Details

sample43.0ms

Algorithm

intervals

Results

7.0ms	181×	body	80	valid
6.0ms	27×	body	2560	valid
6.0ms	31×	body	1280	valid
3.0ms	21×	body	640	valid
3.0ms	81×	body	80	nan
2.0ms	8×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify85.0ms

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: 34.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

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:

35.0ms	(/ (- (- 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))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify928.0ms

Counts

89 → 89

Iterations

Useful iterations: done (925.0ms)

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

prune249.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.2b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite94.0ms

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:

17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
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))))

series529.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
168.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
204.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify822.0ms

Counts

153 → 153

Iterations

Useful iterations: done (815.0ms)

Iter	Nodes	Cost
0	250	4579
1	626	4057
2	2390	3753
done	5000	3751

prune421.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.2b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite297.0ms

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:

17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
40.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
230.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
169.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
206.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify836.0ms

Counts

153 → 153

Iterations

Useful iterations: done (824.0ms)

Iter	Nodes	Cost
0	250	4579
1	626	4057
2	2390	3753
done	5000	3751

prune442.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.5b	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
8.2b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

20.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
27.0ms	(/ (* 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))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
86.0ms	(/ (* 2.0 a) (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
207.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify973.0ms

Counts

125 → 125

Iterations

Useful iterations: done (969.0ms)

Iter	Nodes	Cost
0	223	3302
1	630	3098
2	2842	2550
done	5001	2549

prune330.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

regimes229.0ms

Accuracy

87.1% (3.5b remaining)

Error of 9.0b against oracle of 5.6b and baseline of 32.6b

bsearch250.0ms

Steps

Iters	Range		Point
10	1.1889782913455773e+76	6.845935134449847e+90	6.74838527698993e+90
10	-3.8445276237798955e-99	-1.3107711368463098e-114	-1.3311687138255245e-114
9	-3.339096941797073e+59	-6.124320340976488e+51	-5.109856166749479e+57

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	38	71
1	47	65
done	47	65

end0.0ms

sample1.2s

Algorithm

intervals

Results

272.0ms	1059×	body	2560	valid
250.0ms	5841×	body	80	valid
184.0ms	909×	body	1280	valid
128.0ms	2943×	body	80	nan
74.0ms	464×	body	640	valid
30.0ms	102×	body	5120	valid
30.0ms	234×	body	320	valid
9.0ms	111×	body	160	valid