Average Error: 2.1 → 2.8
Time: 9.6s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r494205 = x;
        double r494206 = y;
        double r494207 = z;
        double r494208 = r494206 * r494207;
        double r494209 = r494205 + r494208;
        double r494210 = t;
        double r494211 = a;
        double r494212 = r494210 * r494211;
        double r494213 = r494209 + r494212;
        double r494214 = r494211 * r494207;
        double r494215 = b;
        double r494216 = r494214 * r494215;
        double r494217 = r494213 + r494216;
        return r494217;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r494218 = y;
        double r494219 = z;
        double r494220 = r494218 * r494219;
        double r494221 = x;
        double r494222 = a;
        double r494223 = t;
        double r494224 = b;
        double r494225 = r494219 * r494224;
        double r494226 = r494223 + r494225;
        double r494227 = r494222 * r494226;
        double r494228 = r494221 + r494227;
        double r494229 = r494220 + r494228;
        return r494229;
}

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
Target0.5
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

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. Simplified2.8

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

  3. Final simplification2.8

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

Reproduce

herbie shell --seed 2019294 
(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 4.75897431883642871e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

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