Average Error: 7.3 → 2.4
Time: 24.8s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\left(x + \frac{\frac{z}{t \cdot z - x}}{\frac{1}{y}}\right) - \frac{x}{t \cdot z - x}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\left(x + \frac{\frac{z}{t \cdot z - x}}{\frac{1}{y}}\right) - \frac{x}{t \cdot z - x}}{x + 1}
double f(double x, double y, double z, double t) {
        double r572531 = x;
        double r572532 = y;
        double r572533 = z;
        double r572534 = r572532 * r572533;
        double r572535 = r572534 - r572531;
        double r572536 = t;
        double r572537 = r572536 * r572533;
        double r572538 = r572537 - r572531;
        double r572539 = r572535 / r572538;
        double r572540 = r572531 + r572539;
        double r572541 = 1.0;
        double r572542 = r572531 + r572541;
        double r572543 = r572540 / r572542;
        return r572543;
}
↓
double f(double x, double y, double z, double t) {
        double r572544 = x;
        double r572545 = z;
        double r572546 = t;
        double r572547 = r572546 * r572545;
        double r572548 = r572547 - r572544;
        double r572549 = r572545 / r572548;
        double r572550 = 1.0;
        double r572551 = y;
        double r572552 = r572550 / r572551;
        double r572553 = r572549 / r572552;
        double r572554 = r572544 + r572553;
        double r572555 = r572544 / r572548;
        double r572556 = r572554 - r572555;
        double r572557 = 1.0;
        double r572558 = r572544 + r572557;
        double r572559 = r572556 / r572558;
        return r572559;
}

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
Target0.4
Herbie2.4
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.3

    \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
  2. Using strategy rm

  3. Applied div-sub7.3

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

  4. Applied associate-+r-7.3

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

  5. Simplified4.7

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

  7. Applied div-inv4.7

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

  8. Applied associate-/r*2.4

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

  9. Final simplification2.4

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))