Average Error: 0.6 → 0.7
Time: 13.7s
Precision: 64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - x \cdot \frac{\frac{1}{y - z}}{y - t}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - x \cdot \frac{\frac{1}{y - z}}{y - t}
double f(double x, double y, double z, double t) {
        double r145618 = 1.0;
        double r145619 = x;
        double r145620 = y;
        double r145621 = z;
        double r145622 = r145620 - r145621;
        double r145623 = t;
        double r145624 = r145620 - r145623;
        double r145625 = r145622 * r145624;
        double r145626 = r145619 / r145625;
        double r145627 = r145618 - r145626;
        return r145627;
}
↓
double f(double x, double y, double z, double t) {
        double r145628 = 1.0;
        double r145629 = x;
        double r145630 = 1.0;
        double r145631 = y;
        double r145632 = z;
        double r145633 = r145631 - r145632;
        double r145634 = r145630 / r145633;
        double r145635 = t;
        double r145636 = r145631 - r145635;
        double r145637 = r145634 / r145636;
        double r145638 = r145629 * r145637;
        double r145639 = r145628 - r145638;
        return r145639;
}

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 0.6

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

  3. Applied div-inv0.7

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

  5. Applied associate-/r*0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019212 +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)))))