Average Error: 1.8 → 0.6
Time: 6.2s
Precision: binary64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
↓
\[\begin{array}{l} \mathbf{if}\;b \leq -8.462647854390503 \cdot 10^{+53} \lor \neg \left(b \leq 3.0227167784787167 \cdot 10^{-171}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y \cdot z + t \cdot a\right) + a \cdot \left(b \cdot z\right)\right)\\ \end{array} \]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;b \leq -8.462647854390503 \cdot 10^{+53} \lor \neg \left(b \leq 3.0227167784787167 \cdot 10^{-171}\right):\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + b \cdot \left(z \cdot a\right)\\

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


\end{array}

(FPCore (x y z t a b)
 :precision binary64
 (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))
↓
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.462647854390503e+53) (not (<= b 3.0227167784787167e-171)))
   (+ (+ (+ x (* y z)) (* t a)) (* b (* z a)))
   (+ x (+ (+ (* y z) (* t a)) (* a (* b z))))))
double code(double x, double y, double z, double t, double a, double b) {
	return ((x + (y * z)) + (t * a)) + ((a * z) * b);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.462647854390503e+53) || !(b <= 3.0227167784787167e-171)) {
		tmp = ((x + (y * z)) + (t * a)) + (b * (z * a));
	} else {
		tmp = x + (((y * z) + (t * a)) + (a * (b * z)));
	}
	return tmp;
}

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

Original1.8
Target0.3
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;z < -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array} \]

Derivation

  1. Split input into 2 regimes

  2. if b < -8.4626478543905025e53 or 3.02271677847872e-171 < b

    1. Initial program 1.0

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

    if -8.4626478543905025e53 < b < 3.02271677847872e-171

    1. Initial program 2.8

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

    2. Simplified0.1

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

    4. Applied distribute-rgt-in_binary640.1

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

    5. Applied associate-+r+_binary640.1

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

    6. Simplified0.1

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.462647854390503 \cdot 10^{+53} \lor \neg \left(b \leq 3.0227167784787167 \cdot 10^{-171}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y \cdot z + t \cdot a\right) + a \cdot \left(b \cdot z\right)\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2021196 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :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)))