Average Error: 0.0 → 0.0
Time: 11.3s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - 1 \cdot \left(a \cdot t - a\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
\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
↓
\left(\left(x - \left(y - 1\right) \cdot z\right) - 1 \cdot \left(a \cdot t - a\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r34542 = x;
        double r34543 = y;
        double r34544 = 1.0;
        double r34545 = r34543 - r34544;
        double r34546 = z;
        double r34547 = r34545 * r34546;
        double r34548 = r34542 - r34547;
        double r34549 = t;
        double r34550 = r34549 - r34544;
        double r34551 = a;
        double r34552 = r34550 * r34551;
        double r34553 = r34548 - r34552;
        double r34554 = r34543 + r34549;
        double r34555 = 2.0;
        double r34556 = r34554 - r34555;
        double r34557 = b;
        double r34558 = r34556 * r34557;
        double r34559 = r34553 + r34558;
        return r34559;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r34560 = x;
        double r34561 = y;
        double r34562 = 1.0;
        double r34563 = r34561 - r34562;
        double r34564 = z;
        double r34565 = r34563 * r34564;
        double r34566 = r34560 - r34565;
        double r34567 = a;
        double r34568 = t;
        double r34569 = r34567 * r34568;
        double r34570 = r34569 - r34567;
        double r34571 = r34562 * r34570;
        double r34572 = r34566 - r34571;
        double r34573 = r34561 + r34568;
        double r34574 = 2.0;
        double r34575 = r34573 - r34574;
        double r34576 = b;
        double r34577 = r34575 * r34576;
        double r34578 = r34572 + r34577;
        return r34578;
}

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 flip--8.4

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

  4. Applied associate-*l/10.8

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

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 
(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)))