Average Error: 7.3 → 2.4
Time: 24.9s
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 r475199 = x;
        double r475200 = y;
        double r475201 = z;
        double r475202 = r475200 * r475201;
        double r475203 = r475202 - r475199;
        double r475204 = t;
        double r475205 = r475204 * r475201;
        double r475206 = r475205 - r475199;
        double r475207 = r475203 / r475206;
        double r475208 = r475199 + r475207;
        double r475209 = 1.0;
        double r475210 = r475199 + r475209;
        double r475211 = r475208 / r475210;
        return r475211;
}
↓
double f(double x, double y, double z, double t) {
        double r475212 = x;
        double r475213 = z;
        double r475214 = t;
        double r475215 = r475214 * r475213;
        double r475216 = r475215 - r475212;
        double r475217 = r475213 / r475216;
        double r475218 = 1.0;
        double r475219 = y;
        double r475220 = r475218 / r475219;
        double r475221 = r475217 / r475220;
        double r475222 = r475212 + r475221;
        double r475223 = r475212 / r475216;
        double r475224 = r475222 - r475223;
        double r475225 = 1.0;
        double r475226 = r475212 + r475225;
        double r475227 = r475224 / r475226;
        return r475227;
}

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)))