Details

analyze274.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample72.0ms (1.4%)

Algorithm

1×

intervals

Results

34.0ms	78×	body	1280	valid
12.0ms	46×	body	640	valid
10.0ms	29×	body	2560	valid
4.0ms	24×	body	320	valid
3.0ms	68×	body	80	valid
1.0ms	11×	body	160	valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

prune5.0ms (0.1%)

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: 52.6b

Counts

2 → 1

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.7b	(+ x (sqrt (+ (* x x) 1.0)))
3.1b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.4b	(sqrt (+ (* x x) 1.0))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

6.0ms	(+ x (sqrt (+ (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(sqrt (+ (* x x) 1.0))

series17.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5075	600

prune139.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.1b

Counts

52 → 7

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
0.1b	(* (pow (/ x (sqrt 1.0)) 3) -1/6)

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`associate-l`
49×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
25×	`unpow-prod-down` `cube-prod`
20×	`sqrt-prod`
10×	`add-exp-log`
8×	`unswap-sqr`
4×	`prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`associate-r`
2×	`pow1` `cube-div` `associate-*l/` `pow-exp` `div-inv` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `flip3-+` `unpow3` `div-exp` `frac-add` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 87

Calls

2 calls:

14.0ms	(* (pow (/ x (sqrt 1.0)) 3) -1/6)
9.0ms	(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))

series45.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
18.0ms	(* (pow (/ x (sqrt 1.0)) 3) -1/6)

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5452	1007

prune299.0ms (5.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	92	8	100

Merged error: 0.1b

Counts

100 → 8

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
0.2b	(pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)
0.8b	(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`pow-pow`
50×	`exp-prod`
38×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
31×	`unpow-prod-down`
22×	`cube-prod`
18×	`sqrt-prod`
14×	`log-prod`
7×	`associate-+r+`
4×	`pow1` `add-exp-log` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `rem-log-exp` `add-cbrt-cube`
2×	`pow-to-exp` `pow-exp` `div-inv`
1×	`+-commutative` `cube-mult` `flip3-+` `unpow3` `sum-log` `log-pow` `flip-+` `distribute-lft-out`

Counts

3 → 104

Calls

3 calls:

19.0ms	(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
13.0ms	(pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)
8.0ms	(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))

series160.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

87.0ms	(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))
43.0ms	(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
31.0ms	(pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)

simplify30.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5306	1228

prune417.0ms (8.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	113	8	121

Merged error: 0.1b

Counts

121 → 8

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* -1/6 (* 2 (log (cbrt (exp (pow (/ x (sqrt 1.0)) 3))))))
0.2b	(pow (cbrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6)
0.8b	(log (pow (cbrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6))
1.0b	(log (cbrt (exp (pow (/ x (sqrt 1.0)) 3))))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`log-prod`
24×	`distribute-rgt-in` `distribute-lft-in`
21×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
12×	`unpow-prod-down`
11×	`pow1`
9×	`add-cbrt-cube`
4×	`rem-log-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `log-pow` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `sqr-pow`
1×	`associate-r` `*-commutative`

Counts

4 → 100

Calls

4 calls:

12.0ms	(* -1/6 (* 2 (log (cbrt (exp (pow (/ x (sqrt 1.0)) 3))))))
8.0ms	(log (pow (cbrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6))
8.0ms	(pow (cbrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6)
8.0ms	(log (cbrt (exp (pow (/ x (sqrt 1.0)) 3))))

series397.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(log (pow (cbrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6))
119.0ms	(* -1/6 (* 2 (log (cbrt (exp (pow (/ x (sqrt 1.0)) 3))))))
85.0ms	(log (cbrt (exp (pow (/ x (sqrt 1.0)) 3))))
58.0ms	(pow (cbrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6)

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4899	1622
1	4899	1622

prune626.0ms (12.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	112	8	120

Merged error: 0.1b

Counts

120 → 8

regimes144.0ms (2.8%)

Accuracy

Total 0.2b remaining (93.2%)

Threshold costs 0.2b (93.2%)

bsearch27.0ms (0.5%)

Steps

Iters	Range		Point
9	0.2768238907569622	14347100.157384831	0.9662551447614324
7	-14.55571598581285	-0.08183750982964474	-1.0350961389186162

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	103	58
1	103	58

end0.0ms (0%)

sample2.2s (42.2%)

Algorithm

1×

intervals

Results

1.1s	2359×	body	1280	valid
440.0ms	1560×	body	640	valid
271.0ms	830×	body	2560	valid
130.0ms	777×	body	320	valid
89.0ms	2091×	body	80	valid
37.0ms	383×	body	160	valid

Details

analyze274.0ms (5.3%)

sample72.0ms (1.4%)

simplify3.0ms (0.1%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

rewrite18.0ms (0.3%)

series17.0ms (0.3%)

simplify43.0ms (0.8%)

prune139.0ms (2.7%)

localize10.0ms (0.2%)

rewrite27.0ms (0.5%)

series45.0ms (0.9%)

simplify46.0ms (0.9%)

prune299.0ms (5.8%)

localize12.0ms (0.2%)

rewrite45.0ms (0.9%)

series160.0ms (3.1%)

simplify30.0ms (0.6%)

prune417.0ms (8.1%)

localize20.0ms (0.4%)

rewrite39.0ms (0.8%)

series397.0ms (7.7%)

simplify58.0ms (1.1%)

prune626.0ms (12.1%)

regimes144.0ms (2.8%)

bsearch27.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (42.2%)

Profiling