Details

analyze218.0ms (2.3%)

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)

sample28.0ms (0.3%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify140.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

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

14.8b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

9.5b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
4.8b	(-.f64 (.f64 b b) (.f64 a a))
0.1b	(/.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))
0.1b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.8b	(-.f64 (.f64 b b) (.f64 a a))
9.5b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite118.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_743`
178×	`add-sqr-sqrt_binary64_759`
153×	`*-un-lft-identity_binary64_737`
121×	`add-cube-cbrt_binary64_772`
58×	`associate-l_binary64_678`
46×	`difference-of-squares_binary64_706`
40×	`cancel-sign-sub-inv_binary64_703`
22×	`div-inv_binary64_734`
19×	`associate-r_binary64_677`
18×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775`
14×	`distribute-lft-in_binary64_686` `distribute-lft-out--_binary64_689` `distribute-rgt-in_binary64_687`
13×	`associate-/l*_binary64_682`
8×	`add-log-exp_binary64_776`
6×	`pow1_binary64_798` `flip3--_binary64_741` `cbrt-undiv_binary64_771` `div-exp_binary64_788` `flip--_binary64_712`
4×	`associate-/r/_binary64_683` `associate-/r*_binary64_681` `sub-neg_binary64_730`
3×	`unswap-sqr_binary64_705` `frac-times_binary64_747` `cbrt-unprod_binary64_770` `prod-exp_binary64_786` `frac-sub_binary64_746` `associate-*r/_binary64_679`
2×	`diff-log_binary64_829`
1×	`frac-2neg_binary64_748` `clear-num_binary64_736` `associate-l/_binary64_680` `associate-/l/_binary64_684` `pow-prod-down_binary64_808` `-commutative_binary64_668`

Counts

4 → 270

Calls

8 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))
0.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

series467.0ms (5%)

Counts

4 → 63

Calls

4 calls:

158.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
148.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
96.0ms	(-.f64 (.f64 b b) (.f64 a a))
65.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 1842 to 1554 computations (15.6% saved)

simplify135.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4966	9384
1	4966	9384

prune532.0ms (5.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	320	13	333
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	322	13	335

Error

0.0b

Counts

335 → 13

Compiler

Compiled 9660 to 4646 computations (51.9% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite108.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-sqr-sqrt_binary64_759`
94×	`*-un-lft-identity_binary64_737`
85×	`times-frac_binary64_743`
42×	`add-cube-cbrt_binary64_772`
37×	`associate-l_binary64_678`
32×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775`
22×	`associate-r_binary64_677`
21×	`difference-of-squares_binary64_706`
17×	`distribute-lft-out--_binary64_689`
16×	`frac-times_binary64_747`
13×	`cancel-sign-sub-inv_binary64_703`
12×	`cbrt-unprod_binary64_770` `prod-exp_binary64_786` `div-inv_binary64_734`
11×	`pow1_binary64_798`
10×	`associate-l/_binary64_680` `associate-r/_binary64_679`
8×	`flip3--_binary64_741` `flip--_binary64_712`
7×	`cbrt-undiv_binary64_771` `div-exp_binary64_788` `distribute-lft-out_binary64_688` `frac-sub_binary64_746`
6×	`associate-/r/_binary64_683` `add-log-exp_binary64_776`
4×	`associate-/r*_binary64_681` `pow-prod-down_binary64_808`
3×	`associate-/l*_binary64_682`
2×	`unswap-sqr_binary64_705` `flip3-+_binary64_740` `flip-+_binary64_711` `*-commutative_binary64_668`
1×	`diff-log_binary64_829` `frac-2neg_binary64_748` `clear-num_binary64_736` `sub-neg_binary64_730`

Counts

4 → 192

Calls

8 calls:

33.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
30.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
15.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
5.0ms	(/.f64 PI.f64 (+.f64 b a))
0.0ms	(/.f64 1/2 (-.f64 b a))

series405.0ms (4.3%)

Counts

4 → 60

Calls

4 calls:

147.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
103.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
92.0ms	(/.f64 PI.f64 (+.f64 b a))
63.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 1734 to 1374 computations (20.8% saved)

simplify98.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5073	5295

prune338.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	247	5	252
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	258	7	265

Error

Counts

265 → 7

Compiler

Compiled 6311 to 3161 computations (49.9% saved)

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.6b	(/.f64 1/2 (*.f64 a b))
0.2b	(/.f64 PI.f64 (+.f64 b a))
0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (.f64 a b)))
0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (.f64 a b)))
0.2b	(/.f64 PI.f64 (+.f64 b a))
0.6b	(/.f64 1/2 (*.f64 a b))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_737`
31×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775` `times-frac_binary64_743`
29×	`add-sqr-sqrt_binary64_759`
24×	`add-cube-cbrt_binary64_772`
18×	`associate-l_binary64_678`
10×	`cbrt-undiv_binary64_771` `div-exp_binary64_788`
9×	`cbrt-unprod_binary64_770` `prod-exp_binary64_786`
7×	`associate-r_binary64_677` `distribute-lft-out_binary64_688`
6×	`associate-/l*_binary64_682`
5×	`associate-/r*_binary64_681` `pow1_binary64_798`
4×	`associate-/r/_binary64_683` `div-inv_binary64_734`
3×	`add-log-exp_binary64_776`
2×	`unswap-sqr_binary64_705` `flip3-+_binary64_740` `frac-2neg_binary64_748` `clear-num_binary64_736` `flip-+_binary64_711`
1×	`frac-times_binary64_747` `associate-l/_binary64_680` `pow-prod-down_binary64_808` `-commutative_binary64_668` `associate-*r/_binary64_679`

