Average Error: 2.1 → 2.1
Time: 4.7s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
\left(\left(x + y \cdot z\right) + t \cdot a\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
double f(double x, double y, double z, double t, double a, double b) {
        double r631554 = x;
        double r631555 = y;
        double r631556 = z;
        double r631557 = r631555 * r631556;
        double r631558 = r631554 + r631557;
        double r631559 = t;
        double r631560 = a;
        double r631561 = r631559 * r631560;
        double r631562 = r631558 + r631561;
        double r631563 = r631560 * r631556;
        double r631564 = b;
        double r631565 = r631563 * r631564;
        double r631566 = r631562 + r631565;
        return r631566;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r631567 = x;
        double r631568 = y;
        double r631569 = z;
        double r631570 = r631568 * r631569;
        double r631571 = r631567 + r631570;
        double r631572 = t;
        double r631573 = a;
        double r631574 = r631572 * r631573;
        double r631575 = r631571 + r631574;
        double r631576 = r631573 * r631569;
        double r631577 = b;
        double r631578 = r631576 * r631577;
        double r631579 = r631575 + r631578;
        return r631579;
}

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

Original2.1
Target0.3
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  2. Final simplification2.1

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000) (+ (* 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)))