Average Error: 1.9 → 1.9
Time: 16.6s
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 r29449449 = x;
        double r29449450 = y;
        double r29449451 = z;
        double r29449452 = r29449450 * r29449451;
        double r29449453 = r29449449 + r29449452;
        double r29449454 = t;
        double r29449455 = a;
        double r29449456 = r29449454 * r29449455;
        double r29449457 = r29449453 + r29449456;
        double r29449458 = r29449455 * r29449451;
        double r29449459 = b;
        double r29449460 = r29449458 * r29449459;
        double r29449461 = r29449457 + r29449460;
        return r29449461;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r29449462 = t;
        double r29449463 = a;
        double r29449464 = r29449462 * r29449463;
        double r29449465 = z;
        double r29449466 = y;
        double r29449467 = r29449465 * r29449466;
        double r29449468 = x;
        double r29449469 = r29449467 + r29449468;
        double r29449470 = r29449464 + r29449469;
        double r29449471 = r29449463 * r29449465;
        double r29449472 = b;
        double r29449473 = r29449471 * r29449472;
        double r29449474 = r29449470 + r29449473;
        return r29449474;
}

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

Original1.9
Target0.3
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  2. Final simplification1.9

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

Reproduce

herbie shell --seed 2019169 
(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)))