Details

sample88.0ms

Algorithm

intervals

Results

18.0ms	34×	body	2560	valid
17.0ms	196×	body	80	valid
8.0ms	20×	body	1280	valid
6.0ms	78×	body	80	nan
5.0ms	15×	body	640	valid
4.0ms	6×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify210.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	64	17
3	114	17
4	141	17
5	151	17
6	155	17
done	155	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

105.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (* b b) (* 4.0 (* a c)))
37.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
68.0ms	(- (* b b) (* 4.0 (* a c)))
109.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts

89 → 89

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	157	1750
1	418	1650
2	1644	1474
done	5000	1466

prune344.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
38.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
30.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series468.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b b) (* 4.0 (* a c)))
176.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
112.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts

137 → 137

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	226	3421
1	588	3066
2	3203	2856
done	5000	2852

prune448.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
203.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
58.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* b b) (* 4.0 (* a c)))
142.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
130.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
116.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

97 → 97

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	183	2003
1	492	1837
2	2395	1573
done	5000	1569

prune375.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.2b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
22×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 141

Calls

4 calls:

70.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
139.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
110.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
30.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
238.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
281.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
108.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

153 → 153

Iterations

Useful iterations: 2 (721.0ms)

Iter	Nodes	Cost
0	250	4579
1	649	4063
2	3620	3761
done	5001	3761

prune720.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

regimes324.0ms

Accuracy

85.9% (4.0b remaining)

Error of 9.8b against oracle of 5.8b and baseline of 34.4b

bsearch297.0ms

Steps

Iters	Range		Point
8	3932480935863.943	2020002846347102.2	2000198799923726.5
7	-4.99730849426316e-201	-1.9360757683614134e-202	-2.860817974822628e-201
6	-2.350179250111568e+55	-1.828939172749339e+54	-7.359940312872037e+54

simplify15.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	40	75
1	51	67
2	55	67
done	55	67

end0.0ms

sample3.2s

Algorithm

intervals

Results

710.0ms	1057×	body	2560	valid
540.0ms	5765×	body	80	valid
504.0ms	446×	body	640	valid
424.0ms	933×	body	1280	valid
223.0ms	2861×	body	80	nan
59.0ms	120×	body	160	valid
58.0ms	115×	body	5120	valid
53.0ms	230×	body	320	valid