Average Error: 7.7 → 0.3
Time: 24.6s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\frac{y}{t - \frac{x}{z}} + x}{x + 1} - \frac{\frac{1}{\frac{t}{\frac{x}{z}} + -1}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\frac{y}{t - \frac{x}{z}} + x}{x + 1} - \frac{\frac{1}{\frac{t}{\frac{x}{z}} + -1}}{x + 1}
double f(double x, double y, double z, double t) {
        double r375418 = x;
        double r375419 = y;
        double r375420 = z;
        double r375421 = r375419 * r375420;
        double r375422 = r375421 - r375418;
        double r375423 = t;
        double r375424 = r375423 * r375420;
        double r375425 = r375424 - r375418;
        double r375426 = r375422 / r375425;
        double r375427 = r375418 + r375426;
        double r375428 = 1.0;
        double r375429 = r375418 + r375428;
        double r375430 = r375427 / r375429;
        return r375430;
}
↓
double f(double x, double y, double z, double t) {
        double r375431 = y;
        double r375432 = t;
        double r375433 = x;
        double r375434 = z;
        double r375435 = r375433 / r375434;
        double r375436 = r375432 - r375435;
        double r375437 = r375431 / r375436;
        double r375438 = r375437 + r375433;
        double r375439 = 1.0;
        double r375440 = r375433 + r375439;
        double r375441 = r375438 / r375440;
        double r375442 = 1.0;
        double r375443 = r375432 / r375435;
        double r375444 = -1.0;
        double r375445 = r375443 + r375444;
        double r375446 = r375442 / r375445;
        double r375447 = r375446 / r375440;
        double r375448 = r375441 - r375447;
        return r375448;
}

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

Original7.7
Target0.3
Herbie0.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.7

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

  3. Applied div-sub7.7

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

  4. Applied associate-+r-7.7

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

  5. Applied div-sub7.7

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

  6. Simplified4.7

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

  8. Applied clear-num4.7

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

  9. Simplified5.3

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

  11. Applied fma-udef5.3

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

  12. Simplified0.9

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

  14. Applied fma-udef0.9

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

  15. Simplified0.3

    \[\leadsto \frac{\frac{y}{t - \frac{x}{z}} + x}{x + 1} - \frac{\frac{1}{\color{blue}{\frac{t}{\frac{x}{z}}} + -1}}{x + 1}\]

  16. Final simplification0.3

    \[\leadsto \frac{\frac{y}{t - \frac{x}{z}} + x}{x + 1} - \frac{\frac{1}{\frac{t}{\frac{x}{z}} + -1}}{x + 1}\]

Reproduce

herbie shell --seed 2019322 +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)))