Counts

3 → 105

Calls

6 calls:

14.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (.f64 a b)))
5.0ms	(/.f64 PI.f64 (+.f64 b a))
4.0ms	(/.f64 1/2 (*.f64 a b))
0.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (.f64 a b)))
0.0ms	(/.f64 PI.f64 (+.f64 b a))

series269.0ms (2.9%)

Counts

3 → 48

Calls

3 calls:

124.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (.f64 a b)))
84.0ms	(/.f64 PI.f64 (+.f64 b a))
60.0ms	(/.f64 1/2 (*.f64 a b))

Compiler

Compiled 1224 to 978 computations (20.1% saved)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4966	2711
1	4966	2711

prune125.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	153	7	160

Error

Counts

160 → 7

Compiler

Compiled 2692 to 1031 computations (61.7% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (.f64 1/2 (/.f64 PI.f64 (+.f64 a b))))
0.2b	(/.f64 PI.f64 (+.f64 a b))
0.1b	(/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))) (-.f64 b a))
0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.1b	(/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))) (-.f64 b a))
0.2b	(/.f64 PI.f64 (+.f64 a b))
0.3b	(.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (.f64 1/2 (/.f64 PI.f64 (+.f64 a b))))

rewrite93.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64_759`
71×	`*-un-lft-identity_binary64_737`
62×	`times-frac_binary64_743`
29×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775`
27×	`add-cube-cbrt_binary64_772`
20×	`difference-of-squares_binary64_706`
19×	`associate-l_binary64_678`
16×	`distribute-lft-out--_binary64_689`
13×	`cancel-sign-sub-inv_binary64_703`
11×	`div-inv_binary64_734`
10×	`cbrt-unprod_binary64_770` `prod-exp_binary64_786` `associate-*r/_binary64_679`
9×	`associate-/r*_binary64_681` `pow1_binary64_798`
7×	`cbrt-undiv_binary64_771` `div-exp_binary64_788` `associate-/l/_binary64_684`
6×	`add-log-exp_binary64_776` `frac-times_binary64_747` `associate-*l/_binary64_680` `flip3--_binary64_741` `flip--_binary64_712`
5×	`frac-sub_binary64_746`
4×	`associate-/r/_binary64_683` `associate-/l*_binary64_682` `distribute-lft-out_binary64_688`
3×	`pow-prod-down_binary64_808`
2×	`frac-2neg_binary64_748` `clear-num_binary64_736`
1×	`diff-log_binary64_829` `flip3-+_binary64_740` `sub-neg_binary64_730` `flip-+_binary64_711` `associate-r_binary64_677` `*-commutative_binary64_668`

Counts

4 → 155

Calls

8 calls:

28.0ms	(/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))) (-.f64 b a))
28.0ms	(.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (.f64 1/2 (/.f64 PI.f64 (+.f64 a b))))
16.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
5.0ms	(/.f64 PI.f64 (+.f64 a b))
0.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

series399.0ms (4.3%)

Counts

4 → 72

Calls

4 calls:

146.0ms	(/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))) (-.f64 b a))
100.0ms	(.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (.f64 1/2 (/.f64 PI.f64 (+.f64 a b))))
88.0ms	(/.f64 PI.f64 (+.f64 a b))
65.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 2025 to 1581 computations (21.9% saved)

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5318	4818

prune231.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	227	7	234

Error

Counts

234 → 7

Compiler

Compiled 5440 to 2632 computations (51.6% saved)

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	516	2314
1	516	2314

regimes247.0ms (2.6%)

Accuracy

Total 0.2b remaining (99.7%)

Threshold costs 0.2b (99.7%)

Compiler

Compiled 2954 to 2230 computations (24.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	13	17

end0.0ms (0%)

sample5.1s (54.6%)

Algorithm

1×

intervals

Results

450.0ms	8000×	body	128	valid
20.0ms	374×	body	128	invalid

Compiler

Compiled 4447 to 3353 computations (24.6% saved)

Pareto

0.22515680408682068

Details

analyze218.0ms (2.3%)

sample28.0ms (0.3%)

simplify140.0ms (1.5%)

prune6.0ms (0.1%)

localize12.0ms (0.1%)

rewrite118.0ms (1.3%)

series467.0ms (5%)

simplify135.0ms (1.4%)

prune532.0ms (5.7%)

localize13.0ms (0.1%)

rewrite108.0ms (1.2%)

series405.0ms (4.3%)

simplify98.0ms (1.1%)

prune338.0ms (3.6%)

localize7.0ms (0.1%)

rewrite32.0ms (0.3%)

series269.0ms (2.9%)

simplify83.0ms (0.9%)

prune125.0ms (1.3%)

localize12.0ms (0.1%)

rewrite93.0ms (1%)

series399.0ms (4.3%)

simplify80.0ms (0.9%)

prune231.0ms (2.5%)

simplify32.0ms (0.3%)

regimes247.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.1s (54.6%)

Profiling