Average Error: 7.3 → 2.4
Time: 24.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\left(x + \frac{\frac{z}{t \cdot z - x}}{\frac{1}{y}}\right) - \frac{x}{t \cdot z - x}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\left(x + \frac{\frac{z}{t \cdot z - x}}{\frac{1}{y}}\right) - \frac{x}{t \cdot z - x}}{x + 1}
double f(double x, double y, double z, double t) {
        double r412246 = x;
        double r412247 = y;
        double r412248 = z;
        double r412249 = r412247 * r412248;
        double r412250 = r412249 - r412246;
        double r412251 = t;
        double r412252 = r412251 * r412248;
        double r412253 = r412252 - r412246;
        double r412254 = r412250 / r412253;
        double r412255 = r412246 + r412254;
        double r412256 = 1.0;
        double r412257 = r412246 + r412256;
        double r412258 = r412255 / r412257;
        return r412258;
}
↓
double f(double x, double y, double z, double t) {
        double r412259 = x;
        double r412260 = z;
        double r412261 = t;
        double r412262 = r412261 * r412260;
        double r412263 = r412262 - r412259;
        double r412264 = r412260 / r412263;
        double r412265 = 1.0;
        double r412266 = y;
        double r412267 = r412265 / r412266;
        double r412268 = r412264 / r412267;
        double r412269 = r412259 + r412268;
        double r412270 = r412259 / r412263;
        double r412271 = r412269 - r412270;
        double r412272 = 1.0;
        double r412273 = r412259 + r412272;
        double r412274 = r412271 / r412273;
        return r412274;
}

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
Target0.4
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. Applied associate-+r-7.3

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

  5. Simplified4.7

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

  7. Applied div-inv4.7

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

  8. Applied associate-/r*2.4

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

  9. Final simplification2.4

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

Reproduce

herbie shell --seed 2019323 
(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)))