Average Error: 7.5 → 0.3
Time: 43.3s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{1 + x}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{1 + x}
double f(double x, double y, double z, double t) {
        double r33447489 = x;
        double r33447490 = y;
        double r33447491 = z;
        double r33447492 = r33447490 * r33447491;
        double r33447493 = r33447492 - r33447489;
        double r33447494 = t;
        double r33447495 = r33447494 * r33447491;
        double r33447496 = r33447495 - r33447489;
        double r33447497 = r33447493 / r33447496;
        double r33447498 = r33447489 + r33447497;
        double r33447499 = 1.0;
        double r33447500 = r33447489 + r33447499;
        double r33447501 = r33447498 / r33447500;
        return r33447501;
}
↓
double f(double x, double y, double z, double t) {
        double r33447502 = x;
        double r33447503 = y;
        double r33447504 = t;
        double r33447505 = z;
        double r33447506 = r33447502 / r33447505;
        double r33447507 = r33447504 - r33447506;
        double r33447508 = r33447503 / r33447507;
        double r33447509 = r33447504 * r33447505;
        double r33447510 = r33447509 - r33447502;
        double r33447511 = r33447502 / r33447510;
        double r33447512 = r33447508 - r33447511;
        double r33447513 = r33447502 + r33447512;
        double r33447514 = 1.0;
        double r33447515 = r33447514 + r33447502;
        double r33447516 = r33447513 / r33447515;
        return r33447516;
}

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
Target0.3
Herbie0.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

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 div-sub2.4

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

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)))