Average Error: 1.9 → 1.5
Time: 18.6s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\left(t \cdot a + \left(z \cdot y + x\right)\right) + \sqrt[3]{b} \cdot \left(\left(\sqrt[3]{b} \cdot a\right) \cdot \left(z \cdot \sqrt[3]{b}\right)\right)\]
\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) + \sqrt[3]{b} \cdot \left(\left(\sqrt[3]{b} \cdot a\right) \cdot \left(z \cdot \sqrt[3]{b}\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r26974421 = x;
        double r26974422 = y;
        double r26974423 = z;
        double r26974424 = r26974422 * r26974423;
        double r26974425 = r26974421 + r26974424;
        double r26974426 = t;
        double r26974427 = a;
        double r26974428 = r26974426 * r26974427;
        double r26974429 = r26974425 + r26974428;
        double r26974430 = r26974427 * r26974423;
        double r26974431 = b;
        double r26974432 = r26974430 * r26974431;
        double r26974433 = r26974429 + r26974432;
        return r26974433;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r26974434 = t;
        double r26974435 = a;
        double r26974436 = r26974434 * r26974435;
        double r26974437 = z;
        double r26974438 = y;
        double r26974439 = r26974437 * r26974438;
        double r26974440 = x;
        double r26974441 = r26974439 + r26974440;
        double r26974442 = r26974436 + r26974441;
        double r26974443 = b;
        double r26974444 = cbrt(r26974443);
        double r26974445 = r26974444 * r26974435;
        double r26974446 = r26974437 * r26974444;
        double r26974447 = r26974445 * r26974446;
        double r26974448 = r26974444 * r26974447;
        double r26974449 = r26974442 + r26974448;
        return r26974449;
}

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
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

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-cbrt2.1

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

  4. Applied associate-*r*2.1

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

  6. Applied *-un-lft-identity2.1

    \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{\color{blue}{1 \cdot b}}\]

  7. Applied cbrt-prod2.1

    \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{b}\right)}\]

  8. Applied associate-*r*2.1

    \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{b}}\]

  9. Simplified1.5

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

  10. Final simplification1.5

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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)))