Average Error: 7.3 → 2.4
Time: 20.7s
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 r441478 = x;
        double r441479 = y;
        double r441480 = z;
        double r441481 = r441479 * r441480;
        double r441482 = r441481 - r441478;
        double r441483 = t;
        double r441484 = r441483 * r441480;
        double r441485 = r441484 - r441478;
        double r441486 = r441482 / r441485;
        double r441487 = r441478 + r441486;
        double r441488 = 1.0;
        double r441489 = r441478 + r441488;
        double r441490 = r441487 / r441489;
        return r441490;
}
↓
double f(double x, double y, double z, double t) {
        double r441491 = x;
        double r441492 = y;
        double r441493 = z;
        double r441494 = t;
        double r441495 = r441494 * r441493;
        double r441496 = r441495 - r441491;
        double r441497 = r441493 / r441496;
        double r441498 = r441492 * r441497;
        double r441499 = 1.0;
        double r441500 = r441499 / r441496;
        double r441501 = r441491 * r441500;
        double r441502 = r441498 - r441501;
        double r441503 = r441491 + r441502;
        double r441504 = 1.0;
        double r441505 = r441491 + r441504;
        double r441506 = r441503 / r441505;
        return r441506;
}

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)))