Details

analyze659.0ms

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

sample67.0ms

Algorithm

intervals

Results

31.0ms	83×	body	1280	valid
15.0ms	59×	body	640	valid
7.0ms	82×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify470.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5131	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: 43.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
4.1b	(- (pow (exp x) 2.0) 1.0)
4.1b	(- (exp x) 1.0)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
71×	`times-frac`
52×	`difference-of-squares`
41×	`sqrt-prod`
31×	`add-cube-cbrt`
28×	`distribute-lft-out--`
12×	`unpow-prod-down` `sqr-pow`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r*` `flip--`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 145

Calls

4 calls:

11.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
18.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
6.0ms	(- (pow (exp x) 2.0) 1.0)
6.0ms	(- (exp x) 1.0)

series39.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
15.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
4.0ms	(- (pow (exp x) 2.0) 1.0)
10.0ms	(- (exp x) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5400	2783

prune285.0ms

Filtered

113 candidates to 157 candidates (-38.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	2	158

Merged error: 0.2b

Counts

158 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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)
10.0ms	(* (* (/ x (sqrt 2)) x) 3/16)
4.0ms	(/ x (sqrt 2))
4.0ms	(/ x (sqrt 2))

series23.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify53.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5135	1163

prune244.0ms

Filtered

98 candidates to 153 candidates (-56.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	153	2	155

Merged error: 0.2b

Counts

155 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series97.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt x) (cbrt x))
25.0ms	(cbrt x)
22.0ms	(cbrt x)
24.0ms	(cbrt x)

simplify47.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5165	356

prune170.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Merged error: 0.2b

Counts

87 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0)))
0.2b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))))
4.1b	(- (pow (exp x) 2.0) 1.0)
4.1b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

899×	`times-frac`
732×	`add-sqr-sqrt`
604×	`*-un-lft-identity`
454×	`difference-of-squares`
254×	`add-cube-cbrt`
243×	`sqrt-prod`
131×	`unpow-prod-down` `sqr-pow`
105×	`distribute-lft-out`
70×	`distribute-lft-out--`
61×	`unpow2`
34×	`associate-/r*`
32×	`associate-/r/`
17×	`div-inv`
15×	`flip3-+` `flip-+`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`associate-/l*`
5×	`pow1`
3×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `clear-num`

Counts

4 → 583

Calls

4 calls:

21.0ms	(/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0)))
37.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))))
6.0ms	(- (pow (exp x) 2.0) 1.0)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series15.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify174.0ms

Algorithm

egg-herbie

Counts

595 → 595

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5553	20439

prune1.5s

Filtered

331 candidates to 595 candidates (-79.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	595	0	595
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	595	3	598

Merged error: 0.2b

Counts

598 → 3

regimes42.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch23.0ms

Steps

Iters	Range		Point
10	-0.006538750209530131	-2.1516596463299053e-21	-6.4460959501863895e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	55
1	59	55

end0.0ms

sample1.6s

Algorithm

intervals

Results

817.0ms	2257×	body	1280	valid
384.0ms	1660×	body	640	valid
128.0ms	821×	body	320	valid
126.0ms	2840×	body	80	valid
42.0ms	422×	body	160	valid
0.0ms	3×	body	80	invalid

Details

analyze659.0ms

sample67.0ms

simplify470.0ms

prune10.0ms

localize10.0ms

rewrite50.0ms

series39.0ms

simplify49.0ms

prune285.0ms

localize9.0ms

rewrite31.0ms

series23.0ms

simplify53.0ms

prune244.0ms

localize19.0ms

rewrite11.0ms

series97.0ms

simplify47.0ms

prune170.0ms

localize13.0ms

rewrite123.0ms

series15.0ms

simplify174.0ms

prune1.5s

regimes42.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling