Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

sample36.0ms (0.4%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5022	33

prune9.0ms (0.1%)

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: 0.1b

Counts

2 → 1

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 5) 5.0)
0.1b	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
0.1b	(/ (pow (fabs x) 3) 3.0)
1.0b	(sqrt PI)

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`times-frac`
69×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-*r/`
24×	`unpow-prod-down`
22×	`associate-l`
19×	`add-exp-log` `associate-/l*`
16×	`frac-add`
13×	`sqrt-prod` `add-cbrt-cube`
12×	`flip3-+` `cube-prod` `flip-+`
8×	`frac-times` `sqr-pow`
7×	`pow1` `div-exp`
6×	`associate-/r*`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`cbrt-undiv` `associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `prod-exp` `clear-num` `cbrt-unprod`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 183

Calls

4 calls:

22.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
7.0ms	(/ (pow (fabs x) 5) 5.0)
6.0ms	(/ (pow (fabs x) 3) 3.0)
1.0ms	(sqrt PI)

series74.0ms (0.8%)

Counts

4 → 10

Calls

4 calls:

52.0ms	(* (/ 1.0 (sqrt PI)) (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))
13.0ms	(/ (pow (fabs x) 5) 5.0)
8.0ms	(/ (pow (fabs x) 3) 3.0)
0.0ms	(sqrt PI)

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4975	4274
1	4975	4274

prune749.0ms (7.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	191	3	194

Merged error: 0b

Counts

194 → 3

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 3) 3.0)
0.3b	(* (/ 1.0 (sqrt PI)) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
0.3b	(* (* (/ 1.0 (sqrt PI)) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
1.0b	(sqrt PI)

rewrite112.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

544×	`associate-*r/`
304×	`sqrt-div` `frac-add`
228×	`flip3-+` `flip-+`
216×	`frac-times`
64×	`add-sqr-sqrt`
58×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
27×	`associate-*l/`
23×	`add-exp-log` `associate-l` `sqrt-prod`
20×	`add-cbrt-cube`
12×	`pow1` `unpow-prod-down` `cube-prod` `associate-r` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`unswap-sqr`
5×	`div-exp`
4×	`cube-mult` `unpow3` `pow-prod-down` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `associate-/r*`
2×	`*-commutative` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num`

Counts

4 → 326

Calls

4 calls:

44.0ms	(* (* (/ 1.0 (sqrt PI)) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
24.0ms	(* (/ 1.0 (sqrt PI)) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
5.0ms	(/ (pow (fabs x) 3) 3.0)
1.0ms	(sqrt PI)

series134.0ms (1.4%)

Counts

4 → 10

Calls

4 calls:

69.0ms	(* (/ 1.0 (sqrt PI)) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
58.0ms	(* (* (/ 1.0 (sqrt PI)) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))))) (sqrt (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0))))))
7.0ms	(/ (pow (fabs x) 3) 3.0)
0.0ms	(sqrt PI)

simplify180.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5017	32569

prune6.5s (66.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	336	3	339

Merged error: 0b

Counts

339 → 3

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ (pow (fabs x) 5) 5.0)
0.1b	(/ (pow (fabs x) 3) 3.0)
0.3b	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt PI))
1.0b	(sqrt PI)

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac`
62×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`associate-/l*`
16×	`add-exp-log`
15×	`sqrt-prod`
12×	`cube-prod` `associate-r/` `associate-/r`
10×	`add-cbrt-cube`
8×	`frac-add` `associate-/l/` `sqr-pow`
7×	`div-exp`
6×	`flip3-+` `flip-+`
5×	`pow1`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-to-exp` `pow-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 170

Calls

4 calls:

21.0ms	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt PI))
5.0ms	(/ (pow (fabs x) 3) 3.0)
5.0ms	(/ (pow (fabs x) 5) 5.0)
1.0ms	(sqrt PI)

series64.0ms (0.6%)

Counts

4 → 10

Calls

4 calls:

47.0ms	(/ (+ (* 2.0 (+ (fabs x) (/ (pow (fabs x) 3) 3.0))) (* 1.0 (+ (/ (pow (fabs x) 5) 5.0) (/ (pow (fabs x) 7) 21.0)))) (sqrt PI))
9.0ms	(/ (pow (fabs x) 5) 5.0)
7.0ms	(/ (pow (fabs x) 3) 3.0)
0.0ms	(sqrt PI)

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5607	3447

prune649.0ms (6.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	180	3	183

Merged error: 0b

Counts

183 → 3

regimes74.0ms (0.8%)

Accuracy

Total 0.1b remaining (66.8%)

Threshold costs 0.1b (66.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	33
1	32	33

end0.0ms (0%)

sample904.0ms (9.2%)

Algorithm

1×

intervals

Results

717.0ms	8000×	body	80	valid
83.0ms	8000×	pre	80	true

Details

analyze5.0ms (0%)

sample36.0ms (0.4%)

simplify50.0ms (0.5%)

prune9.0ms (0.1%)

localize21.0ms (0.2%)

rewrite43.0ms (0.4%)

series74.0ms (0.8%)

simplify68.0ms (0.7%)

prune749.0ms (7.6%)

localize24.0ms (0.2%)

rewrite112.0ms (1.1%)

series134.0ms (1.4%)

simplify180.0ms (1.8%)

prune6.5s (66.4%)

localize21.0ms (0.2%)

rewrite38.0ms (0.4%)

series64.0ms (0.6%)

simplify46.0ms (0.5%)

prune649.0ms (6.6%)

regimes74.0ms (0.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample904.0ms (9.2%)

Profiling