Average Error: 2.1 → 1.0
Time: 5.6s
Precision: binary64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq -\infty:\\ \;\;\;\;x + \left(y \cdot z + \sqrt[3]{t + z \cdot b} \cdot \left(a \cdot \left(\sqrt[3]{t + z \cdot b} \cdot \sqrt[3]{t + z \cdot b}\right)\right)\right)\\ \mathbf{elif}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq -4.3783930036826777 \cdot 10^{-23}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{b} \cdot \left(a \cdot \left(z \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq -\infty:\\
\;\;\;\;x + \left(y \cdot z + \sqrt[3]{t + z \cdot b} \cdot \left(a \cdot \left(\sqrt[3]{t + z \cdot b} \cdot \sqrt[3]{t + z \cdot b}\right)\right)\right)\\

\mathbf{elif}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq -4.3783930036826777 \cdot 10^{-23}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{b} \cdot \left(a \cdot \left(z \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\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 (<= (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b)) (- INFINITY))
   (+
    x
    (+
     (* y z)
     (*
      (cbrt (+ t (* z b)))
      (* a (* (cbrt (+ t (* z b))) (cbrt (+ t (* z b))))))))
   (if (<= (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b)) -4.3783930036826777e-23)
     (+ (+ (+ x (* y z)) (* t a)) (* (* z a) b))
     (+
      (+ (+ x (* y z)) (* t a))
      (* (cbrt b) (* a (* z (* (cbrt b) (cbrt b)))))))))
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 ((((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (z * a)) * b)))) <= ((double) -(((double) INFINITY))))) {
		tmp = ((double) (x + ((double) (((double) (y * z)) + ((double) (((double) cbrt(((double) (t + ((double) (z * b)))))) * ((double) (a * ((double) (((double) cbrt(((double) (t + ((double) (z * b)))))) * ((double) cbrt(((double) (t + ((double) (z * b))))))))))))))));
	} else {
		double tmp_1;
		if ((((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (z * a)) * b)))) <= -4.3783930036826777e-23)) {
			tmp_1 = ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) (z * a)) * b))));
		} else {
			tmp_1 = ((double) (((double) (((double) (x + ((double) (y * z)))) + ((double) (t * a)))) + ((double) (((double) cbrt(b)) * ((double) (a * ((double) (z * ((double) (((double) cbrt(b)) * ((double) cbrt(b))))))))))));
		}
		tmp = tmp_1;
	}
	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 3 regimes

  2. if (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < -inf.0

    1. Initial program Error: 64.0 bits

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

    2. SimplifiedError: 0.2 bits

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

    4. Applied add-cube-cbrtError: 0.9 bits

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

    5. Applied associate-*r*Error: 0.9 bits

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

    if -inf.0 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < -4.3783930036826777e-23

    1. Initial program Error: 0.1 bits

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

    if -4.3783930036826777e-23 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))

    1. Initial program Error: 2.2 bits

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
    2. Using strategy rm

    3. Applied add-cube-cbrtError: 2.3 bits

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

    4. Applied associate-*r*Error: 2.3 bits

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

    5. SimplifiedError: 1.8 bits

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

  4. Final simplificationError: 1.0 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq -\infty:\\ \;\;\;\;x + \left(y \cdot z + \sqrt[3]{t + z \cdot b} \cdot \left(a \cdot \left(\sqrt[3]{t + z \cdot b} \cdot \sqrt[3]{t + z \cdot b}\right)\right)\right)\\ \mathbf{elif}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b \leq -4.3783930036826777 \cdot 10^{-23}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt[3]{b} \cdot \left(a \cdot \left(z \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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)))