Details

analyze346.0ms (3.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5007	54
0	2	2
1	2	2

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)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5241	29

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

Error

13.7b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.4b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.8b	(-.f64 (.f64 b b) (.f64 a a))
9.1b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite552.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `distribute-lft-out--_binary64_712`
13×	`associate-/l*_binary64_705`
8×	`add-log-exp_binary64_799`
6×	`pow1_binary64_821` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `flip3--_binary64_764` `flip--_binary64_735`
4×	`sub-neg_binary64_753` `associate-/r/_binary64_706` `associate-/r*_binary64_704`
3×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `frac-sub_binary64_769` `frac-times_binary64_770` `unswap-sqr_binary64_728` `associate-*r/_binary64_702`
2×	`diff-log_binary64_852`
1×	`pow-prod-down_binary64_831` `associate-l/_binary64_703` `-commutative_binary64_691` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

4 → 270

Calls

4 calls:

48.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
14.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 8765 to 4259 computations (51.4% saved)

series479.0ms (5.1%)

Error

9.3b

Counts

4 → 51

Calls

4 calls:

141.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
107.0ms	(-.f64 (.f64 b b) (.f64 a a))
106.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
69.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 2538 to 1979 computations (22% saved)

simplify140.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4978	8828
1	4978	8828

prune453.0ms (4.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	312	9	321
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	314	9	323

Error

0.0b

Counts

323 → 9

Compiler

Compiled 9166 to 4375 computations (52.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite808.0ms (8.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

289×	`times-frac_binary64_766`
240×	`add-sqr-sqrt_binary64_782`
221×	`*-un-lft-identity_binary64_760`
129×	`add-cube-cbrt_binary64_795`
78×	`add-exp-log_binary64_798`
72×	`associate-r_binary64_700`
50×	`add-cbrt-cube_binary64_796`
45×	`difference-of-squares_binary64_729`
41×	`distribute-lft-out--_binary64_712`
37×	`associate-l_binary64_701`
31×	`prod-exp_binary64_809`
26×	`div-exp_binary64_811`
23×	`div-inv_binary64_757`
17×	`cbrt-unprod_binary64_793`
16×	`cbrt-undiv_binary64_794` `frac-times_binary64_770`
13×	`associate-/l*_binary64_705` `cancel-sign-sub-inv_binary64_726`
11×	`pow1_binary64_821`
10×	`associate-l/_binary64_703` `associate-r/_binary64_702`
9×	`flip3--_binary64_764` `flip--_binary64_735`
7×	`frac-sub_binary64_769`
6×	`add-log-exp_binary64_799` `associate-/r/_binary64_706`
5×	`associate-/r*_binary64_704`
4×	`pow-prod-down_binary64_831` `1-exp_binary64_804` `rec-exp_binary64_810`
3×	`unswap-sqr_binary64_728` `distribute-lft-out_binary64_711`
2×	`*-commutative_binary64_691`
1×	`flip3-+_binary64_763` `flip-+_binary64_734` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `diff-log_binary64_852` `sub-neg_binary64_753`

Counts

4 → 324

Calls

4 calls:

53.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
39.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
15.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))

Compiler

Compiled 10692 to 6167 computations (42.3% saved)

series456.0ms (4.8%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

139.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
107.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
84.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
72.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 2544 to 1868 computations (26.6% saved)

simplify106.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5010	9373

prune571.0ms (6.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	368	4	372
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	372	9	381

Error

Counts

381 → 9

Compiler

Compiled 10845 to 5972 computations (44.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 b a))
0.0b	(.f64 1/2 (/.f64 PI.f64 (.f64 a b)))
0.2b	(.f64 (/.f64 1 (+.f64 b a)) (.f64 1/2 (/.f64 PI.f64 (*.f64 a b))))
1.0b	(/.f64 PI.f64 (*.f64 a b))

rewrite181.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

82×	`add-exp-log_binary64_798`
52×	`add-cbrt-cube_binary64_796`
40×	`*-un-lft-identity_binary64_760`
37×	`prod-exp_binary64_809`
30×	`times-frac_binary64_766`
28×	`add-sqr-sqrt_binary64_782`
26×	`add-cube-cbrt_binary64_795`
22×	`div-exp_binary64_811`
21×	`cbrt-unprod_binary64_793` `associate-l_binary64_701`
13×	`cbrt-undiv_binary64_794`
12×	`pow1_binary64_821`
8×	`associate-r_binary64_700`
7×	`distribute-lft-out_binary64_711`
6×	`associate-/l*_binary64_705`
5×	`associate-/r*_binary64_704` `1-exp_binary64_804` `rec-exp_binary64_810`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757` `pow-prod-down_binary64_831` `associate-*r/_binary64_702` `associate-/r/_binary64_706`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759` `flip3-+_binary64_763` `flip-+_binary64_734` `*-commutative_binary64_691`
1×	`frac-times_binary64_770` `associate-*l/_binary64_703` `unswap-sqr_binary64_728` `inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 141

