Average Error: 7.0 → 2.3
Time: 17.4s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
↓
\[\frac{1}{1.0 + x} \cdot \left(x + \left(\frac{z}{z \cdot t - x} \cdot y - \frac{x}{z \cdot t - x}\right)\right)\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}
↓
\frac{1}{1.0 + x} \cdot \left(x + \left(\frac{z}{z \cdot t - x} \cdot y - \frac{x}{z \cdot t - x}\right)\right)
double f(double x, double y, double z, double t) {
        double r32690573 = x;
        double r32690574 = y;
        double r32690575 = z;
        double r32690576 = r32690574 * r32690575;
        double r32690577 = r32690576 - r32690573;
        double r32690578 = t;
        double r32690579 = r32690578 * r32690575;
        double r32690580 = r32690579 - r32690573;
        double r32690581 = r32690577 / r32690580;
        double r32690582 = r32690573 + r32690581;
        double r32690583 = 1.0;
        double r32690584 = r32690573 + r32690583;
        double r32690585 = r32690582 / r32690584;
        return r32690585;
}
↓
double f(double x, double y, double z, double t) {
        double r32690586 = 1.0;
        double r32690587 = 1.0;
        double r32690588 = x;
        double r32690589 = r32690587 + r32690588;
        double r32690590 = r32690586 / r32690589;
        double r32690591 = z;
        double r32690592 = t;
        double r32690593 = r32690591 * r32690592;
        double r32690594 = r32690593 - r32690588;
        double r32690595 = r32690591 / r32690594;
        double r32690596 = y;
        double r32690597 = r32690595 * r32690596;
        double r32690598 = r32690588 / r32690594;
        double r32690599 = r32690597 - r32690598;
        double r32690600 = r32690588 + r32690599;
        double r32690601 = r32690590 * r32690600;
        return r32690601;
}

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

Original7.0
Target0.2
Herbie2.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

Derivation

  1. Initial program 7.0

    \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
  2. Using strategy rm

  3. Applied div-sub7.0

    \[\leadsto \frac{x + \color{blue}{\left(\frac{y \cdot z}{t \cdot z - x} - \frac{x}{t \cdot z - x}\right)}}{x + 1.0}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity7.0

    \[\leadsto \frac{x + \left(\frac{y \cdot z}{\color{blue}{1 \cdot \left(t \cdot z - x\right)}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

  6. Applied times-frac2.2

    \[\leadsto \frac{x + \left(\color{blue}{\frac{y}{1} \cdot \frac{z}{t \cdot z - x}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

  7. Simplified2.2

    \[\leadsto \frac{x + \left(\color{blue}{y} \cdot \frac{z}{t \cdot z - x} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]
  8. Using strategy rm

  9. Applied div-inv2.3

    \[\leadsto \color{blue}{\left(x + \left(y \cdot \frac{z}{t \cdot z - x} - \frac{x}{t \cdot z - x}\right)\right) \cdot \frac{1}{x + 1.0}}\]

  10. Final simplification2.3

    \[\leadsto \frac{1}{1.0 + x} \cdot \left(x + \left(\frac{z}{z \cdot t - x} \cdot y - \frac{x}{z \cdot t - x}\right)\right)\]

Reproduce

herbie shell --seed 2019158 
(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)))