Average Error: 0.7 → 0.7
Time: 8.2s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\frac{1}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)}{\sqrt[3]{\sqrt[3]{y - z}} \cdot \sqrt[3]{\sqrt[3]{y - z}}} \cdot \frac{\frac{\sqrt[3]{x}}{y - t}}{\sqrt[3]{\sqrt[3]{y - z}}}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\frac{1}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)}{\sqrt[3]{\sqrt[3]{y - z}} \cdot \sqrt[3]{\sqrt[3]{y - z}}} \cdot \frac{\frac{\sqrt[3]{x}}{y - t}}{\sqrt[3]{\sqrt[3]{y - z}}}
double f(double x, double y, double z, double t) {
        double r326590 = 1.0;
        double r326591 = x;
        double r326592 = y;
        double r326593 = z;
        double r326594 = r326592 - r326593;
        double r326595 = t;
        double r326596 = r326592 - r326595;
        double r326597 = r326594 * r326596;
        double r326598 = r326591 / r326597;
        double r326599 = r326590 - r326598;
        return r326599;
}
↓
double f(double x, double y, double z, double t) {
        double r326600 = 1.0;
        double r326601 = 1.0;
        double r326602 = y;
        double r326603 = z;
        double r326604 = r326602 - r326603;
        double r326605 = cbrt(r326604);
        double r326606 = r326605 * r326605;
        double r326607 = r326601 / r326606;
        double r326608 = x;
        double r326609 = cbrt(r326608);
        double r326610 = r326609 * r326609;
        double r326611 = r326607 * r326610;
        double r326612 = cbrt(r326605);
        double r326613 = r326612 * r326612;
        double r326614 = r326611 / r326613;
        double r326615 = t;
        double r326616 = r326602 - r326615;
        double r326617 = r326609 / r326616;
        double r326618 = r326617 / r326612;
        double r326619 = r326614 * r326618;
        double r326620 = r326600 - r326619;
        return r326620;
}

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 *-un-lft-identity1.3

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

  8. Applied times-frac1.3

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

  9. Applied associate-*l*1.3

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

  10. Simplified1.3

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

  12. Applied add-cube-cbrt1.4

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

  13. Applied *-un-lft-identity1.4

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

  14. Applied add-cube-cbrt1.4

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

  15. Applied times-frac1.4

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

  16. Applied times-frac0.9

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

  17. Applied associate-*r*0.7

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

  18. Simplified0.7

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

  19. Final simplification0.7

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

Reproduce

herbie shell --seed 2020062 
(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)))))