Details

analyze218.0ms (4.3%)

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)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify145.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5241	29

prune6.0ms (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

Error

13.1b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

6.3b	(-.f64 (.f64 b b) (.f64 a a))
5.7b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
0.4b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.4b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.7b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
6.3b	(-.f64 (.f64 b b) (.f64 a a))

rewrite115.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_766`
178×	`add-sqr-sqrt_binary64_782`
153×	`*-un-lft-identity_binary64_760`
121×	`add-cube-cbrt_binary64_795`
58×	`associate-l_binary64_701`
46×	`difference-of-squares_binary64_729`
40×	`cancel-sign-sub-inv_binary64_726`
22×	`div-inv_binary64_757`
19×	`associate-r_binary64_700`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `distribute-lft-out--_binary64_712`
13×	`associate-/l*_binary64_705`
8×	`add-log-exp_binary64_799`
6×	`cbrt-undiv_binary64_794` `div-exp_binary64_811` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
4×	`associate-/r/_binary64_706` `associate-/r*_binary64_704` `sub-neg_binary64_753`
3×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `frac-times_binary64_770` `frac-sub_binary64_769` `associate-*r/_binary64_702` `cbrt-unprod_binary64_793`
2×	`diff-log_binary64_852`
1×	`frac-2neg_binary64_771` `associate-l/_binary64_703` `associate-/l/_binary64_707` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 270

Calls

8 calls:

49.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
15.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.0ms	(-.f64 (.f64 b b) (.f64 a a))
0.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

series346.0ms (6.9%)

Counts

4 → 45

Calls

4 calls:

99.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
95.0ms	(-.f64 (.f64 b b) (.f64 a a))
86.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
66.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 1368 to 1170 computations (14.5% saved)

simplify130.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5126	8519

prune492.0ms (9.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	307	8	315
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	309	8	317

Error

0.0b

Counts

317 → 8

Compiler

Compiled 8910 to 4243 computations (52.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_766`
79×	`*-un-lft-identity_binary64_760`
60×	`add-exp-log_binary64_798`
51×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
39×	`add-cbrt-cube_binary64_796`
29×	`div-exp_binary64_811`
19×	`prod-exp_binary64_809`
17×	`cbrt-undiv_binary64_794`
14×	`distribute-lft-out_binary64_711` `associate-/l*_binary64_705`
10×	`cbrt-unprod_binary64_793`
7×	`div-inv_binary64_757`
6×	`1-exp_binary64_804`
5×	`associate-/r*_binary64_704`
2×	`frac-2neg_binary64_771` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `add-log-exp_binary64_799` `pow1_binary64_821` `clear-num_binary64_759`
1×	`associate-*l/_binary64_703` `flip3-+_binary64_763` `flip-+_binary64_734`

Counts

2 → 122

Calls

4 calls:

18.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
0.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
0.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series160.0ms (3.2%)

Counts

2 → 24

Calls

2 calls:

88.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
71.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

Compiler

Compiled 780 to 648 computations (16.9% saved)

simplify112.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4956	3080
1	4956	3080

prune156.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	145	9	154

Error

Counts

154 → 9

Compiler

Compiled 2941 to 1440 computations (51% saved)

localize9.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.3b	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
0.2b	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
0.0b	(/.f64 1/2 (+.f64 b a))
0.0b	(/.f64 1/2 (+.f64 b a))
0.2b	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
0.3b	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))

rewrite41.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log_binary64_798`
42×	`add-cbrt-cube_binary64_796`
35×	`*-un-lft-identity_binary64_760`
29×	`prod-exp_binary64_809`
26×	`times-frac_binary64_766` `add-sqr-sqrt_binary64_782`
21×	`add-cube-cbrt_binary64_795`
20×	`div-exp_binary64_811`
18×	`associate-r_binary64_700`
16×	`cbrt-unprod_binary64_793`
12×	`cbrt-undiv_binary64_794`
7×	`distribute-lft-out_binary64_711`
6×	`1-exp_binary64_804`
5×	`associate-/r*_binary64_704` `pow1_binary64_821`
4×	`associate-/r/_binary64_706` `associate-/l*_binary64_705`
3×	`add-log-exp_binary64_799` `div-inv_binary64_757` `associate-l_binary64_701`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-*r/_binary64_702` `clear-num_binary64_759`
1×	`associate-l/_binary64_703` `associate-/l/_binary64_707` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

3 → 106

Calls

6 calls:

13.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
12.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
6.0ms	(/.f64 1/2 (+.f64 b a))
0.0ms	(/.f64 1/2 (+.f64 b a))
0.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))

series215.0ms (4.3%)

Counts

3 → 36

Calls

3 calls:

83.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
74.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
58.0ms	(/.f64 1/2 (+.f64 b a))

Compiler

Compiled 1188 to 996 computations (16.2% saved)

