Average Error: 1.9 → 2.0
Time: 17.9s
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 r32242796 = x;
        double r32242797 = y;
        double r32242798 = z;
        double r32242799 = r32242797 * r32242798;
        double r32242800 = r32242796 + r32242799;
        double r32242801 = t;
        double r32242802 = a;
        double r32242803 = r32242801 * r32242802;
        double r32242804 = r32242800 + r32242803;
        double r32242805 = r32242802 * r32242798;
        double r32242806 = b;
        double r32242807 = r32242805 * r32242806;
        double r32242808 = r32242804 + r32242807;
        return r32242808;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r32242809 = b;
        double r32242810 = cbrt(r32242809);
        double r32242811 = a;
        double r32242812 = z;
        double r32242813 = r32242811 * r32242812;
        double r32242814 = r32242810 * r32242810;
        double r32242815 = r32242813 * r32242814;
        double r32242816 = r32242810 * r32242815;
        double r32242817 = cbrt(r32242816);
        double r32242818 = r32242813 * r32242809;
        double r32242819 = cbrt(r32242818);
        double r32242820 = r32242819 * r32242819;
        double r32242821 = r32242817 * r32242820;
        double r32242822 = t;
        double r32242823 = r32242822 * r32242811;
        double r32242824 = y;
        double r32242825 = r32242812 * r32242824;
        double r32242826 = x;
        double r32242827 = r32242825 + r32242826;
        double r32242828 = r32242823 + r32242827;
        double r32242829 = r32242821 + r32242828;
        return r32242829;
}

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)))