Average Error: 7.3 → 2.4
Time: 26.0s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(\frac{\frac{z}{t \cdot z - x}}{\frac{1}{y}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(\frac{\frac{z}{t \cdot z - x}}{\frac{1}{y}} - \frac{x}{t \cdot z - x}\right)}{x + 1}
double f(double x, double y, double z, double t) {
        double r480568 = x;
        double r480569 = y;
        double r480570 = z;
        double r480571 = r480569 * r480570;
        double r480572 = r480571 - r480568;
        double r480573 = t;
        double r480574 = r480573 * r480570;
        double r480575 = r480574 - r480568;
        double r480576 = r480572 / r480575;
        double r480577 = r480568 + r480576;
        double r480578 = 1.0;
        double r480579 = r480568 + r480578;
        double r480580 = r480577 / r480579;
        return r480580;
}
↓
double f(double x, double y, double z, double t) {
        double r480581 = x;
        double r480582 = z;
        double r480583 = t;
        double r480584 = r480583 * r480582;
        double r480585 = r480584 - r480581;
        double r480586 = r480582 / r480585;
        double r480587 = 1.0;
        double r480588 = y;
        double r480589 = r480587 / r480588;
        double r480590 = r480586 / r480589;
        double r480591 = r480581 / r480585;
        double r480592 = r480590 - r480591;
        double r480593 = r480581 + r480592;
        double r480594 = 1.0;
        double r480595 = r480581 + r480594;
        double r480596 = r480593 / r480595;
        return r480596;
}

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. Simplified4.7

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

  6. Applied div-inv4.7

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

  7. Applied associate-/r*2.4

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

  8. Final simplification2.4

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

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)))