Average Error: 7.2 → 2.3
Time: 12.6s
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 r987335 = x;
        double r987336 = y;
        double r987337 = z;
        double r987338 = r987336 * r987337;
        double r987339 = r987338 - r987335;
        double r987340 = t;
        double r987341 = r987340 * r987337;
        double r987342 = r987341 - r987335;
        double r987343 = r987339 / r987342;
        double r987344 = r987335 + r987343;
        double r987345 = 1.0;
        double r987346 = r987335 + r987345;
        double r987347 = r987344 / r987346;
        return r987347;
}
↓
double f(double x, double y, double z, double t) {
        double r987348 = x;
        double r987349 = y;
        double r987350 = 1.0;
        double r987351 = t;
        double r987352 = z;
        double r987353 = r987351 * r987352;
        double r987354 = r987353 - r987348;
        double r987355 = r987354 / r987352;
        double r987356 = r987350 / r987355;
        double r987357 = r987349 * r987356;
        double r987358 = r987348 / r987354;
        double r987359 = r987357 - r987358;
        double r987360 = r987348 + r987359;
        double r987361 = 1.0;
        double r987362 = r987348 + r987361;
        double r987363 = r987360 / r987362;
        return r987363;
}

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 
(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)))