Details

sample48.0ms

Algorithm

intervals

Results

9.0ms	34×	body	2560	valid
8.0ms	41×	body	1280	valid
7.0ms	174×	body	80	valid
6.0ms	94×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	6×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	28	17
2	63	17
3	114	17
4	130	17
5	136	17
6	139	17
done	139	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
2.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite53.0ms

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:

33.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify945.0ms

Counts

89 → 89

Iterations

Useful iterations: done (942.0ms)

Iter	Nodes	Cost
0	157	1750
1	405	1650
2	1328	1474
done	5000	1459

prune246.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
2.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.3b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
77×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
20×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`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 → 138

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
24.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* 4.0 (* a c)))
176.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
215.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
78.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify889.0ms

Counts

150 → 150

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	249	4460
1	624	3954
2	2410	3652
done	5001	3650

prune432.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

5.5b	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
6.5b	(/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
42×	`times-frac`
34×	`add-sqr-sqrt` `sqrt-prod`
24×	`-un-lft-identity` `associate-/r`
17×	`cbrt-undiv` `div-exp`
16×	`add-cube-cbrt`
13×	`prod-exp` `cbrt-unprod`
10×	`sqrt-div`
8×	`difference-of-squares`
7×	`associate-/r/`
6×	`pow1`
5×	`flip3--` `flip--`
4×	`div-inv` `distribute-lft-out--` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l*`

Counts

4 → 125

Calls

4 calls:

29.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
28.0ms	(/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series1.2s

Counts

4 → 12

Calls

4 calls:

310.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
746.0ms	(/ (* 4.0 (* a c)) (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

137 → 137

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	255	3747
1	702	3328
2	3008	2885
done	5001	2881

prune428.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
2.5b	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
9.3b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
30×	`times-frac`
28×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`associate-/r*`
17×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
8×	`difference-of-squares`
7×	`sqrt-prod` `associate-/r/`
6×	`add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv` `distribute-lft-out--`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l*`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 110

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
30.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
23.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* 4.0 (* a c)))
92.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
217.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts

122 → 122

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	221	3183
1	623	2995
2	2883	2449
done	5000	2448

prune310.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 4.0b

regimes321.0ms

Accuracy

82.7% (4.6b remaining)

Error of 10.1b against oracle of 5.5b and baseline of 31.9b

bsearch226.0ms

Steps

Iters	Range		Point
10	9.447687191993962e+42	3.6320219268964787e+53	3.599095900900979e+53
8	-5.624252222434776e-141	-8.495612805601153e-144	-5.527751925950661e-141
3	-1.5135282028271172e-83	-1.144585171485834e-83	-1.1676441109446642e-83
8	-7.845778557459706e+107	-1.6117226283259372e+105	-4.283911837099757e+106

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	89
1	46	89
done	46	89

end0.0ms

sample1.2s

Algorithm

intervals

Results

269.0ms	1076×	body	2560	valid
241.0ms	5778×	body	80	valid
190.0ms	967×	body	1280	valid
116.0ms	2868×	body	80	nan
71.0ms	460×	body	640	valid
32.0ms	109×	body	5120	valid
27.0ms	234×	body	320	valid
8.0ms	107×	body	160	valid