Average Error: 2.2 → 0.4
Time: 7.4s
Precision: binary64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
↓
\[\begin{array}{l} t_1 := y \cdot z + a \cdot t\\ \mathbf{if}\;a \leq -3.8807719241511593 \cdot 10^{-106} \lor \neg \left(a \leq 1.8547959827284203 \cdot 10^{+87}\right):\\ \;\;\;\;x + \left(t_1 + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 + z \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
t_1 := y \cdot z + a \cdot t\\
\mathbf{if}\;a \leq -3.8807719241511593 \cdot 10^{-106} \lor \neg \left(a \leq 1.8547959827284203 \cdot 10^{+87}\right):\\
\;\;\;\;x + \left(t_1 + a \cdot \left(z \cdot b\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x + \left(t_1 + z \cdot \left(a \cdot b\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
 (let* ((t_1 (+ (* y z) (* a t))))
   (if (or (<= a -3.8807719241511593e-106) (not (<= a 1.8547959827284203e+87)))
     (+ x (+ t_1 (* a (* z b))))
     (+ x (+ t_1 (* z (* a 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 t_1 = (y * z) + (a * t);
	double tmp;
	if ((a <= -3.8807719241511593e-106) || !(a <= 1.8547959827284203e+87)) {
		tmp = x + (t_1 + (a * (z * b)));
	} else {
		tmp = x + (t_1 + (z * (a * 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

Original2.2
Target0.4
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 2 regimes

  2. if a < -3.88077192415115929e-106 or 1.8547959827284203e87 < a

    1. Initial program 4.7

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

    2. Simplified0.5

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

    4. Applied distribute-lft-in_binary640.5

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

    5. Applied associate-+r+_binary640.5

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

    if -3.88077192415115929e-106 < a < 1.8547959827284203e87

    1. Initial program 0.6

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

    2. Simplified4.1

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

    4. Applied distribute-rgt-in_binary644.1

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

    5. Applied associate-+r+_binary644.1

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

    6. Simplified4.1

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

    8. Applied associate-*l*_binary640.3

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

    9. Simplified0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8807719241511593 \cdot 10^{-106} \lor \neg \left(a \leq 1.8547959827284203 \cdot 10^{+87}\right):\\ \;\;\;\;x + \left(\left(y \cdot z + a \cdot t\right) + a \cdot \left(z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y \cdot z + a \cdot t\right) + z \cdot \left(a \cdot b\right)\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2021190 
(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)))