Average Error: 7.2 → 0.3
Time: 15.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}
double f(double x, double y, double z, double t) {
        double r350153 = x;
        double r350154 = y;
        double r350155 = z;
        double r350156 = r350154 * r350155;
        double r350157 = r350156 - r350153;
        double r350158 = t;
        double r350159 = r350158 * r350155;
        double r350160 = r350159 - r350153;
        double r350161 = r350157 / r350160;
        double r350162 = r350153 + r350161;
        double r350163 = 1.0;
        double r350164 = r350153 + r350163;
        double r350165 = r350162 / r350164;
        return r350165;
}
↓
double f(double x, double y, double z, double t) {
        double r350166 = x;
        double r350167 = y;
        double r350168 = t;
        double r350169 = z;
        double r350170 = r350166 / r350169;
        double r350171 = r350168 - r350170;
        double r350172 = r350167 / r350171;
        double r350173 = r350168 * r350169;
        double r350174 = r350173 - r350166;
        double r350175 = r350166 / r350174;
        double r350176 = r350172 - r350175;
        double r350177 = r350166 + r350176;
        double r350178 = 1.0;
        double r350179 = r350166 + r350178;
        double r350180 = r350177 / r350179;
        return r350180;
}

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

Original7.2
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 7.2

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

  3. Applied div-sub7.2

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

  4. Simplified2.3

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

  6. Applied clear-num2.3

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

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

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

  9. Applied associate-*l*2.3

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020042 +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)))