Average Error: 7.3 → 2.4
Time: 21.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(y \cdot \frac{z}{t \cdot z - x} - x \cdot \frac{1}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(y \cdot \frac{z}{t \cdot z - x} - x \cdot \frac{1}{t \cdot z - x}\right)}{x + 1}
double f(double x, double y, double z, double t) {
        double r461258 = x;
        double r461259 = y;
        double r461260 = z;
        double r461261 = r461259 * r461260;
        double r461262 = r461261 - r461258;
        double r461263 = t;
        double r461264 = r461263 * r461260;
        double r461265 = r461264 - r461258;
        double r461266 = r461262 / r461265;
        double r461267 = r461258 + r461266;
        double r461268 = 1.0;
        double r461269 = r461258 + r461268;
        double r461270 = r461267 / r461269;
        return r461270;
}
↓
double f(double x, double y, double z, double t) {
        double r461271 = x;
        double r461272 = y;
        double r461273 = z;
        double r461274 = t;
        double r461275 = r461274 * r461273;
        double r461276 = r461275 - r461271;
        double r461277 = r461273 / r461276;
        double r461278 = r461272 * r461277;
        double r461279 = 1.0;
        double r461280 = r461279 / r461276;
        double r461281 = r461271 * r461280;
        double r461282 = r461278 - r461281;
        double r461283 = r461271 + r461282;
        double r461284 = 1.0;
        double r461285 = r461271 + r461284;
        double r461286 = r461283 / r461285;
        return r461286;
}

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
Target0.3
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. Simplified2.4

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

  6. Applied div-inv2.4

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

  7. Final simplification2.4

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

Reproduce

herbie shell --seed 2019325 
(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)))