Average Error: 7.7 → 0.4
Time: 25.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\left(\frac{1}{\frac{t - \frac{x}{z}}{y}} - \frac{1}{\frac{t \cdot z - x}{x}}\right) + x}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\left(\frac{1}{\frac{t - \frac{x}{z}}{y}} - \frac{1}{\frac{t \cdot z - x}{x}}\right) + x}{x + 1}
double f(double x, double y, double z, double t) {
        double r459954 = x;
        double r459955 = y;
        double r459956 = z;
        double r459957 = r459955 * r459956;
        double r459958 = r459957 - r459954;
        double r459959 = t;
        double r459960 = r459959 * r459956;
        double r459961 = r459960 - r459954;
        double r459962 = r459958 / r459961;
        double r459963 = r459954 + r459962;
        double r459964 = 1.0;
        double r459965 = r459954 + r459964;
        double r459966 = r459963 / r459965;
        return r459966;
}
↓
double f(double x, double y, double z, double t) {
        double r459967 = 1.0;
        double r459968 = t;
        double r459969 = x;
        double r459970 = z;
        double r459971 = r459969 / r459970;
        double r459972 = r459968 - r459971;
        double r459973 = y;
        double r459974 = r459972 / r459973;
        double r459975 = r459967 / r459974;
        double r459976 = r459968 * r459970;
        double r459977 = r459976 - r459969;
        double r459978 = r459977 / r459969;
        double r459979 = r459967 / r459978;
        double r459980 = r459975 - r459979;
        double r459981 = r459980 + r459969;
        double r459982 = 1.0;
        double r459983 = r459969 + r459982;
        double r459984 = r459981 / r459983;
        return r459984;
}

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
Target0.3
Herbie0.4
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

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

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

  6. Applied clear-num2.3

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

  8. Applied pow12.3

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

  9. Applied pow12.3

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

  10. Applied pow-prod-down2.3

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

  11. Simplified0.3

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

  13. Applied clear-num0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2019322 
(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)))