Details

sample55.0ms

Algorithm

intervals

Results

13.0ms	46×	body	1280	valid
9.0ms	135×	body	80	valid
8.0ms	37×	body	640	valid
5.0ms	27×	body	320	valid
1.0ms	11×	body	160	valid

simplify680.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	350
14	350
13	346
12	340
11	329
10	222
9	96
8	75
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize96.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite406.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 107

Calls

3 calls:

45.0ms	(/ x (+ x 1.0))
65.0ms	(/ (+ x 1.0) (- x 1.0))
278.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series320.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ x (+ x 1.0))
69.0ms	(/ (+ x 1.0) (- x 1.0))
189.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.7s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1291
1	411
0	179

prune675.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.1b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
3.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite904.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
72×	`times-frac`
60×	`add-sqr-sqrt`
31×	`distribute-lft-out--`
26×	`add-cube-cbrt` `distribute-lft-out`
17×	`log-pow`
16×	`exp-prod`
13×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `div-exp` `exp-sum` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 139

Calls

4 calls:

22.0ms	(/ x (+ x 1.0))
47.0ms	(/ (+ x 1.0) (- x 1.0))
613.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
206.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ x (+ x 1.0))
64.0ms	(/ (+ x 1.0) (- x 1.0))
191.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
152.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.6s

Counts

151 → 151

Iterations

Iter	Nodes
done	5000
2	1455
1	484
0	215

prune934.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize192.0ms

Local error

Found 4 expressions with local error:

3.1b	(log (exp (cbrt (* (* (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))
3.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite731.0ms

Algorithm

rewrite-expression-head

Rules

144×	`*-un-lft-identity`
60×	`times-frac`
42×	`add-sqr-sqrt`
39×	`distribute-lft-out--`
24×	`distribute-lft-out`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `log-pow`
4×	`exp-prod` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`log-prod` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`
1×	`cbrt-prod` `rem-log-exp`

Counts

4 → 98

Calls

4 calls:

11.0ms	(log (exp (cbrt (* (* (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))
252.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
242.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
210.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series785.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(log (exp (cbrt (* (* (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))
219.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
194.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
209.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.9s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
3	1656
2	513
1	199
0	97

prune987.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize108.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
20.6b	(- (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite603.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
25×	`times-frac`
16×	`cbrt-prod`
10×	`difference-of-squares`
7×	`add-cube-cbrt` `distribute-lft-out--`
6×	`cbrt-div` `add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 74

Calls

4 calls:

8.0ms	(cbrt (+ x 1.0))
9.0ms	(cbrt (+ x 1.0))
11.0ms	(cbrt (+ x 1.0))
570.0ms	(- (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (+ x 1.0))
130.0ms	(cbrt (+ x 1.0))
150.0ms	(cbrt (+ x 1.0))
201.0ms	(- (/ (/ x (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify5.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	3098
2	989
1	355
0	151

prune964.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes242.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.9b

bsearch155.0ms

Steps

Iters	Range		Point
7	986.1969312707462	23716.851585869685	12671.507747924104
9	-209901990.47645873	-0.28008678268591264	-15613.93143224409

simplify33.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample2.2s

Algorithm

intervals

Results

917.0ms	1331×	body	640	valid
661.0ms	1701×	body	1280	valid
279.0ms	4038×	body	80	valid
132.0ms	621×	body	320	valid
45.0ms	309×	body	160	valid