Details

sample59.0ms

Algorithm

intervals

Results

15.0ms	202×	body	80	valid
10.0ms	31×	body	2560	valid
6.0ms	24×	body	1280	valid
4.0ms	79×	body	80	nan
4.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify86.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

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:

13.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify681.0ms

Counts

89 → 89

Iterations

Useful iterations: done (678.0ms)

Iter	Nodes	Cost
0	155	1752
1	398	1653
2	1310	1483
done	5001	1473

prune177.0ms

Filtered

64 candidates to 89 candidates (-39.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Merged error: 6.2b

Counts

90 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

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:

20.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify945.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (158.0ms)

Iter	Nodes	Cost
0	181	2005
1	461	1796
2	1555	1574
done	5000	1574

prune153.0ms

Filtered

64 candidates to 97 candidates (-51.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Merged error: 6.2b

Counts

105 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.2b	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.6b	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

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:

8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
20.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
17.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
28.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
41.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify913.0ms

Counts

153 → 153

Iterations

Useful iterations: 2 (335.0ms)

Iter	Nodes	Cost
0	251	5246
1	629	4750
2	2103	4068
done	5001	4068

prune297.0ms

Filtered

110 candidates to 153 candidates (-39.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	153	7	160

Merged error: 6.2b

Counts

160 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
5.7b	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

8.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify650.0ms

Counts

88 → 88

Iterations

Useful iterations: done (648.0ms)

Iter	Nodes	Cost
0	164	1804
1	418	1652
2	1353	1526
done	5001	1521

prune131.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	88	7	95

Merged error: 6.2b

Counts

95 → 7

regimes281.0ms

Accuracy

87.3% (3.4b remaining)

Error of 9.3b against oracle of 5.9b and baseline of 32.7b

bsearch110.0ms

Steps

Iters	Range		Point
10	1.1487243557305423e+102	3.920821933018458e+112	1.8449991398001852e+109
7	-5.1440606176194e-107	-1.3691623995958124e-108	-1.6677459094321907e-108
9	-5050.104235080154	-0.0001616040529746431	-660.2639796459094

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	75
1	46	75
done	46	75

end0.0ms

sample1.7s

Algorithm

intervals

Results

342.0ms	1061×	body	2560	valid
330.0ms	5949×	body	80	valid
218.0ms	858×	body	1280	valid
160.0ms	2992×	body	80	nan
94.0ms	454×	body	640	valid
46.0ms	116×	body	5120	valid
36.0ms	236×	body	320	valid
11.0ms	111×	body	160	valid

Details

sample59.0ms

simplify86.0ms

prune3.0ms

localize12.0ms

rewrite35.0ms

series62.0ms

simplify681.0ms

prune177.0ms

localize13.0ms

rewrite39.0ms

series62.0ms

simplify945.0ms

prune153.0ms

localize19.0ms

rewrite55.0ms

series100.0ms

simplify913.0ms

prune297.0ms

localize14.0ms

rewrite39.0ms

series86.0ms

simplify650.0ms

prune131.0ms

regimes281.0ms

bsearch110.0ms

simplify4.0ms

end0.0ms

sample1.7s

Profiling