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4962	2232
1	4962	2232

prune122.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	142	9	151

Error

Counts

151 → 9

Compiler

Compiled 2580 to 1289 computations (50% saved)

localize10.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.9b	(/.f64 1 (*.f64 b a))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
0.2b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
0.2b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
0.9b	(/.f64 1 (*.f64 b a))

rewrite56.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

215×	`add-exp-log_binary64_798`
115×	`prod-exp_binary64_809`
103×	`times-frac_binary64_766`
84×	`*-un-lft-identity_binary64_760`
77×	`div-exp_binary64_811`
67×	`add-cbrt-cube_binary64_796`
56×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
37×	`1-exp_binary64_804`
26×	`cbrt-unprod_binary64_793`
22×	`cbrt-undiv_binary64_794`
16×	`associate-/l*_binary64_705` `rec-exp_binary64_810`
14×	`distribute-lft-out_binary64_711`
11×	`pow1_binary64_821`
8×	`div-inv_binary64_757`
7×	`associate-r_binary64_700`
5×	`associate-/r*_binary64_704`
4×	`pow-prod-down_binary64_831`
3×	`associate-*l/_binary64_703` `add-log-exp_binary64_799`
2×	`frac-2neg_binary64_771` `associate-/r/_binary64_706` `clear-num_binary64_759` `pow-flip_binary64_834`
1×	`flip3-+_binary64_763` `associate-/l/_binary64_707` `inv-pow_binary64_845` `flip-+_binary64_734` `frac-times_binary64_770` `associate-l_binary64_701` `associate-r/_binary64_702` `un-div-inv_binary64_758` `-commutative_binary64_691`

Counts

3 → 197

Calls

6 calls:

19.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
12.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
5.0ms	(/.f64 1 (*.f64 b a))
0.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
0.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series219.0ms (4.3%)

Counts

3 → 30

Calls

3 calls:

88.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
73.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
57.0ms	(/.f64 1 (*.f64 b a))

Compiler

Compiled 996 to 840 computations (15.7% saved)

simplify119.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5023	4168

prune214.0ms (4.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	227	9	236

Error

Counts

236 → 9

Compiler

Compiled 4187 to 2148 computations (48.7% saved)

simplify25.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	423	1839
1	423	1839

regimes186.0ms (3.7%)

Compiler: Compiled 2244 to 1656 computations (26.2% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.4%)

Compiler: Compiled 68 to 76 computations (-11.8% saved)

bsearch0.0ms (0%)

regimes54.0ms (1.1%)

Compiler: Compiled 46 to 58 computations (-26.1% saved)

bsearch43.0ms (0.9%)

Steps

Iters	Range		Point
8	8.517374529690697e-31	3.0644311477116758e-28	3.031150181682306e-28
9	-2.22924745420428e-17	-6.849914300618618e-24	-1.092269238366496e-17

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes38.0ms (0.8%)

Compiler: Compiled 28 to 42 computations (-50% saved)

bsearch29.0ms (0.6%)

Steps

Iters	Range		Point
6	1.563425929255999e+44	6.3437690306833865e+44	6.2873135324240956e+44
7	-2.5419418430075572e+76	-3.02482660971481e+74	-2.0274635750868906e+75

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes17.0ms (0.3%)

Accuracy

Total 0.2b remaining (98.3%)

Threshold costs 0.2b (98.3%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 78 to 61 computations (21.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	106
1	47	106

end0.0ms (0%)

sample1.6s (31%)

Algorithm

1×

intervals

Results

436.0ms	8000×	body	128	valid
19.0ms	348×	body	128	invalid

Compiler

Compiled 1212 to 904 computations (25.4% saved)

Pareto

0.27125298917412777

Details

analyze218.0ms (4.3%)

sample24.0ms (0.5%)

simplify145.0ms (2.9%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite115.0ms (2.3%)

series346.0ms (6.9%)

simplify130.0ms (2.6%)

prune492.0ms (9.8%)

localize8.0ms (0.2%)

rewrite39.0ms (0.8%)

series160.0ms (3.2%)

simplify112.0ms (2.2%)

prune156.0ms (3.1%)

localize9.0ms (0.2%)

rewrite41.0ms (0.8%)

series215.0ms (4.3%)

simplify81.0ms (1.6%)

prune122.0ms (2.4%)

localize10.0ms (0.2%)

rewrite56.0ms (1.1%)

series219.0ms (4.3%)

simplify119.0ms (2.4%)

prune214.0ms (4.3%)

simplify25.0ms (0.5%)

regimes186.0ms (3.7%)

bsearch0.0ms (0%)

regimes22.0ms (0.4%)

bsearch0.0ms (0%)

regimes54.0ms (1.1%)

bsearch43.0ms (0.9%)

regimes38.0ms (0.8%)

bsearch29.0ms (0.6%)

regimes17.0ms (0.3%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (31%)

Profiling