Average Error: 0.0 → 0.4
Time: 6.1s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
\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) - \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
double f(double x, double y, double z, double t, double a, double b) {
        double r32354 = x;
        double r32355 = y;
        double r32356 = 1.0;
        double r32357 = r32355 - r32356;
        double r32358 = z;
        double r32359 = r32357 * r32358;
        double r32360 = r32354 - r32359;
        double r32361 = t;
        double r32362 = r32361 - r32356;
        double r32363 = a;
        double r32364 = r32362 * r32363;
        double r32365 = r32360 - r32364;
        double r32366 = r32355 + r32361;
        double r32367 = 2.0;
        double r32368 = r32366 - r32367;
        double r32369 = b;
        double r32370 = r32368 * r32369;
        double r32371 = r32365 + r32370;
        return r32371;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r32372 = x;
        double r32373 = y;
        double r32374 = 1.0;
        double r32375 = r32373 - r32374;
        double r32376 = z;
        double r32377 = r32375 * r32376;
        double r32378 = r32372 - r32377;
        double r32379 = t;
        double r32380 = r32379 - r32374;
        double r32381 = a;
        double r32382 = cbrt(r32381);
        double r32383 = r32382 * r32382;
        double r32384 = r32380 * r32383;
        double r32385 = r32384 * r32382;
        double r32386 = r32378 - r32385;
        double r32387 = r32373 + r32379;
        double r32388 = 2.0;
        double r32389 = r32387 - r32388;
        double r32390 = b;
        double r32391 = r32389 * r32390;
        double r32392 = r32386 + r32391;
        return r32392;
}

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 add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(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)))