Details

analyze219.0ms (6.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	80	valid
1.0ms	12×	body	80	invalid

simplify15.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	5167	21

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: 16.3b

Counts

2 → 1

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
3.9b	(- (* b b) (* a a))
11.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite50.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
30×	`associate-r`
14×	`frac-times` `associate-l`
13×	`prod-exp` `cbrt-unprod`
12×	`difference-of-squares`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `diff-log` `clear-num`

Counts

4 → 150

Calls

4 calls:

22.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))
13.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))

series35.0ms (1%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
6.0ms	(- (* b b) (* a a))

simplify49.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5018	2608

prune297.0ms (8.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	153	9	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	9	163

Merged error: 11.4b

Counts

163 → 9

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
11.6b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite87.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/`

Counts

4 → 286

Calls

4 calls:

32.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
28.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
8.0ms	(/ (/ PI 2.0) (+ b a))
5.0ms	(/ 1.0 (- b a))

series36.0ms (1%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
12.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
7.0ms	(/ (/ PI 2.0) (+ b a))
5.0ms	(/ 1.0 (- b a))

simplify54.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	6239	4466

prune666.0ms (18.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	290	8	298
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	295	12	307

Merged error: 0.0b

Counts

307 → 12

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ (/ PI 2.0) (+ b a)) 1.0)) (- b a))
0.2b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ (/ PI 2.0) (+ b a)) 1.0))

rewrite83.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l`
12×	`associate-l` `distribute-lft-out--`
11×	`div-inv`
10×	`difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`associate-/r/`
3×	`pow-prod-down`
2×	`frac-2neg` `associate-*r/` `clear-num`
1×	`sub-neg` `flip3-+` `diff-log` `associate-r` `*-commutative` `flip-+`

Counts

4 → 185

Calls

4 calls:

30.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ (/ PI 2.0) (+ b a)) 1.0)) (- b a))
25.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ (/ PI 2.0) (+ b a)) 1.0))
12.0ms	(- (/ 1.0 a) (/ 1.0 b))
8.0ms	(/ (/ PI 2.0) (+ b a))

series36.0ms (1%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ (/ PI 2.0) (+ b a)) 1.0))
13.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ (/ PI 2.0) (+ b a)) 1.0)) (- b a))
7.0ms	(/ (/ PI 2.0) (+ b a))
4.0ms	(- (/ 1.0 a) (/ 1.0 b))

simplify55.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4988	3060
1	4988	3060

prune363.0ms (10.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	193	4	197
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	197	12	209

Merged error: 0.0b

Counts

209 → 12

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
0.2b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite86.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

226×	`times-frac`
193×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
79×	`associate-l`
52×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`frac-times` `associate-r/` `associate-/l`
15×	`div-inv`
13×	`associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`flip3--` `associate-/r/` `flip--`
6×	`sub-neg` `frac-sub`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 286

Calls

4 calls:

32.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
25.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
7.0ms	(/ (/ PI 2.0) (+ b a))
5.0ms	(/ 1.0 (- b a))

series32.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
7.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
7.0ms	(/ (/ PI 2.0) (+ b a))
5.0ms	(/ 1.0 (- b a))

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	6239	4864

prune513.0ms (14.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	295	3	298
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	299	11	310

Merged error: 0b

Counts

310 → 11

regimes125.0ms (3.5%)

Accuracy

Total 0.2b remaining (88.7%)

Threshold costs 0.2b (88.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	13
1	14	13

end0.0ms (0%)

sample609.0ms (17.2%)

Algorithm

1×

intervals

Results

452.0ms	8000×	body	80	valid
23.0ms	386×	body	80	invalid

Details

analyze219.0ms (6.2%)

sample22.0ms (0.6%)

simplify15.0ms (0.4%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

rewrite50.0ms (1.4%)

series35.0ms (1%)

simplify49.0ms (1.4%)

prune297.0ms (8.4%)

localize12.0ms (0.3%)

rewrite87.0ms (2.4%)

series36.0ms (1%)

simplify54.0ms (1.5%)

prune666.0ms (18.8%)

localize12.0ms (0.3%)

rewrite83.0ms (2.3%)

series36.0ms (1%)

simplify55.0ms (1.5%)

prune363.0ms (10.2%)

localize13.0ms (0.4%)

rewrite86.0ms (2.4%)

series32.0ms (0.9%)

simplify57.0ms (1.6%)

prune513.0ms (14.5%)

regimes125.0ms (3.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample609.0ms (17.2%)

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