Average Error: 2.1 → 1.0
Time: 5.1s
Precision: binary64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \leq -4.279510569832783 \cdot 10^{+80} \lor \neg \left(b \leq 4.62171941043673 \cdot 10^{-190}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + b \cdot z\right)\right)\\ \end{array}\]
\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 -4.279510569832783 \cdot 10^{+80} \lor \neg \left(b \leq 4.62171941043673 \cdot 10^{-190}\right):\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + b \cdot \left(z \cdot a\right)\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot z + a \cdot \left(t + 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 -4.279510569832783e+80) (not (<= b 4.62171941043673e-190)))
   (+ (+ (+ x (* y z)) (* t a)) (* b (* z a)))
   (+ x (+ (* y z) (* a (+ t (* b z)))))))
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (a * z)) * b))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((b <= -4.279510569832783e+80) || !(b <= 4.62171941043673e-190))) {
		tmp = ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (b * ((double) (z * a))))));
	} else {
		tmp = ((double) (x + ((double) (((double) (y * z)) + ((double) (a * ((double) (t + ((double) (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

Original2.1
Target0.4
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z < -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -4.2795105698327829e80 or 4.6217194104367302e-190 < b

    1. Initial program 1.5

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

    if -4.2795105698327829e80 < b < 4.6217194104367302e-190

    1. Initial program 2.8

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

    2. Simplified0.3

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.279510569832783 \cdot 10^{+80} \lor \neg \left(b \leq 4.62171941043673 \cdot 10^{-190}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + b \cdot \left(z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + b \cdot z\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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)))