Average Error: 1.9 → 2.6
Time: 16.2s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\left(a \cdot \left(b \cdot z + t\right) + x\right) + z \cdot y\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\left(a \cdot \left(b \cdot z + t\right) + x\right) + z \cdot y
double f(double x, double y, double z, double t, double a, double b) {
        double r28973018 = x;
        double r28973019 = y;
        double r28973020 = z;
        double r28973021 = r28973019 * r28973020;
        double r28973022 = r28973018 + r28973021;
        double r28973023 = t;
        double r28973024 = a;
        double r28973025 = r28973023 * r28973024;
        double r28973026 = r28973022 + r28973025;
        double r28973027 = r28973024 * r28973020;
        double r28973028 = b;
        double r28973029 = r28973027 * r28973028;
        double r28973030 = r28973026 + r28973029;
        return r28973030;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r28973031 = a;
        double r28973032 = b;
        double r28973033 = z;
        double r28973034 = r28973032 * r28973033;
        double r28973035 = t;
        double r28973036 = r28973034 + r28973035;
        double r28973037 = r28973031 * r28973036;
        double r28973038 = x;
        double r28973039 = r28973037 + r28973038;
        double r28973040 = y;
        double r28973041 = r28973033 * r28973040;
        double r28973042 = r28973039 + r28973041;
        return r28973042;
}

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
Target0.4
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

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. Simplified2.6

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

  3. Final simplification2.6

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

Reproduce

herbie shell --seed 2019162 
(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)))