Average Error: 2.3 → 2.3
Time: 13.0s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\left(t \cdot a + \left(z \cdot y + x\right)\right) + \left(a \cdot z\right) \cdot b\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\left(t \cdot a + \left(z \cdot y + x\right)\right) + \left(a \cdot z\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r27202443 = x;
        double r27202444 = y;
        double r27202445 = z;
        double r27202446 = r27202444 * r27202445;
        double r27202447 = r27202443 + r27202446;
        double r27202448 = t;
        double r27202449 = a;
        double r27202450 = r27202448 * r27202449;
        double r27202451 = r27202447 + r27202450;
        double r27202452 = r27202449 * r27202445;
        double r27202453 = b;
        double r27202454 = r27202452 * r27202453;
        double r27202455 = r27202451 + r27202454;
        return r27202455;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r27202456 = t;
        double r27202457 = a;
        double r27202458 = r27202456 * r27202457;
        double r27202459 = z;
        double r27202460 = y;
        double r27202461 = r27202459 * r27202460;
        double r27202462 = x;
        double r27202463 = r27202461 + r27202462;
        double r27202464 = r27202458 + r27202463;
        double r27202465 = r27202457 * r27202459;
        double r27202466 = b;
        double r27202467 = r27202465 * r27202466;
        double r27202468 = r27202464 + r27202467;
        return r27202468;
}

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

Target

Original2.3
Target0.3
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Initial program 2.3

    \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]

  2. Final simplification2.3

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"

  :herbie-target
  (if (< z -1.1820553527347888e+19) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))