-sub2.3

    \[\leadsto \frac{x + \left(\frac{y}{\color{blue}{\frac{t \cdot z}{z} - \frac{x}{z}}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

  8. Simplified0.3

    \[\leadsto \frac{x + \left(\frac{y}{\color{blue}{t} - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

  9. Final simplification0.3

    \[\leadsto \frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{1.0 + x}\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))