Average Error: 6.9 → 0.4
Time: 15.8s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\left(x + \frac{y}{t - \frac{x}{z}}\right) - \frac{1}{\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}} \cdot \frac{x}{\sqrt[3]{t \cdot z - x}}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\left(x + \frac{y}{t - \frac{x}{z}}\right) - \frac{1}{\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}} \cdot \frac{x}{\sqrt[3]{t \cdot z - x}}}{x + 1}
double f(double x, double y, double z, double t) {
        double r718154 = x;
        double r718155 = y;
        double r718156 = z;
        double r718157 = r718155 * r718156;
        double r718158 = r718157 - r718154;
        double r718159 = t;
        double r718160 = r718159 * r718156;
        double r718161 = r718160 - r718154;
        double r718162 = r718158 / r718161;
        double r718163 = r718154 + r718162;
        double r718164 = 1.0;
        double r718165 = r718154 + r718164;
        double r718166 = r718163 / r718165;
        return r718166;
}
↓
double f(double x, double y, double z, double t) {
        double r718167 = x;
        double r718168 = y;
        double r718169 = t;
        double r718170 = z;
        double r718171 = r718167 / r718170;
        double r718172 = r718169 - r718171;
        double r718173 = r718168 / r718172;
        double r718174 = r718167 + r718173;
        double r718175 = 1.0;
        double r718176 = r718169 * r718170;
        double r718177 = r718176 - r718167;
        double r718178 = cbrt(r718177);
        double r718179 = r718178 * r718178;
        double r718180 = r718175 / r718179;
        double r718181 = r718167 / r718178;
        double r718182 = r718180 * r718181;
        double r718183 = r718174 - r718182;
        double r718184 = 1.0;
        double r718185 = r718167 + r718184;
        double r718186 = r718183 / r718185;
        return r718186;
}

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

Original6.9
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 6.9

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

  3. Applied div-sub6.9

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

  4. Applied associate-+r-6.9

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

  8. Applied div-sub2.2

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

  9. Simplified0.3

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

  11. Applied add-cube-cbrt0.4

    \[\leadsto \frac{\left(x + \frac{y}{\frac{t}{1} - \frac{x}{z}}\right) - \frac{x}{\color{blue}{\left(\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}\right) \cdot \sqrt[3]{t \cdot z - x}}}}{x + 1}\]

  12. Applied *-un-lft-identity0.4

    \[\leadsto \frac{\left(x + \frac{y}{\frac{t}{1} - \frac{x}{z}}\right) - \frac{\color{blue}{1 \cdot x}}{\left(\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}\right) \cdot \sqrt[3]{t \cdot z - x}}}{x + 1}\]

  13. Applied times-frac0.4

    \[\leadsto \frac{\left(x + \frac{y}{\frac{t}{1} - \frac{x}{z}}\right) - \color{blue}{\frac{1}{\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}} \cdot \frac{x}{\sqrt[3]{t \cdot z - x}}}}{x + 1}\]

  14. Final simplification0.4

    \[\leadsto \frac{\left(x + \frac{y}{t - \frac{x}{z}}\right) - \frac{1}{\sqrt[3]{t \cdot z - x} \cdot \sqrt[3]{t \cdot z - x}} \cdot \frac{x}{\sqrt[3]{t \cdot z - x}}}{x + 1}\]

Reproduce

herbie shell --seed 2020045 +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)))