Details

analyze7.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample66.0ms (1.1%)

Algorithm

1×

intervals

Results

52.0ms	256×	body	80	valid
3.0ms	262×	pre	80	true
1.0ms	6×	body	80	invalid

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5216	49

prune15.0ms (0.3%)

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: 1.7b

Counts

2 → 2

localize36.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)
1.1b	(pow (exp (fabs x)) (fabs x))
1.3b	(pow (/ 1.0 (fabs x)) 7)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`unpow-prod-down`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log`
9×	`pow-unpow`
8×	`pow1`
6×	`pow-pow`
5×	`pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqrt-prod` `sqr-pow`
2×	`div-exp` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 89

Calls

4 calls:

5.0ms	(pow (/ 1.0 (fabs x)) 7)
4.0ms	(pow (/ 1.0 (fabs x)) 5)
3.0ms	(pow (exp (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series55.0ms (0.9%)

Counts

4 → 10

Calls

4 calls:

27.0ms	(pow (exp (fabs x)) (fabs x))
15.0ms	(pow (/ 1.0 (fabs x)) 7)
12.0ms	(pow (/ 1.0 (fabs x)) 5)
0.0ms	(sqrt PI)

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4958	897
1	4958	897

prune473.0ms (7.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	82	17	99
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	83	18	101

Merged error: 1.1b

Counts

101 → 18

localize35.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.8b	(* (pow (exp (fabs x)) (fabs x)) (+ (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3)) (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 5)) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 7)))))))
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)
1.1b	(pow (exp (fabs x)) (fabs x))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`frac-add`
27×	`associate-*r/`
25×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`unpow-prod-down`
19×	`add-cube-cbrt`
17×	`associate-*l/`
11×	`add-exp-log`
10×	`cube-div`
9×	`times-frac`
8×	`frac-times`
7×	`pow1` `associate-l`
6×	`pow-unpow` `add-cbrt-cube`
5×	`pow-pow` `flip3-+` `flip-+`
4×	`associate-r` `pow-exp` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `exp-prod` `prod-exp` `sqrt-prod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `div-exp` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 108

Calls

4 calls:

31.0ms	(* (pow (exp (fabs x)) (fabs x)) (+ (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3)) (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 5)) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 7)))))))
4.0ms	(pow (/ 1.0 (fabs x)) 5)
3.0ms	(pow (exp (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series137.0ms (2.3%)

Counts

4 → 10

Calls

4 calls:

94.0ms	(* (pow (exp (fabs x)) (fabs x)) (+ (/ 1.0 (fabs x)) (+ (* (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3)) (+ (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 5)) (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 7)))))))
30.0ms	(pow (exp (fabs x)) (fabs x))
12.0ms	(pow (/ 1.0 (fabs x)) 5)
0.0ms	(sqrt PI)

simplify49.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5569	3631

prune736.0ms (12.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	107	11	118
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	116	20	136

Merged error: 0.4b

Counts

136 → 20

localize36.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.7b	(pow (exp (fabs x)) (/ (fabs x) 2))
0.7b	(pow (exp (fabs x)) (/ (fabs x) 2))
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
29×	`pow-unpow`
27×	`times-frac`
19×	`unpow-prod-down`
9×	`pow-pow`
8×	`pow1`
7×	`add-exp-log`
6×	`exp-prod`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `sqrt-prod` `div-inv` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`

Counts

4 → 101

Calls

4 calls:

5.0ms	(pow (/ 1.0 (fabs x)) 5)
4.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
4.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
1.0ms	(sqrt PI)

series72.0ms (1.2%)

Counts

4 → 10

Calls

4 calls:

30.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
29.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
13.0ms	(pow (/ 1.0 (fabs x)) 5)
0.0ms	(sqrt PI)

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5006	1013

prune628.0ms (10.4%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	6	13	19
Picked	0	1	1
Done	0	0	0
Total	106	25	131

Merged error: 0.3b

Counts

131 → 25

localize42.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.7b	(pow (exp (fabs x)) (/ (fabs x) 2))
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)
1.1b	(pow (/ 1.0 (fabs x)) 5)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
29×	`unpow-prod-down`
27×	`times-frac`
19×	`pow-unpow`
10×	`add-exp-log`
8×	`pow1`
6×	`pow-pow`
5×	`pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqrt-prod` `div-inv` `sqr-pow`
2×	`div-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 99

Calls

4 calls:

5.0ms	(pow (/ 1.0 (fabs x)) 5)
5.0ms	(pow (/ 1.0 (fabs x)) 5)
4.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
1.0ms	(sqrt PI)

series59.0ms (1%)

Counts

4 → 10

Calls

4 calls:

30.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
16.0ms	(pow (/ 1.0 (fabs x)) 5)
13.0ms	(pow (/ 1.0 (fabs x)) 5)
0.0ms	(sqrt PI)

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5486	1036

prune961.0ms (15.9%)

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	4	19	23
Picked	0	1	1
Done	0	1	1
Total	108	26	134

Merged error: 0.3b

Counts

134 → 26

regimes633.0ms (10.5%)

Accuracy

Total 0.9b remaining (74.1%)

Threshold costs 0.9b (74.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	60
1	44	60

end0.0ms (0%)

sample1.8s (29.2%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	80	valid
93.0ms	8121×	pre	80	true
23.0ms	121×	body	80	invalid

Details

analyze7.0ms (0.1%)

sample66.0ms (1.1%)

simplify17.0ms (0.3%)

prune15.0ms (0.3%)

localize36.0ms (0.6%)

rewrite16.0ms (0.3%)

series55.0ms (0.9%)

simplify35.0ms (0.6%)

prune473.0ms (7.8%)

localize35.0ms (0.6%)

rewrite44.0ms (0.7%)

series137.0ms (2.3%)

simplify49.0ms (0.8%)

prune736.0ms (12.2%)

localize36.0ms (0.6%)

rewrite19.0ms (0.3%)

series72.0ms (1.2%)

simplify48.0ms (0.8%)

prune628.0ms (10.4%)

localize42.0ms (0.7%)

rewrite18.0ms (0.3%)

series59.0ms (1%)

simplify33.0ms (0.6%)

prune961.0ms (15.9%)

regimes633.0ms (10.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (29.2%)

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