Average Error: 7.6 → 0.3
Time: 19.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\left(\frac{y}{t - \frac{x}{z}} + x\right) - \frac{1}{\frac{t \cdot z - x}{x}}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\left(\frac{y}{t - \frac{x}{z}} + x\right) - \frac{1}{\frac{t \cdot z - x}{x}}}{x + 1}
double f(double x, double y, double z, double t) {
        double r570515 = x;
        double r570516 = y;
        double r570517 = z;
        double r570518 = r570516 * r570517;
        double r570519 = r570518 - r570515;
        double r570520 = t;
        double r570521 = r570520 * r570517;
        double r570522 = r570521 - r570515;
        double r570523 = r570519 / r570522;
        double r570524 = r570515 + r570523;
        double r570525 = 1.0;
        double r570526 = r570515 + r570525;
        double r570527 = r570524 / r570526;
        return r570527;
}
↓
double f(double x, double y, double z, double t) {
        double r570528 = y;
        double r570529 = t;
        double r570530 = x;
        double r570531 = z;
        double r570532 = r570530 / r570531;
        double r570533 = r570529 - r570532;
        double r570534 = r570528 / r570533;
        double r570535 = r570534 + r570530;
        double r570536 = 1.0;
        double r570537 = r570529 * r570531;
        double r570538 = r570537 - r570530;
        double r570539 = r570538 / r570530;
        double r570540 = r570536 / r570539;
        double r570541 = r570535 - r570540;
        double r570542 = 1.0;
        double r570543 = r570530 + r570542;
        double r570544 = r570541 / r570543;
        return r570544;
}

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

Original7.6
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 7.6

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

  3. Applied div-sub7.6

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

  4. Applied associate-+r-7.6

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

  5. Simplified2.3

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

  7. Applied clear-num2.3

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

  9. Applied *-un-lft-identity2.3

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

  10. Applied associate-*l*2.3

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

  11. Simplified0.3

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

  13. Applied clear-num0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2019306 
(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)))