Average Error: 1.9 → 2.0
Time: 17.5s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\sqrt[3]{\sqrt[3]{b} \cdot \left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)} \cdot \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) + \left(t \cdot a + \left(z \cdot y + x\right)\right)\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\sqrt[3]{\sqrt[3]{b} \cdot \left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)} \cdot \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) + \left(t \cdot a + \left(z \cdot y + x\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r32048212 = x;
        double r32048213 = y;
        double r32048214 = z;
        double r32048215 = r32048213 * r32048214;
        double r32048216 = r32048212 + r32048215;
        double r32048217 = t;
        double r32048218 = a;
        double r32048219 = r32048217 * r32048218;
        double r32048220 = r32048216 + r32048219;
        double r32048221 = r32048218 * r32048214;
        double r32048222 = b;
        double r32048223 = r32048221 * r32048222;
        double r32048224 = r32048220 + r32048223;
        return r32048224;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r32048225 = b;
        double r32048226 = cbrt(r32048225);
        double r32048227 = a;
        double r32048228 = z;
        double r32048229 = r32048227 * r32048228;
        double r32048230 = r32048226 * r32048226;
        double r32048231 = r32048229 * r32048230;
        double r32048232 = r32048226 * r32048231;
        double r32048233 = cbrt(r32048232);
        double r32048234 = r32048229 * r32048225;
        double r32048235 = cbrt(r32048234);
        double r32048236 = r32048235 * r32048235;
        double r32048237 = r32048233 * r32048236;
        double r32048238 = t;
        double r32048239 = r32048238 * r32048227;
        double r32048240 = y;
        double r32048241 = r32048228 * r32048240;
        double r32048242 = x;
        double r32048243 = r32048241 + r32048242;
        double r32048244 = r32048239 + r32048243;
        double r32048245 = r32048237 + r32048244;
        return r32048245;
}

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
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

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. Using strategy rm

  3. Applied add-cube-cbrt2.0

    \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.0

    \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) \cdot \sqrt[3]{\left(a \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)}}\]

  6. Applied associate-*r*2.0

    \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) \cdot \sqrt[3]{\color{blue}{\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}}}\]

  7. Final simplification2.0

    \[\leadsto \sqrt[3]{\sqrt[3]{b} \cdot \left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)} \cdot \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) + \left(t \cdot a + \left(z \cdot y + x\right)\right)\]

Reproduce

herbie shell --seed 2019172 
(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)))