Details

sample958.0ms

Algorithm

intervals

Results

71.0ms	195×	body	80	valid
55.0ms	18×	body	2560	valid
40.0ms	34×	body	1280	valid
15.0ms	107×	body	80	nan
10.0ms	3×	body	5120	valid
4.0ms	13×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	29
5	29
4	27
3	25
2	22
1	14
0	10

prune167.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize232.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
0.9b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.0b	(- (* b_2 b_2) (* c a))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

419.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
311.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
459.0ms	(- (* b_2 b_2) (* c a))
157.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series1.8s

Counts

4 → 12

Calls

4 calls:

550.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
153.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
429.0ms	(- (* b_2 b_2) (* c a))
686.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify15.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	4237
2	1049
1	376
0	155

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* c a))) b_2) (/ 1 a))
0.9b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.0b	(- (* b_2 b_2) (* c a))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite4.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

3.8s	(* (- (sqrt (- (* b_2 b_2) (* c a))) b_2) (/ 1 a))
126.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
28.0ms	(- (* b_2 b_2) (* c a))
35.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series1.1s

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (- (sqrt (- (* b_2 b_2) (* c a))) b_2) (/ 1 a))
250.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
107.0ms	(- (* b_2 b_2) (* c a))
340.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify16.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
3	4799
2	1374
1	444
0	175

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
0.9b	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.0b	(- (* b_2 b_2) (* c a))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite746.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

338.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
188.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
178.0ms	(- (* b_2 b_2) (* c a))
28.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series974.0ms

Counts

4 → 12

Calls

4 calls:

516.0ms	(/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) a)
213.0ms	(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
110.0ms	(- (* b_2 b_2) (* c a))
135.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify12.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	4237
2	1049
1	376
0	155

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.9b

localize81.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* c a))
1.0b	(- (* b_2 b_2) (* c a))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))
21.8b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

19.0ms	(- (* b_2 b_2) (* c a))
247.0ms	(- (* b_2 b_2) (* c a))
19.0ms	(sqrt (- (* b_2 b_2) (* c a)))
14.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series856.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (* b_2 b_2) (* c a))
384.0ms	(- (* b_2 b_2) (* c a))
178.0ms	(sqrt (- (* b_2 b_2) (* c a)))
157.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify16.6s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
4	4870
3	1376
2	418
1	149
0	59

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.9b

regimes1.4s

Accuracy

82.5% (5.1b remaining)

Error of 10.6b against oracle of 5.5b and baseline of 34.6b

bsearch1.0s

Steps

Iters	Range		Point
9	1.177766511972955e-157	7.998381519079639e-153	7.923524897992037e-153
6	-4.525167845450207e+100	-9.36795079059543e+99	-2.7668189408748547e+100

simplify11.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample20.6s

Algorithm

intervals

Results

6.1s	1086×	body	2560	valid
4.4s	2815×	body	80	nan
4.0s	5756×	body	80	valid
3.2s	924×	body	1280	valid
1.3s	97×	body	5120	valid
468.0ms	476×	body	640	valid
126.0ms	239×	body	320	valid
69.0ms	116×	body	160	valid