Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	206×	body	80	valid
5.0ms	27×	body	2560	valid
4.0ms	29×	body	1280	valid
3.0ms	105×	body	80	nan
2.0ms	13×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	6×	body	160	valid
0.0ms	4×	body	320	valid

simplify63.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	88	16
5	96	16
done	96	16

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

64.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
47.0ms	(- (* b b) (* (* 3.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify821.0ms

Counts

82 → 82

Iterations

Useful iterations: done (819.0ms)

Iter	Nodes	Cost
0	154	1565
1	395	1463
2	1305	1247
done	5001	1235

prune215.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt`
4×	`div-exp`
3×	`times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `flip3--` `pow-flip` `sqrt-div` `1-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `neg-log` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 70

Calls

4 calls:

10.0ms	(/ 1 (* 3.0 a))
7.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ 1 (* 3.0 a))
46.0ms	(- (* b b) (* (* 3.0 a) c))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts

82 → 82

Iterations

Useful iterations: 3 (910.0ms)

Iter	Nodes	Cost
0	139	1051
1	331	934
2	1035	830
3	4095	820
done	5001	820

prune194.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`add-exp-log`
22×	`add-cube-cbrt` `associate-r`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 107

Calls

4 calls:

92.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
39.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
46.0ms	(- (* b b) (* (* 3.0 a) c))
85.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
77.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.0s

Counts

119 → 119

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	220	2448
1	569	2235
2	1835	1959
done	5000	1955

prune299.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1 3.0) (/ 1 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

23.0ms	(* (/ 1 3.0) (/ 1 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (/ 1 3.0) (/ 1 a))
47.0ms	(- (* b b) (* (* 3.0 a) c))
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.7s

Counts

124 → 124

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	210	1601
1	544	1339
2	1457	1167
3	4232	1140
done	5002	1138

prune269.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.2b

regimes348.0ms

Accuracy

84.3% (4.4b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 33.6b

bsearch147.0ms

Steps

Iters	Range		Point
6	2.0335150395734557e+19	1.0746392320557105e+20	3.973757644581715e+19
6	3.6410892437809104e-110	3.0960233903298005e-109	6.194358139220984e-110
8	1.0691773024250323e-170	5.5548132533506025e-168	5.480131987291899e-168
5	-1.2890659370140747e+99	-5.778998546738359e+98	-1.26989575591942e+99

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	40	81
1	52	75
done	52	75

end0.0ms

sample1.1s

Algorithm

intervals

Results

209.0ms	1041×	body	2560	valid
199.0ms	5926×	body	80	valid
142.0ms	905×	body	1280	valid
90.0ms	2854×	body	80	nan
56.0ms	464×	body	640	valid
24.0ms	102×	body	5120	valid
21.0ms	225×	body	320	valid
6.0ms	94×	body	160	valid