Average Error: 7.7 → 2.3
Time: 21.7s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(\frac{z}{t \cdot z - x} \cdot y - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(\frac{z}{t \cdot z - x} \cdot y - \frac{x}{t \cdot z - x}\right)}{x + 1}
double f(double x, double y, double z, double t) {
        double r494153 = x;
        double r494154 = y;
        double r494155 = z;
        double r494156 = r494154 * r494155;
        double r494157 = r494156 - r494153;
        double r494158 = t;
        double r494159 = r494158 * r494155;
        double r494160 = r494159 - r494153;
        double r494161 = r494157 / r494160;
        double r494162 = r494153 + r494161;
        double r494163 = 1.0;
        double r494164 = r494153 + r494163;
        double r494165 = r494162 / r494164;
        return r494165;
}
↓
double f(double x, double y, double z, double t) {
        double r494166 = x;
        double r494167 = z;
        double r494168 = t;
        double r494169 = r494168 * r494167;
        double r494170 = r494169 - r494166;
        double r494171 = r494167 / r494170;
        double r494172 = y;
        double r494173 = r494171 * r494172;
        double r494174 = r494166 / r494170;
        double r494175 = r494173 - r494174;
        double r494176 = r494166 + r494175;
        double r494177 = 1.0;
        double r494178 = r494166 + r494177;
        double r494179 = r494176 / r494178;
        return r494179;
}

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
Target0.4
Herbie2.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.7

    \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
  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. Simplified2.3

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

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

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

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

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

  8. Applied times-frac2.3

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

  9. Simplified2.3

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

  10. Final simplification2.3

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

Reproduce

herbie shell --seed 2019303 
(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)))