Average Error: 2.1 → 2.1
Time: 3.9s
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 r739482 = x;
        double r739483 = y;
        double r739484 = z;
        double r739485 = r739483 * r739484;
        double r739486 = r739482 + r739485;
        double r739487 = t;
        double r739488 = a;
        double r739489 = r739487 * r739488;
        double r739490 = r739486 + r739489;
        double r739491 = r739488 * r739484;
        double r739492 = b;
        double r739493 = r739491 * r739492;
        double r739494 = r739490 + r739493;
        return r739494;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r739495 = x;
        double r739496 = y;
        double r739497 = z;
        double r739498 = r739496 * r739497;
        double r739499 = r739495 + r739498;
        double r739500 = t;
        double r739501 = a;
        double r739502 = r739500 * r739501;
        double r739503 = r739499 + r739502;
        double r739504 = r739501 * r739497;
        double r739505 = b;
        double r739506 = r739504 * r739505;
        double r739507 = r739503 + r739506;
        return r739507;
}

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
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

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 2020020 
(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)))