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 r272987 = 1.0;
        double r272988 = x;
        double r272989 = y;
        double r272990 = z;
        double r272991 = r272989 - r272990;
        double r272992 = t;
        double r272993 = r272989 - r272992;
        double r272994 = r272991 * r272993;
        double r272995 = r272988 / r272994;
        double r272996 = r272987 - r272995;
        return r272996;
}
↓
double f(double x, double y, double z, double t) {
        double r272997 = 1.0;
        double r272998 = x;
        double r272999 = cbrt(r272998);
        double r273000 = r272999 * r272999;
        double r273001 = 1.0;
        double r273002 = r273000 * r273001;
        double r273003 = y;
        double r273004 = z;
        double r273005 = r273003 - r273004;
        double r273006 = cbrt(r273005);
        double r273007 = r273006 * r273006;
        double r273008 = r273002 / r273007;
        double r273009 = t;
        double r273010 = r273003 - r273009;
        double r273011 = r272999 / r273010;
        double r273012 = r273011 / r273006;
        double r273013 = r273008 * r273012;
        double r273014 = r272997 - r273013;
        return r273014;
}

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 
(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)))))