Average Error: 0.0 → 0.4
Time: 5.8s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[x + \left(\left(\left(-\left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)\]
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
x + \left(\left(\left(-\left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r32604 = x;
        double r32605 = y;
        double r32606 = 1.0;
        double r32607 = r32605 - r32606;
        double r32608 = z;
        double r32609 = r32607 * r32608;
        double r32610 = r32604 - r32609;
        double r32611 = t;
        double r32612 = r32611 - r32606;
        double r32613 = a;
        double r32614 = r32612 * r32613;
        double r32615 = r32610 - r32614;
        double r32616 = r32605 + r32611;
        double r32617 = 2.0;
        double r32618 = r32616 - r32617;
        double r32619 = b;
        double r32620 = r32618 * r32619;
        double r32621 = r32615 + r32620;
        return r32621;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r32622 = x;
        double r32623 = y;
        double r32624 = 1.0;
        double r32625 = r32623 - r32624;
        double r32626 = z;
        double r32627 = r32625 * r32626;
        double r32628 = -r32627;
        double r32629 = t;
        double r32630 = r32629 - r32624;
        double r32631 = a;
        double r32632 = cbrt(r32631);
        double r32633 = r32632 * r32632;
        double r32634 = r32630 * r32633;
        double r32635 = r32634 * r32632;
        double r32636 = r32628 - r32635;
        double r32637 = r32623 + r32629;
        double r32638 = 2.0;
        double r32639 = r32637 - r32638;
        double r32640 = b;
        double r32641 = r32639 * r32640;
        double r32642 = r32636 + r32641;
        double r32643 = r32622 + r32642;
        return r32643;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto \left(\color{blue}{\left(x + \left(-\left(y - 1\right) \cdot z\right)\right)} - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

  4. Applied associate--l+0.0

    \[\leadsto \color{blue}{\left(x + \left(\left(-\left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b\]

  5. Applied associate-+l+0.0

    \[\leadsto \color{blue}{x + \left(\left(\left(-\left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.3

    \[\leadsto x + \left(\left(\left(-\left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)}\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)\]

  8. Applied associate-*r*0.4

    \[\leadsto x + \left(\left(\left(-\left(y - 1\right) \cdot z\right) - \color{blue}{\left(\left(t - 1\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}}\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)\]

  9. Final simplification0.4

    \[\leadsto x + \left(\left(\left(-\left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)\]

Reproduce

herbie shell --seed 2020021 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b)))