Average Error: 0.7 → 0.4
Time: 7.1s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot 1}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\frac{\sqrt[3]{x}}{y - t}}{\sqrt[3]{y - z}}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot 1}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\frac{\sqrt[3]{x}}{y - t}}{\sqrt[3]{y - z}}
double f(double x, double y, double z, double t) {
        double r289225 = 1.0;
        double r289226 = x;
        double r289227 = y;
        double r289228 = z;
        double r289229 = r289227 - r289228;
        double r289230 = t;
        double r289231 = r289227 - r289230;
        double r289232 = r289229 * r289231;
        double r289233 = r289226 / r289232;
        double r289234 = r289225 - r289233;
        return r289234;
}
↓
double f(double x, double y, double z, double t) {
        double r289235 = 1.0;
        double r289236 = x;
        double r289237 = cbrt(r289236);
        double r289238 = r289237 * r289237;
        double r289239 = 1.0;
        double r289240 = r289238 * r289239;
        double r289241 = y;
        double r289242 = z;
        double r289243 = r289241 - r289242;
        double r289244 = cbrt(r289243);
        double r289245 = r289244 * r289244;
        double r289246 = r289240 / r289245;
        double r289247 = t;
        double r289248 = r289241 - r289247;
        double r289249 = r289237 / r289248;
        double r289250 = r289249 / r289244;
        double r289251 = r289246 * r289250;
        double r289252 = r289235 - r289251;
        return r289252;
}

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

Derivation

  1. Initial program 0.7

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

  3. Applied *-un-lft-identity0.7

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

  4. Applied times-frac1.1

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

  6. Applied add-cube-cbrt1.3

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

  7. Applied add-sqr-sqrt1.3

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

  8. Applied times-frac1.3

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

  9. Applied associate-*l*1.3

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

  10. Simplified1.3

    \[\leadsto 1 - \frac{\sqrt{1}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \color{blue}{\frac{\frac{x}{y - t}}{\sqrt[3]{y - z}}}\]
  11. Using strategy rm

  12. Applied *-un-lft-identity1.3

    \[\leadsto 1 - \frac{\sqrt{1}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\frac{x}{y - t}}{\color{blue}{1 \cdot \sqrt[3]{y - z}}}\]

  13. Applied *-un-lft-identity1.3

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

  14. Applied add-cube-cbrt1.4

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

  15. Applied times-frac1.4

    \[\leadsto 1 - \frac{\sqrt{1}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1} \cdot \frac{\sqrt[3]{x}}{y - t}}}{1 \cdot \sqrt[3]{y - z}}\]

  16. Applied times-frac0.8

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

  17. Applied associate-*r*0.4

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

  18. Simplified0.4

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

  19. Final simplification0.4

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1 (/ x (* (- y z) (- y t)))))