Average Error: 2.3 → 0.6
Time: 9.9s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.110831076426873971512380791406333640803 \cdot 10^{72} \lor \neg \left(z \le 169489966796033468445753344\right):\\ \;\;\;\;\left(z \cdot \left(\left(\sqrt[3]{y + b \cdot a} \cdot \sqrt[3]{y + b \cdot a}\right) \cdot \left(\sqrt[3]{\sqrt[3]{y + b \cdot a} \cdot \sqrt[3]{y + b \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y + b \cdot a}}\right)\right) + x\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.110831076426873971512380791406333640803 \cdot 10^{72} \lor \neg \left(z \le 169489966796033468445753344\right):\\
\;\;\;\;\left(z \cdot \left(\left(\sqrt[3]{y + b \cdot a} \cdot \sqrt[3]{y + b \cdot a}\right) \cdot \left(\sqrt[3]{\sqrt[3]{y + b \cdot a} \cdot \sqrt[3]{y + b \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y + b \cdot a}}\right)\right) + x\right) + a \cdot t\\

\mathbf{else}:\\
\;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r385226 = x;
        double r385227 = y;
        double r385228 = z;
        double r385229 = r385227 * r385228;
        double r385230 = r385226 + r385229;
        double r385231 = t;
        double r385232 = a;
        double r385233 = r385231 * r385232;
        double r385234 = r385230 + r385233;
        double r385235 = r385232 * r385228;
        double r385236 = b;
        double r385237 = r385235 * r385236;
        double r385238 = r385234 + r385237;
        return r385238;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r385239 = z;
        double r385240 = -1.110831076426874e+72;
        bool r385241 = r385239 <= r385240;
        double r385242 = 1.6948996679603347e+26;
        bool r385243 = r385239 <= r385242;
        double r385244 = !r385243;
        bool r385245 = r385241 || r385244;
        double r385246 = y;
        double r385247 = b;
        double r385248 = a;
        double r385249 = r385247 * r385248;
        double r385250 = r385246 + r385249;
        double r385251 = cbrt(r385250);
        double r385252 = r385251 * r385251;
        double r385253 = cbrt(r385252);
        double r385254 = cbrt(r385251);
        double r385255 = r385253 * r385254;
        double r385256 = r385252 * r385255;
        double r385257 = r385239 * r385256;
        double r385258 = x;
        double r385259 = r385257 + r385258;
        double r385260 = t;
        double r385261 = r385248 * r385260;
        double r385262 = r385259 + r385261;
        double r385263 = r385246 * r385239;
        double r385264 = r385258 + r385263;
        double r385265 = r385239 * r385247;
        double r385266 = r385265 + r385260;
        double r385267 = r385248 * r385266;
        double r385268 = r385264 + r385267;
        double r385269 = r385245 ? r385262 : r385268;
        return r385269;
}

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
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.110831076426874e+72 or 1.6948996679603347e+26 < z

    1. Initial program 6.6

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-+l+6.6

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

    4. Simplified9.8

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

    6. Applied distribute-lft-in9.8

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

    7. Applied associate-+r+9.8

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

    8. Simplified0.1

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

    10. Applied add-cube-cbrt0.9

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

    12. Applied add-cube-cbrt1.0

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

    13. Applied cbrt-prod1.0

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

    if -1.110831076426874e+72 < z < 1.6948996679603347e+26

    1. Initial program 0.5

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-+l+0.5

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

    4. Simplified0.4

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{a \cdot \left(z \cdot b + t\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.110831076426873971512380791406333640803 \cdot 10^{72} \lor \neg \left(z \le 169489966796033468445753344\right):\\ \;\;\;\;\left(z \cdot \left(\left(\sqrt[3]{y + b \cdot a} \cdot \sqrt[3]{y + b \cdot a}\right) \cdot \left(\sqrt[3]{\sqrt[3]{y + b \cdot a} \cdot \sqrt[3]{y + b \cdot a}} \cdot \sqrt[3]{\sqrt[3]{y + b \cdot a}}\right)\right) + x\right) + a \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019298 
(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)))