Details

analyze679.0ms

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

sample62.0ms

Algorithm

intervals

Results

29.0ms	74×	body	1280	valid
12.0ms	52×	body	640	valid
5.0ms	92×	body	80	valid
4.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify477.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5131	12

prune11.0ms

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: 40.8b

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)
4.1b	(- (pow (exp x) 2.0) 1.0)
4.1b	(- (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)

series61.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(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)
25.0ms	(- (exp x) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4984	1624
1	4984	1624

prune215.0ms

Filtered

82 candidates to 113 candidates (-37.8%)

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

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

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (/ x (sqrt 2)) x)
5.0ms	(/ x (sqrt 2))
6.0ms	(/ x (sqrt 2))
7.0ms	(* (* (/ x (sqrt 2)) x) 3/16)

simplify57.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5135	1163

prune249.0ms

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

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(pow (exp x) 2)
4.1b	(- (pow (exp x) 2.0) 1.0)
4.1b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `pow-pow` `add-log-exp`
7×	`difference-of-squares`
6×	`pow1` `pow-unpow` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `unpow2`
1×	`distribute-lft-out--`

Counts

4 → 71

Calls

4 calls:

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

series26.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (exp x) 2.0)
3.0ms	(pow (exp x) 2)
4.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify30.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4908	612
1	4908	612

prune145.0ms

Filtered

60 candidates to 83 candidates (-38.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	82	4	86

Merged error: 0b

Counts

86 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (pow (exp x) 2.0) 1.0) 3)
0.1b	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
4.1b	(- (pow (exp x) 2) (* 1.0 1.0))
4.1b	(- (pow (exp x) 2.0) 1.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
20×	`cbrt-prod` `unpow-prod-down` `*-un-lft-identity`
19×	`difference-of-squares`
14×	`cube-prod`
10×	`add-cube-cbrt`
8×	`add-log-exp` `sqr-pow`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `unpow2` `rem-cube-cbrt`

Counts

4 → 94

Calls

4 calls:

7.0ms	(pow (- (pow (exp x) 2.0) 1.0) 3)
7.0ms	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
6.0ms	(- (pow (exp x) 2.0) 1.0)

series22.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(pow (- (pow (exp x) 2.0) 1.0) 3)
4.0ms	(cbrt (pow (- (pow (exp x) 2.0) 1.0) 3))
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
4.0ms	(- (pow (exp x) 2.0) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4945	1210
1	4945	1210

prune182.0ms

Filtered

64 candidates to 106 candidates (-65.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	106	4	110

Merged error: 0b

Counts

110 → 4

regimes46.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.0b

bsearch27.0ms

Steps

Iters	Range		Point
9	-8.8717875496476e-12	-6.3535144877712146e-21	-1.6478513007102085e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	43
1	52	43

end0.0ms

sample1.6s

Algorithm

intervals

Results

831.0ms	2300×	body	1280	valid
386.0ms	1662×	body	640	valid
127.0ms	813×	body	320	valid
126.0ms	2809×	body	80	valid
42.0ms	416×	body	160	valid
0.0ms	3×	body	80	invalid

Details

analyze679.0ms

sample62.0ms

simplify477.0ms

prune11.0ms

localize11.0ms

rewrite30.0ms

series61.0ms

simplify66.0ms

prune215.0ms

localize10.0ms

rewrite28.0ms

series24.0ms

simplify57.0ms

prune249.0ms

localize14.0ms

rewrite18.0ms

series26.0ms

simplify30.0ms

prune145.0ms

localize16.0ms

rewrite29.0ms

series22.0ms

simplify41.0ms

prune182.0ms

regimes46.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling