Average Error: 7.5 → 0.5
Time: 20.5s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\left(\left(x + \frac{y}{t - \frac{x}{z}}\right) - \frac{x}{t \cdot z - x}\right) \cdot \frac{1}{1 + x}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\left(\left(x + \frac{y}{t - \frac{x}{z}}\right) - \frac{x}{t \cdot z - x}\right) \cdot \frac{1}{1 + x}
double f(double x, double y, double z, double t) {
        double r37508559 = x;
        double r37508560 = y;
        double r37508561 = z;
        double r37508562 = r37508560 * r37508561;
        double r37508563 = r37508562 - r37508559;
        double r37508564 = t;
        double r37508565 = r37508564 * r37508561;
        double r37508566 = r37508565 - r37508559;
        double r37508567 = r37508563 / r37508566;
        double r37508568 = r37508559 + r37508567;
        double r37508569 = 1.0;
        double r37508570 = r37508559 + r37508569;
        double r37508571 = r37508568 / r37508570;
        return r37508571;
}
↓
double f(double x, double y, double z, double t) {
        double r37508572 = x;
        double r37508573 = y;
        double r37508574 = t;
        double r37508575 = z;
        double r37508576 = r37508572 / r37508575;
        double r37508577 = r37508574 - r37508576;
        double r37508578 = r37508573 / r37508577;
        double r37508579 = r37508572 + r37508578;
        double r37508580 = r37508574 * r37508575;
        double r37508581 = r37508580 - r37508572;
        double r37508582 = r37508572 / r37508581;
        double r37508583 = r37508579 - r37508582;
        double r37508584 = 1.0;
        double r37508585 = 1.0;
        double r37508586 = r37508585 + r37508572;
        double r37508587 = r37508584 / r37508586;
        double r37508588 = r37508583 * r37508587;
        return r37508588;
}

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

Original7.5
Target0.4
Herbie0.5
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.5

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

  3. Applied div-sub7.5

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

  5. Applied associate-/l*2.4

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

  7. Applied *-un-lft-identity2.4

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

  8. Applied associate-/r*2.4

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

  9. Simplified0.4

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

  11. Applied div-inv0.5

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

  12. Final simplification0.5

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

Reproduce

herbie shell --seed 2019169 
(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)))