Details

analyze669.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample60.0ms

Algorithm

intervals

Results

26.0ms	65×	body	1280	valid
14.0ms	63×	body	640	valid
5.0ms	31×	body	320	valid
3.0ms	79×	body	80	valid
2.0ms	18×	body	160	valid

simplify478.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4920	12
1	4920	12

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 44.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
0.0b	(pow (exp x) 2.0)
4.7b	(- (pow (exp x) 2.0) 1.0)
4.7b	(- (exp x) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
41×	`sqrt-prod`
36×	`times-frac`
26×	`difference-of-squares`
20×	`add-cube-cbrt`
14×	`distribute-lft-out--`
9×	`unpow-prod-down`
8×	`add-log-exp`
7×	`sqr-pow`
6×	`pow1`
4×	`add-exp-log` `pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `exp-prod` `flip3--` `flip--`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `associate-/r/`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `div-inv`

Counts

4 → 101

Calls

4 calls:

11.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
3.0ms	(pow (exp x) 2.0)
5.0ms	(- (pow (exp x) 2.0) 1.0)
6.0ms	(- (exp x) 1.0)

series52.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
16.0ms	(pow (exp x) 2.0)
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify91.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4920	1622
1	4920	1622

prune179.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	3	114

Merged error: 0.0b

Counts

114 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (sqrt 2)) x)
0.2b	(* (* (/ x (sqrt 2)) x) 3/16)
0.4b	(/ x (sqrt 2))
0.4b	(/ x (sqrt 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
56×	`times-frac`
49×	`add-cube-cbrt` `*-un-lft-identity`
34×	`sqrt-prod`
23×	`associate-l`
22×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `pow-prod-down` `add-log-exp`
3×	`associate-*l/` `div-inv` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 141

Calls

4 calls:

8.0ms	(* (/ x (sqrt 2)) x)
7.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
4.0ms	(/ x (sqrt 2))
4.0ms	(/ x (sqrt 2))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (/ x (sqrt 2)) x)
7.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
8.0ms	(/ x (sqrt 2))
6.0ms	(/ x (sqrt 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5021	1163

prune229.0ms

Filtered

98 candidates to 153 candidates (-56.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	153	3	156

Merged error: 0.0b

Counts

156 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2)
0.0b	(+ (exp x) 1.0)
4.7b	(- (pow (exp x) 2.0) 1.0)
4.7b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt` `difference-of-squares`
5×	`pow1` `unpow-prod-down`
4×	`add-exp-log` `pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `exp-prod` `sqr-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `unpow2`
1×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `sum-log` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

3.0ms	(pow (exp x) 2)
4.0ms	(+ (exp x) 1.0)
5.0ms	(- (pow (exp x) 2.0) 1.0)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series12.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (exp x) 2)
2.0ms	(+ (exp x) 1.0)
4.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5003	578

prune127.0ms

Filtered

55 candidates to 75 candidates (-36.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	74	4	78

Merged error: 0b

Counts

78 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3))
0.1b	(pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3)
4.7b	(- (pow (exp x) 2.0) 1.0)
4.7b	(- (exp x) 1.0)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

225×	`add-sqr-sqrt`
164×	`sqrt-prod`
162×	`*-un-lft-identity`
140×	`times-frac`
109×	`unpow-prod-down`
94×	`cbrt-prod`
92×	`difference-of-squares`
88×	`cube-prod`
62×	`add-cube-cbrt`
50×	`distribute-lft-out--`
23×	`sqr-pow`
8×	`associate-/r/` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`add-exp-log` `add-cbrt-cube`
4×	`div-inv`
3×	`pow-unpow` `pow-pow`
2×	`cube-div` `cube-mult` `sub-neg` `sqrt-div` `diff-log` `unpow3`
1×	`pow-to-exp` `cbrt-div` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 241

Calls

4 calls:

17.0ms	(cbrt (pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3))
15.0ms	(pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3)
5.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (exp x) 1.0)

series43.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt (pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3))
23.0ms	(pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3)
4.0ms	(- (pow (exp x) 2.0) 1.0)
2.0ms	(- (exp x) 1.0)

simplify87.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5360	5637

prune298.0ms

Filtered

111 candidates to 253 candidates (-127.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	253	4	257

Merged error: 0b

Counts

257 → 4

regimes43.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.4b

bsearch7.0ms

Steps

Iters	Range		Point
2	-2.0634241421081868e-08	-1.8101740561488882e-08	-2.0317678813632748e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	43
1	32	43

end0.0ms

analyze463.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

sample1.6s

Algorithm

intervals

Results

832.0ms	2270×	body	1280	valid
374.0ms	1604×	body	640	valid
131.0ms	839×	body	320	valid
126.0ms	2834×	body	80	valid
47.0ms	453×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze669.0ms

sample60.0ms

simplify478.0ms

prune10.0ms

localize11.0ms

rewrite30.0ms

series52.0ms

simplify91.0ms

prune179.0ms

localize9.0ms

rewrite28.0ms

series26.0ms

simplify51.0ms

prune229.0ms

localize13.0ms

rewrite18.0ms

series12.0ms

simplify55.0ms

prune127.0ms

localize11.0ms

rewrite59.0ms

series43.0ms

simplify87.0ms

prune298.0ms

regimes43.0ms

bsearch7.0ms

simplify2.0ms

end0.0ms

analyze463.0ms

sample1.6s

Profiling