Average Error: 0.7 → 0.7
Time: 5.1s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \frac{\frac{\sqrt[3]{x}}{y - z}}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \frac{\frac{\sqrt[3]{x}}{y - z}}{y - t}
double f(double x, double y, double z, double t) {
        double r331102 = 1.0;
        double r331103 = x;
        double r331104 = y;
        double r331105 = z;
        double r331106 = r331104 - r331105;
        double r331107 = t;
        double r331108 = r331104 - r331107;
        double r331109 = r331106 * r331108;
        double r331110 = r331103 / r331109;
        double r331111 = r331102 - r331110;
        return r331111;
}
↓
double f(double x, double y, double z, double t) {
        double r331112 = 1.0;
        double r331113 = x;
        double r331114 = cbrt(r331113);
        double r331115 = r331114 * r331114;
        double r331116 = y;
        double r331117 = z;
        double r331118 = r331116 - r331117;
        double r331119 = r331114 / r331118;
        double r331120 = t;
        double r331121 = r331116 - r331120;
        double r331122 = r331119 / r331121;
        double r331123 = r331115 * r331122;
        double r331124 = r331112 - r331123;
        return r331124;
}

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 add-cube-cbrt0.9

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

  4. Applied times-frac0.7

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

  6. Applied div-inv0.7

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

  7. Applied associate-*l*0.7

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

  8. Simplified0.7

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

  9. Final simplification0.7

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

Reproduce

herbie shell --seed 2020001 
(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)))))