Average Error: 7.2 → 2.3
Time: 16.9s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(y \cdot \frac{1}{\frac{t \cdot z - x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(y \cdot \frac{1}{\frac{t \cdot z - x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}
double f(double x, double y, double z, double t) {
        double r746477 = x;
        double r746478 = y;
        double r746479 = z;
        double r746480 = r746478 * r746479;
        double r746481 = r746480 - r746477;
        double r746482 = t;
        double r746483 = r746482 * r746479;
        double r746484 = r746483 - r746477;
        double r746485 = r746481 / r746484;
        double r746486 = r746477 + r746485;
        double r746487 = 1.0;
        double r746488 = r746477 + r746487;
        double r746489 = r746486 / r746488;
        return r746489;
}
↓
double f(double x, double y, double z, double t) {
        double r746490 = x;
        double r746491 = y;
        double r746492 = 1.0;
        double r746493 = t;
        double r746494 = z;
        double r746495 = r746493 * r746494;
        double r746496 = r746495 - r746490;
        double r746497 = r746496 / r746494;
        double r746498 = r746492 / r746497;
        double r746499 = r746491 * r746498;
        double r746500 = r746490 / r746496;
        double r746501 = r746499 - r746500;
        double r746502 = r746490 + r746501;
        double r746503 = 1.0;
        double r746504 = r746490 + r746503;
        double r746505 = r746502 / r746504;
        return r746505;
}

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

Original7.2
Target0.3
Herbie2.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.2

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

  3. Applied div-sub7.2

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

  4. Simplified2.3

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

  6. Applied clear-num2.3

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

  7. Final simplification2.3

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(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)))