Details

analyze223.0ms (3.8%)

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

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample26.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify209.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5209	29

prune7.0ms (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: 13.3b

Counts

2 → 2

Compiler

Compiled 99 to 79 computations (20.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.5b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.4b	(-.f64 (.f64 b b) (.f64 a a))
8.1b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite119.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_773`
178×	`add-sqr-sqrt_binary64_789`
153×	`*-un-lft-identity_binary64_767`
121×	`add-cube-cbrt_binary64_802`
58×	`associate-l_binary64_708`
46×	`difference-of-squares_binary64_736`
40×	`cancel-sign-sub-inv_binary64_733`
22×	`div-inv_binary64_764`
19×	`associate-r_binary64_707`
18×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
14×	`distribute-rgt-in_binary64_717` `distribute-lft-out--_binary64_719` `distribute-lft-in_binary64_716`
13×	`associate-/l*_binary64_712`
8×	`add-log-exp_binary64_806`
6×	`cbrt-undiv_binary64_801` `pow1_binary64_828` `flip--_binary64_742` `div-exp_binary64_818` `flip3--_binary64_771`
4×	`associate-/r*_binary64_711` `associate-/r/_binary64_713` `sub-neg_binary64_760`
3×	`frac-times_binary64_777` `unswap-sqr_binary64_735` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `frac-sub_binary64_776` `associate-*r/_binary64_709`
2×	`diff-log_binary64_859`
1×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `-commutative_binary64_698` `associate-l/_binary64_710` `pow-prod-down_binary64_838` `clear-num_binary64_766`

Counts

4 → 270

Calls

4 calls:

49.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
20.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
10.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series230.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
64.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
48.0ms	(-.f64 (.f64 b b) (.f64 a a))
21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify144.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4947	7997
1	4947	7997

prune722.0ms (12.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	274	8	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	276	8	284

Merged error: 0.0b

Counts

284 → 8

Compiler

Compiled 15008 to 8812 computations (41.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_773`
79×	`*-un-lft-identity_binary64_767`
60×	`add-exp-log_binary64_805`
51×	`add-sqr-sqrt_binary64_789` `add-cube-cbrt_binary64_802`
39×	`add-cbrt-cube_binary64_803`
29×	`div-exp_binary64_818`
19×	`prod-exp_binary64_816`
17×	`cbrt-undiv_binary64_801`
14×	`distribute-lft-out_binary64_718` `associate-/l*_binary64_712`
10×	`cbrt-unprod_binary64_800`
7×	`div-inv_binary64_764`
6×	`1-exp_binary64_811`
5×	`associate-/r*_binary64_711`
2×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `associate-/r/_binary64_713` `pow1_binary64_828` `add-log-exp_binary64_806` `clear-num_binary64_766`
1×	`flip-+_binary64_741` `associate-*l/_binary64_710` `flip3-+_binary64_770`

Counts

2 → 122

Calls

2 calls:

16.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series143.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

78.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
65.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5176	2615

prune233.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	128	8	136

Merged error: 0b

Counts

136 → 8

Compiler

Compiled 4517 to 2871 computations (36.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
0.3b	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
0.3b	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

rewrite127.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

621×	`times-frac_binary64_773`
410×	`*-un-lft-identity_binary64_767`
278×	`add-sqr-sqrt_binary64_789` `add-cube-cbrt_binary64_802`
202×	`add-exp-log_binary64_805`
120×	`div-exp_binary64_818`
71×	`associate-/r*_binary64_711`
66×	`distribute-lft-out_binary64_718`
62×	`add-cbrt-cube_binary64_803`
61×	`prod-exp_binary64_816`
35×	`1-exp_binary64_811`
31×	`cbrt-undiv_binary64_801`
28×	`div-inv_binary64_764`
15×	`rec-exp_binary64_817`
13×	`cbrt-unprod_binary64_800`
8×	`associate-/l*_binary64_712`
6×	`associate-/r/_binary64_713`
4×	`pow1_binary64_828`
3×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `add-log-exp_binary64_806` `clear-num_binary64_766`
1×	`pow-flip_binary64_841` `flip-+_binary64_741` `associate-*l/_binary64_710` `flip3-+_binary64_770` `inv-pow_binary64_852`

Counts

3 → 408

Calls

3 calls:

33.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
19.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
9.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series204.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
68.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
58.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify164.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4953	10043
1	4953	10043

prune554.0ms (9.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	415	2	417
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	417	8	425

Merged error: 0b

Counts

425 → 8

Compiler

Compiled 9977 to 5266 computations (47.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) (*.f64 b a))
0.3b	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
0.3b	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

rewrite203.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

1666×	`times-frac_binary64_773`
934×	`*-un-lft-identity_binary64_767`
646×	`add-sqr-sqrt_binary64_789` `add-cube-cbrt_binary64_802`
183×	`associate-/l*_binary64_712`
144×	`distribute-lft-out_binary64_718`
103×	`add-exp-log_binary64_805`
71×	`associate-/r*_binary64_711`
68×	`div-exp_binary64_818`
60×	`div-inv_binary64_764`
49×	`add-cbrt-cube_binary64_803`
29×	`cbrt-undiv_binary64_801`
14×	`associate-/r/_binary64_713`
10×	`prod-exp_binary64_816`
9×	`1-exp_binary64_811` `rec-exp_binary64_817`
4×	`cbrt-unprod_binary64_800` `pow1_binary64_828`
3×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `add-log-exp_binary64_806` `clear-num_binary64_766`
1×	`pow-flip_binary64_841` `flip-+_binary64_741` `flip3-+_binary64_770` `inv-pow_binary64_852`

Counts

3 → 734

Calls

3 calls:

50.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) (*.f64 b a))
18.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
9.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series221.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

87.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) (*.f64 b a))
68.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
65.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

simplify236.0ms (4%)

Algorithm

1×	egg-herbie

Counts

743 → 743

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4998	20285
1	4998	20285

prune1.1s (19.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	742	1	743
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	744	7	751

Merged error: 0b

Counts

751 → 7

Compiler

Compiled 18661 to 9758 computations (47.7% saved)

regimes31.0ms (0.5%)

Compiler: Compiled 214 to 182 computations (15% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	20
1	15	20

end0.0ms (0%)

sample765.0ms (13.1%)

Algorithm

1×

intervals

Results

460.0ms	8000×	body	128	valid
20.0ms	348×	body	128	invalid

Compiler

Compiled 140 to 118 computations (15.7% saved)

Details

analyze223.0ms (3.8%)

sample26.0ms (0.4%)

simplify209.0ms (3.6%)

prune7.0ms (0.1%)

localize16.0ms (0.3%)

rewrite119.0ms (2%)

series230.0ms (3.9%)

simplify144.0ms (2.5%)

prune722.0ms (12.3%)

localize9.0ms (0.1%)

rewrite42.0ms (0.7%)

series143.0ms (2.4%)

simplify66.0ms (1.1%)

prune233.0ms (4%)

localize10.0ms (0.2%)

rewrite127.0ms (2.2%)

series204.0ms (3.5%)

simplify164.0ms (2.8%)

prune554.0ms (9.5%)

localize9.0ms (0.2%)

rewrite203.0ms (3.5%)

series221.0ms (3.8%)

simplify236.0ms (4%)

prune1.1s (19.5%)

regimes31.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample765.0ms (13.1%)

Profiling