Average Error: 7.3 → 0.3
Time: 21.4s
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 r32147508 = x;
        double r32147509 = y;
        double r32147510 = z;
        double r32147511 = r32147509 * r32147510;
        double r32147512 = r32147511 - r32147508;
        double r32147513 = t;
        double r32147514 = r32147513 * r32147510;
        double r32147515 = r32147514 - r32147508;
        double r32147516 = r32147512 / r32147515;
        double r32147517 = r32147508 + r32147516;
        double r32147518 = 1.0;
        double r32147519 = r32147508 + r32147518;
        double r32147520 = r32147517 / r32147519;
        return r32147520;
}
↓
double f(double x, double y, double z, double t) {
        double r32147521 = x;
        double r32147522 = y;
        double r32147523 = t;
        double r32147524 = z;
        double r32147525 = r32147521 / r32147524;
        double r32147526 = r32147523 - r32147525;
        double r32147527 = r32147522 / r32147526;
        double r32147528 = r32147523 * r32147524;
        double r32147529 = r32147528 - r32147521;
        double r32147530 = r32147521 / r32147529;
        double r32147531 = r32147527 - r32147530;
        double r32147532 = r32147521 + r32147531;
        double r32147533 = 1.0;
        double r32147534 = r32147533 + r32147521;
        double r32147535 = r32147532 / r32147534;
        return r32147535;
}

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 
(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)))