Calls

4 calls:

14.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 1/2 (/.f64 PI.f64 (*.f64 a b))))
7.0ms	(.f64 1/2 (/.f64 PI.f64 (.f64 a b)))
5.0ms	(/.f64 1 (+.f64 b a))
4.0ms	(/.f64 PI.f64 (*.f64 a b))

Compiler

Compiled 2927 to 1274 computations (56.5% saved)

series327.0ms (3.5%)

Error

Counts

4 → 42

Calls

4 calls:

94.0ms	(.f64 (/.f64 1 (+.f64 b a)) (.f64 1/2 (/.f64 PI.f64 (*.f64 a b))))
78.0ms	(.f64 1/2 (/.f64 PI.f64 (.f64 a b)))
61.0ms	(/.f64 PI.f64 (*.f64 a b))
54.0ms	(/.f64 1 (+.f64 b a))

Compiler

Compiled 1758 to 1289 computations (26.7% saved)

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5108	2794

prune164.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	3	4	7
Picked	0	1	1
Done	1	0	1
Total	184	8	192

Error

Counts

192 → 8

Compiler

Compiled 3236 to 1431 computations (55.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite81.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

28×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
22×	`times-frac_binary64_766`
16×	`*-un-lft-identity_binary64_760`
12×	`div-exp_binary64_811` `cbrt-undiv_binary64_794`
11×	`associate-/l*_binary64_705`
8×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
6×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `associate-/r/_binary64_706`
5×	`associate-/r*_binary64_704`
4×	`distribute-lft-out_binary64_711` `div-inv_binary64_757`
3×	`flip3-+_binary64_763` `flip-+_binary64_734`
2×	`pow1_binary64_821` `add-log-exp_binary64_799` `frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`associate-/l/_binary64_707`

Counts

2 → 69

Calls

2 calls:

10.0ms	(/.f64 (/.f64 (.f64 PI.f64 1/2) (+.f64 a b)) (.f64 a b))
6.0ms	(/.f64 (*.f64 PI.f64 1/2) (+.f64 a b))

Compiler

Compiled 1339 to 554 computations (58.6% saved)

series209.0ms (2.2%)

Error

Counts

2 → 30

Calls

2 calls:

97.0ms	(/.f64 (/.f64 (.f64 PI.f64 1/2) (+.f64 a b)) (.f64 a b))
81.0ms	(/.f64 (*.f64 PI.f64 1/2) (+.f64 a b))

Compiler

Compiled 1380 to 1007 computations (27% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4977	1964
1	4977	1964

prune84.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	101	6	107

Error

Counts

107 → 6

Compiler

Compiled 1644 to 684 computations (58.4% saved)

regimes814.0ms (8.6%)

Accuracy

Total 0.2b remaining (99.9%)

Threshold costs 0.2b (99.9%)

Compiler

Compiled 10945 to 8163 computations (25.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms (0%)

sample3.4s (36%)

Algorithm

1×

intervals

Results

442.0ms	8000×	body	128	valid
17.0ms	327×	body	128	invalid

Compiler

Compiled 3666 to 2736 computations (25.4% saved)

Details

analyze346.0ms (3.7%)

sample27.0ms (0.3%)

simplify54.0ms (0.6%)

prune5.0ms (0.1%)

localize12.0ms (0.1%)

rewrite552.0ms (5.9%)

series479.0ms (5.1%)

simplify140.0ms (1.5%)

prune453.0ms (4.8%)

localize13.0ms (0.1%)

rewrite808.0ms (8.6%)

series456.0ms (4.8%)

simplify106.0ms (1.1%)

prune571.0ms (6.1%)

localize9.0ms (0.1%)

rewrite181.0ms (1.9%)

series327.0ms (3.5%)

simplify56.0ms (0.6%)

prune164.0ms (1.7%)

localize7.0ms (0.1%)

rewrite81.0ms (0.9%)

series209.0ms (2.2%)

simplify77.0ms (0.8%)

prune84.0ms (0.9%)

regimes814.0ms (8.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.4s (36%)

Profiling