Average Error: 7.1 → 0.3
Time: 3.9s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\left(x + \frac{y}{t - \frac{x}{z}}\right) - \frac{x}{t \cdot z - x}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\left(x + \frac{y}{t - \frac{x}{z}}\right) - \frac{x}{t \cdot z - x}}{x + 1}
double f(double x, double y, double z, double t) {
        double r678184 = x;
        double r678185 = y;
        double r678186 = z;
        double r678187 = r678185 * r678186;
        double r678188 = r678187 - r678184;
        double r678189 = t;
        double r678190 = r678189 * r678186;
        double r678191 = r678190 - r678184;
        double r678192 = r678188 / r678191;
        double r678193 = r678184 + r678192;
        double r678194 = 1.0;
        double r678195 = r678184 + r678194;
        double r678196 = r678193 / r678195;
        return r678196;
}
↓
double f(double x, double y, double z, double t) {
        double r678197 = x;
        double r678198 = y;
        double r678199 = t;
        double r678200 = z;
        double r678201 = r678197 / r678200;
        double r678202 = r678199 - r678201;
        double r678203 = r678198 / r678202;
        double r678204 = r678197 + r678203;
        double r678205 = r678199 * r678200;
        double r678206 = r678205 - r678197;
        double r678207 = r678197 / r678206;
        double r678208 = r678204 - r678207;
        double r678209 = 1.0;
        double r678210 = r678197 + r678209;
        double r678211 = r678208 / r678210;
        return r678211;
}

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

Original7.1
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 7.1

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

  3. Applied div-sub7.1

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

  4. Applied associate-+r-7.1

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

  6. Applied associate-/l*2.2

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

  7. Taylor expanded around 0 0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020062 
(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)))