Average Error: 0.7 → 0.4
Time: 21.6s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{y - t}}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{y - t}}
double f(double x, double y, double z, double t) {
        double r217388 = 1.0;
        double r217389 = x;
        double r217390 = y;
        double r217391 = z;
        double r217392 = r217390 - r217391;
        double r217393 = t;
        double r217394 = r217390 - r217393;
        double r217395 = r217392 * r217394;
        double r217396 = r217389 / r217395;
        double r217397 = r217388 - r217396;
        return r217397;
}
↓
double f(double x, double y, double z, double t) {
        double r217398 = 1.0;
        double r217399 = x;
        double r217400 = cbrt(r217399);
        double r217401 = r217400 * r217400;
        double r217402 = y;
        double r217403 = z;
        double r217404 = r217402 - r217403;
        double r217405 = cbrt(r217404);
        double r217406 = r217405 * r217405;
        double r217407 = r217401 / r217406;
        double r217408 = t;
        double r217409 = r217402 - r217408;
        double r217410 = cbrt(r217409);
        double r217411 = r217410 * r217410;
        double r217412 = r217407 / r217411;
        double r217413 = r217400 / r217405;
        double r217414 = r217413 / r217410;
        double r217415 = r217412 * r217414;
        double r217416 = r217398 - r217415;
        return r217416;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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 associate-/r*1.0

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

  5. Applied add-cube-cbrt1.2

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

  6. Applied add-cube-cbrt1.3

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

  7. Applied add-cube-cbrt1.3

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

  8. Applied times-frac1.3

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

  9. Applied times-frac0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019235 +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)))))