Average Error: 2.3 → 2.3
Time: 9.8s
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 r571081 = x;
        double r571082 = y;
        double r571083 = z;
        double r571084 = r571082 * r571083;
        double r571085 = r571081 + r571084;
        double r571086 = t;
        double r571087 = a;
        double r571088 = r571086 * r571087;
        double r571089 = r571085 + r571088;
        double r571090 = r571087 * r571083;
        double r571091 = b;
        double r571092 = r571090 * r571091;
        double r571093 = r571089 + r571092;
        return r571093;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r571094 = t;
        double r571095 = a;
        double r571096 = r571094 * r571095;
        double r571097 = z;
        double r571098 = y;
        double r571099 = r571097 * r571098;
        double r571100 = x;
        double r571101 = r571099 + r571100;
        double r571102 = r571096 + r571101;
        double r571103 = r571095 * r571097;
        double r571104 = b;
        double r571105 = r571103 * r571104;
        double r571106 = r571102 + r571105;
        return r571106;
}

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 
(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)))