Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample24.0ms

Algorithm

intervals

Results

6.0ms	42×	body	1280	valid
6.0ms	48×	body	640	valid
5.0ms	141×	body	80	valid
1.0ms	12×	body	320	valid
1.0ms	13×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	8	13

prune6.0ms

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: 26.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite45.0ms

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-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 103

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5324	1405

prune181.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 0.1b

Counts

113 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.3b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
72×	`times-frac`
52×	`add-sqr-sqrt`
39×	`distribute-lft-out--`
32×	`exp-prod`
28×	`distribute-lft-out`
17×	`log-pow`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`log-prod` `associate-/r*`
3×	`sub-neg` `associate-/l*`
2×	`exp-diff` `diff-log` `exp-sum` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `frac-sub` `flip--` `flip-+` `div-inv`

Counts

4 → 115

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
34.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
34.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

series24.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ x 1.0))
7.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
8.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4978	1527
1	4978	1527

prune172.0ms

Filtered

80 candidates to 127 candidates (-58.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	126	6	132

Merged error: 0.0b

Counts

132 → 6

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* x (/ 1 (+ x 1.0)))
6.0b	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
46×	`times-frac`
33×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `distribute-lft-out`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `frac-sub` `flip--` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 136

Calls

4 calls:

5.0ms	(/ 1 (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
10.0ms	(* x (/ 1 (+ x 1.0)))
16.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series14.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1 (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
3.0ms	(* x (/ 1 (+ x 1.0)))
7.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5053	1495

prune172.0ms

Filtered

92 candidates to 148 candidates (-60.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Merged error: 0.0b

Counts

154 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
0.1b	(/ (- x 1.0) (sqrt (+ x 1.0)))
6.9b	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

645×	`times-frac`
584×	`*-un-lft-identity`
444×	`add-sqr-sqrt`
362×	`sqrt-prod`
261×	`add-cube-cbrt`
93×	`distribute-lft-out`
78×	`difference-of-squares`
67×	`distribute-lft-out--`
52×	`associate-/r*`
21×	`associate-/r/`
20×	`sqrt-div`
15×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
11×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log` `div-sub` `frac-sub`

Counts

4 → 478

Calls

4 calls:

8.0ms	(/ x (+ x 1.0))
21.0ms	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
8.0ms	(/ (- x 1.0) (sqrt (+ x 1.0)))
210.0ms	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ x 1.0))
3.0ms	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
7.0ms	(/ (- x 1.0) (sqrt (+ x 1.0)))
8.0ms	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

simplify159.0ms

Algorithm

egg-herbie

Counts

490 → 490

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4972	9643
1	4972	9643

prune580.0ms

Filtered

194 candidates to 490 candidates (-152.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	490	0	490
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	490	6	496

Merged error: 0.0b

Counts

496 → 6

regimes82.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	45
1	37	45

end0.0ms

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample726.0ms

Algorithm

intervals

Results

268.0ms	1723×	body	1280	valid
154.0ms	1277×	body	640	valid
136.0ms	4093×	body	80	valid
54.0ms	598×	body	320	valid
19.0ms	309×	body	160	valid

Details

analyze4.0ms

sample24.0ms

simplify3.0ms

prune6.0ms

localize7.0ms

rewrite45.0ms

series12.0ms

simplify63.0ms

prune181.0ms

localize10.0ms

rewrite107.0ms

series24.0ms

simplify62.0ms

prune172.0ms

localize7.0ms

rewrite43.0ms

series14.0ms

simplify53.0ms

prune172.0ms

localize9.0ms

rewrite281.0ms

series21.0ms

simplify159.0ms

prune580.0ms

regimes82.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

analyze4.0ms

sample726.0ms

Profiling