Details

analyze218.0ms (4.7%)

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)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify144.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

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

12.2b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.7b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.7b	(-.f64 (.f64 b b) (.f64 a a))
7.6b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite115.0ms (2.5%)

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

4 calls:

51.0ms	(.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)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series114.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
34.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
22.0ms	(-.f64 (.f64 b b) (.f64 a a))
11.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify120.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5154	7997

prune391.0ms (8.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	272	10	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	274	10	284

Error

0.0b

Counts

284 → 10

Compiler

Compiled 8387 to 4016 computations (52.1% saved)

localize8.0ms (0.2%)

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))

rewrite38.0ms (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

2 calls:

14.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series81.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

51.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
30.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5189	2615

prune127.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	131	7	138

Error

Counts

138 → 7

Compiler

Compiled 2554 to 1263 computations (50.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (-.f64 b a))
0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
0.3b	(/.f64 PI.f64 (+.f64 b a))
0.5b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

rewrite91.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`*-un-lft-identity_binary64_760`
86×	`add-sqr-sqrt_binary64_782`
73×	`times-frac_binary64_766`
43×	`add-cube-cbrt_binary64_795`
37×	`associate-l_binary64_701`
34×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
22×	`associate-r_binary64_700`
16×	`difference-of-squares_binary64_729` `frac-times_binary64_770`
14×	`distribute-lft-out--_binary64_712`
12×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`pow1_binary64_821`
10×	`associate-l/_binary64_703` `associate-r/_binary64_702`
9×	`associate-/r*_binary64_704`
8×	`cbrt-undiv_binary64_794` `associate-/r/_binary64_706` `div-inv_binary64_757` `div-exp_binary64_811` `flip--_binary64_735` `flip3--_binary64_764`
7×	`distribute-lft-out_binary64_711`
6×	`associate-/l*_binary64_705` `frac-sub_binary64_769`
4×	`add-log-exp_binary64_799` `pow-prod-down_binary64_831`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `flip3-+_binary64_763` `flip-+_binary64_734` `clear-num_binary64_759` `*-commutative_binary64_691`

Counts

4 → 188

Calls

4 calls:

32.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
30.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
6.0ms	(/.f64 1/2 (-.f64 b a))
5.0ms	(/.f64 PI.f64 (+.f64 b a))

series135.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
27.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
27.0ms	(/.f64 PI.f64 (+.f64 b a))
26.0ms	(/.f64 1/2 (-.f64 b a))

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5027	4131

prune222.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	200	7	207

Error

Counts

207 → 7

Compiler

Compiled 5150 to 2614 computations (49.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (-.f64 b a))
0.2b	(/.f64 (.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))) PI.f64) (+.f64 b a))
0.3b	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))) PI.f64)
0.5b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

rewrite109.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_782`
63×	`*-un-lft-identity_binary64_760`
53×	`times-frac_binary64_766`
34×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
29×	`add-cube-cbrt_binary64_795`
24×	`associate-r_binary64_700`
23×	`associate-*l/_binary64_703`
20×	`associate-l_binary64_701`
16×	`difference-of-squares_binary64_729`
14×	`distribute-lft-out--_binary64_712`
12×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`pow1_binary64_821`
9×	`associate-/r*_binary64_704` `frac-times_binary64_770`
8×	`cbrt-undiv_binary64_794` `div-exp_binary64_811` `flip--_binary64_735` `flip3--_binary64_764`
7×	`associate-/l/_binary64_707` `div-inv_binary64_757`
6×	`associate-/r/_binary64_706` `frac-sub_binary64_769`
4×	`add-log-exp_binary64_799` `associate-/l*_binary64_705` `pow-prod-down_binary64_831`
3×	`associate-*r/_binary64_702`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `distribute-lft-out_binary64_711` `clear-num_binary64_759` `*-commutative_binary64_691`
1×	`flip3-+_binary64_763` `flip-+_binary64_734`

Counts

4 → 162

Calls

4 calls:

31.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
28.0ms	(/.f64 (.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))) PI.f64) (+.f64 b a))
27.0ms	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))) PI.f64)
5.0ms	(/.f64 1/2 (-.f64 b a))

series142.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(/.f64 (.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))) PI.f64) (+.f64 b a))
35.0ms	(.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))) PI.f64)
28.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
24.0ms	(/.f64 1/2 (-.f64 b a))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5681	3628

prune185.0ms (4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	174	7	181

Error

Counts

181 → 7

Compiler

Compiled 4366 to 2406 computations (44.9% saved)

regimes355.0ms (7.7%)

Accuracy

Total 0.2b remaining (98.6%)

Threshold costs 0.2b (98.6%)

Compiler

Compiled 4700 to 3384 computations (28% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	17
1	16	17

end0.0ms (0%)

sample1.8s (38.3%)

Algorithm

1×

intervals

Results

444.0ms	8000×	body	128	valid
18.0ms	341×	body	128	invalid

Compiler

Compiled 1563 to 1125 computations (28% saved)

Details

analyze218.0ms (4.7%)

sample22.0ms (0.5%)

simplify144.0ms (3.1%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite115.0ms (2.5%)

series114.0ms (2.5%)

simplify120.0ms (2.6%)

prune391.0ms (8.5%)

localize8.0ms (0.2%)

rewrite38.0ms (0.8%)

series81.0ms (1.7%)

simplify65.0ms (1.4%)

prune127.0ms (2.7%)

localize11.0ms (0.2%)

rewrite91.0ms (2%)

series135.0ms (2.9%)

simplify69.0ms (1.5%)

prune222.0ms (4.8%)

localize12.0ms (0.3%)

rewrite109.0ms (2.4%)

series142.0ms (3.1%)

simplify63.0ms (1.4%)

prune185.0ms (4%)

regimes355.0ms (7.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (38.3%)

Profiling