Average Error: 2.3 → 0.4
Time: 5.0s
Precision: binary64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \leq -1.0091276599937923 \cdot 10^{+48}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{b \cdot \left(z \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot a\right)}\right) \cdot \sqrt[3]{\sqrt[3]{b} \cdot \left(\left(z \cdot a\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)}\\ \mathbf{elif}\;b \leq 2.97334263332371 \cdot 10^{+36}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + b \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt{b} \cdot \left(\left(z \cdot a\right) \cdot \sqrt{b}\right)\\ \end{array}\]
\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 -1.0091276599937923 \cdot 10^{+48}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{b \cdot \left(z \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot a\right)}\right) \cdot \sqrt[3]{\sqrt[3]{b} \cdot \left(\left(z \cdot a\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)}\\

\mathbf{elif}\;b \leq 2.97334263332371 \cdot 10^{+36}:\\
\;\;\;\;x + \left(y \cdot z + a \cdot \left(t + b \cdot z\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt{b} \cdot \left(\left(z \cdot a\right) \cdot \sqrt{b}\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 (<= b -1.0091276599937923e+48)
   (+
    (+ (+ x (* y z)) (* t a))
    (*
     (* (cbrt (* b (* z a))) (cbrt (* b (* z a))))
     (cbrt (* (cbrt b) (* (* z a) (* (cbrt b) (cbrt b)))))))
   (if (<= b 2.97334263332371e+36)
     (+ x (+ (* y z) (* a (+ t (* b z)))))
     (+ (+ (+ x (* y z)) (* t a)) (* (sqrt b) (* (* z a) (sqrt b)))))))
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 <= -1.0091276599937923e+48) {
		tmp = ((x + (y * z)) + (t * a)) + ((cbrt(b * (z * a)) * cbrt(b * (z * a))) * cbrt(cbrt(b) * ((z * a) * (cbrt(b) * cbrt(b)))));
	} else if (b <= 2.97334263332371e+36) {
		tmp = x + ((y * z) + (a * (t + (b * z))));
	} else {
		tmp = ((x + (y * z)) + (t * a)) + (sqrt(b) * ((z * a) * sqrt(b)));
	}
	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

Original2.3
Target0.3
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z < -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -1.00912765999379234e48

    1. Initial program 0.6

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

    3. Applied add-cube-cbrt_binary640.9

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

    5. Applied add-cube-cbrt_binary640.9

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

    6. Applied associate-*r*_binary640.9

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

    if -1.00912765999379234e48 < b < 2.97334263332370997e36

    1. Initial program 3.3

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

    2. Simplified0.2

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

    if 2.97334263332370997e36 < b

    1. Initial program 0.4

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

    3. Applied add-sqr-sqrt_binary640.5

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

    4. Applied associate-*r*_binary640.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.0091276599937923 \cdot 10^{+48}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{b \cdot \left(z \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot a\right)}\right) \cdot \sqrt[3]{\sqrt[3]{b} \cdot \left(\left(z \cdot a\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)}\\ \mathbf{elif}\;b \leq 2.97334263332371 \cdot 10^{+36}:\\ \;\;\;\;x + \left(y \cdot z + a \cdot \left(t + b \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \sqrt{b} \cdot \left(\left(z \cdot a\right) \cdot \sqrt{b}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020220 
(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)))