Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	37×	body	1280	valid
7.0ms	33×	body	2560	valid
7.0ms	178×	body	80	valid
3.0ms	22×	body	640	valid
3.0ms	79×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	6×	body	160	valid

simplify73.0ms

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: 37.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

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)))
14.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify740.0ms

Counts

89 → 89

Iterations

Useful iterations: done (738.0ms)

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

prune237.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
4.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.7b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.8b	(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)))
44.0ms	(/ (/ (+ 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))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* 4.0 (* a c)))
170.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
202.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify945.0ms

Counts

150 → 150

Iterations

Useful iterations: done (940.0ms)

Iter	Nodes	Cost
0	249	4460
1	622	3954
2	2408	3652
done	5000	3650

prune393.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 4 expressions with local error:

7.8b	(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
8.6b	(/ (+ 0 (* 4.0 (* a c))) (- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`difference-of-squares`
4×	`flip3--` `sqrt-div` `associate-/r*` `flip--`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 78

Calls

4 calls:

21.0ms	(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
35.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
204.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify477.0ms

Counts

90 → 90

Iterations

Useful iterations: done (474.0ms)

Iter	Nodes	Cost
0	154	2879
1	371	1788
2	1275	1680
done	5000	1673

prune313.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
4.5b	(* (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
9.7b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
51×	`add-exp-log`
42×	`*-un-lft-identity`
40×	`times-frac`
28×	`add-cube-cbrt`
27×	`add-cbrt-cube`
24×	`associate-l`
20×	`prod-exp`
16×	`div-exp`
14×	`difference-of-squares`
10×	`sqrt-prod`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `associate-r` `distribute-lft-out--`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 136

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
63.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
24.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
162.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
196.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify939.0ms

Counts

148 → 148

Iterations

Useful iterations: done (934.0ms)

Iter	Nodes	Cost
0	254	4174
1	713	3610
2	2651	3178
done	5000	3176

prune352.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes191.0ms

Accuracy

83.1% (4.4b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 32.0b

bsearch86.0ms

Steps

Iters	Range		Point
8	1.5276508475467709e+44	4.1560730947117816e+46	4.1199128263687574e+46
5	-1.2023865605984147e-79	-5.347575839305805e-80	-8.364554704106616e-80

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	41
1	36	41
done	36	41

end0.0ms

sample1.1s

Algorithm

intervals

Results

239.0ms	1073×	body	2560	valid
218.0ms	5862×	body	80	valid
162.0ms	902×	body	1280	valid
102.0ms	2862×	body	80	nan
69.0ms	459×	body	640	valid
32.0ms	114×	body	5120	valid
25.0ms	213×	body	320	valid
8.0ms	116×	body	160	valid