Average Error: 1.9 → 2.0
Time: 15.3s
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 r26046662 = x;
        double r26046663 = y;
        double r26046664 = z;
        double r26046665 = r26046663 * r26046664;
        double r26046666 = r26046662 + r26046665;
        double r26046667 = t;
        double r26046668 = a;
        double r26046669 = r26046667 * r26046668;
        double r26046670 = r26046666 + r26046669;
        double r26046671 = r26046668 * r26046664;
        double r26046672 = b;
        double r26046673 = r26046671 * r26046672;
        double r26046674 = r26046670 + r26046673;
        return r26046674;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r26046675 = b;
        double r26046676 = cbrt(r26046675);
        double r26046677 = a;
        double r26046678 = z;
        double r26046679 = r26046677 * r26046678;
        double r26046680 = r26046676 * r26046676;
        double r26046681 = r26046679 * r26046680;
        double r26046682 = r26046676 * r26046681;
        double r26046683 = cbrt(r26046682);
        double r26046684 = r26046679 * r26046675;
        double r26046685 = cbrt(r26046684);
        double r26046686 = r26046685 * r26046685;
        double r26046687 = r26046683 * r26046686;
        double r26046688 = t;
        double r26046689 = r26046688 * r26046677;
        double r26046690 = y;
        double r26046691 = r26046678 * r26046690;
        double r26046692 = x;
        double r26046693 = r26046691 + r26046692;
        double r26046694 = r26046689 + r26046693;
        double r26046695 = r26046687 + r26046694;
        return r26046695;
}

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 +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)))