Details

analyze665.0ms (14.3%)

Algorithm

1×

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

sample55.0ms (1.2%)

Algorithm

1×

intervals

Results

21.0ms	63×	body	1280	valid
13.0ms	55×	body	640	valid
5.0ms	36×	body	320	valid
5.0ms	91×	body	80	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	80	invalid

simplify484.0ms (10.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5131	12

prune7.0ms (0.2%)

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: 40.8b

Counts

2 → 1

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.6b	(- (exp (* 2.0 x)) 1.0)
3.6b	(- (exp x) 1.0)

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
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 → 121

Calls

4 calls:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.0ms	(- (exp x) 1.0)
4.0ms	(- (exp (* 2.0 x)) 1.0)

series45.0ms (1%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (exp (* 2.0 x)) 1.0)
11.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms	(- (exp x) 1.0)
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5066	2150

prune304.0ms (6.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	3	134

Merged error: 0b

Counts

134 → 3

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+ 2.0 (* x (+ (* x 0.5) 1.0)))
9.6b	(sqrt (+ 2.0 (* x (+ (* x 0.5) 1.0))))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `associate-+r+` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 28

Calls

2 calls:

5.0ms	(sqrt (+ 2.0 (* x (+ (* x 0.5) 1.0))))
3.0ms	(+ 2.0 (* x (+ (* x 0.5) 1.0)))

series8.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(sqrt (+ 2.0 (* x (+ (* x 0.5) 1.0))))
3.0ms	(+ 2.0 (* x (+ (* x 0.5) 1.0)))

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5605	475

prune64.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Merged error: 0b

Counts

37 → 3

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2)
0.0b	(+ (exp x) 1.0)
3.6b	(- (pow (exp x) 2.0) 1.0)
3.6b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite20.0ms (0.4%)

Algorithm

1×	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:

6.0ms	(- (pow (exp x) 2.0) 1.0)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
4.0ms	(+ (exp x) 1.0)
3.0ms	(pow (exp x) 2)

series12.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

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

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5112	578

prune158.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	75	3	78

Merged error: 0b

Counts

78 → 3

localize11.0ms (0.2%)

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)
3.6b	(- (pow (exp x) 2.0) 1.0)
3.6b	(- (exp x) 1.0)

rewrite63.0ms (1.4%)

Algorithm

1×	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:

18.0ms	(pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3)
18.0ms	(cbrt (pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3))
6.0ms	(- (pow (exp x) 2.0) 1.0)
4.0ms	(- (exp x) 1.0)

series48.0ms (1%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))) 3)
14.0ms	(cbrt (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)

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5044	5637

prune739.0ms (15.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	253	3	256

Merged error: 0b

Counts

256 → 3

regimes37.0ms (0.8%)

Accuracy

Total 0.2b remaining (83.1%)

Threshold costs 0.2b (83.1%)

bsearch18.0ms (0.4%)

Steps

Iters	Range		Point
9	-0.00023126046997282165	-4.0086703064809486e-10	-1.397327525252979e-05

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	35
1	49	35

end0.0ms (0%)

sample1.6s (35.2%)

Algorithm

1×

intervals

Results

822.0ms	2309×	body	1280	valid
383.0ms	1686×	body	640	valid
132.0ms	862×	body	320	valid
122.0ms	2742×	body	80	valid
39.0ms	401×	body	160	valid
0.0ms	4×	body	80	invalid

Details

analyze665.0ms (14.3%)

sample55.0ms (1.2%)

simplify484.0ms (10.4%)

prune7.0ms (0.2%)

localize11.0ms (0.2%)

rewrite33.0ms (0.7%)

series45.0ms (1%)

simplify39.0ms (0.8%)

prune304.0ms (6.6%)

localize7.0ms (0.1%)

rewrite9.0ms (0.2%)

series8.0ms (0.2%)

simplify49.0ms (1.1%)

prune64.0ms (1.4%)

localize13.0ms (0.3%)

rewrite20.0ms (0.4%)

series12.0ms (0.3%)

simplify49.0ms (1.1%)

prune158.0ms (3.4%)

localize11.0ms (0.2%)

rewrite63.0ms (1.4%)

series48.0ms (1%)

simplify56.0ms (1.2%)

prune739.0ms (15.9%)

regimes37.0ms (0.8%)

bsearch18.0ms (0.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (35.2%)

Profiling