Details

analyze1.5s (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
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample88.0ms (0.5%)

Algorithm

1×

intervals

Results

47.0ms	106×	body	1024	valid
11.0ms	40×	body	512	valid
8.0ms	88×	body	128	valid
8.0ms	9×	body	2048	valid
2.0ms	13×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify120.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.9b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.8b	(cos.f64 (+.f64 a b))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`add-sqr-sqrt_binary64_441`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
5×	`pow1_binary64_480`
3×	`times-frac_binary64_425` `add-log-exp_binary64_458` `associate-r_binary64_359` `associate-l_binary64_360` `associate-/r*_binary64_363`
2×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `cos-sum_binary64_553` `div-inv_binary64_416` `unswap-sqr_binary64_387` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l_binary64_364`

Counts

3 → 47

Calls

3 calls:

5.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms	(*.f64 r (sin.f64 b))
4.0ms	(cos.f64 (+.f64 a b))

series200.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

152.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
31.0ms	(*.f64 r (sin.f64 b))
16.0ms	(cos.f64 (+.f64 a b))

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5418	692

prune182.0ms (1%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	26	30	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	31	57

Merged error: 0.3b

Counts

57 → 31

Compiler

Compiled 1176 to 463 computations (60.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_441`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`pow1_binary64_480`
6×	`add-log-exp_binary64_458` `associate-r_binary64_359` `associate-l_binary64_360`
5×	`sin-mult_binary64_574`
4×	`associate-/r/_binary64_365` `cos-mult_binary64_573`
3×	`times-frac_binary64_425` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r*_binary64_363`
2×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `flip3--_binary64_423` `*-commutative_binary64_350` `flip--_binary64_394` `sub-div_binary64_426` `div-exp_binary64_470` `frac-sub_binary64_428` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `div-inv_binary64_416` `frac-2neg_binary64_430` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385` `associate-/l*_binary64_364`

Counts

4 → 76

Calls

4 calls:

18.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
10.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
8.0ms	(*.f64 r (sin.f64 b))

series515.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

345.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
88.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
41.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
40.0ms	(*.f64 r (sin.f64 b))

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4954	1592
1	4954	1592

prune812.0ms (4.3%)

Pruning

74 alts after pruning (72 fresh and 2 done)

	Pruned	Kept	Total
New	43	45	88
Fresh	2	27	29
Picked	0	1	1
Done	0	1	1
Total	45	74	119

Merged error: 0.1b

Counts

119 → 74

Compiler

Compiled 3402 to 1223 computations (64.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_441`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`add-log-exp_binary64_458` `pow1_binary64_480`
6×	`associate-r_binary64_359` `associate-l_binary64_360`
3×	`times-frac_binary64_425` `sin-mult_binary64_574` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `frac-add_binary64_427` `unswap-sqr_binary64_387` `sum-log_binary64_510` `cos-mult_binary64_573` `*-commutative_binary64_350` `flip-+_binary64_393` `distribute-neg-frac_binary64_383` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `unsub-neg_binary64_413` `div-inv_binary64_416` `frac-2neg_binary64_430` `associate-+r-_binary64_353` `neg-log_binary64_512` `+-commutative_binary64_349` `associate-/l*_binary64_364` `neg-sub0_binary64_414`

Counts

4 → 76

Calls

4 calls:

10.0ms	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
7.0ms	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
4.0ms	(*.f64 r (sin.f64 b))

series572.0ms (3%)

Counts

4 → 12

Calls

4 calls:

360.0ms	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (*.f64 (sin.f64 b) (sin.f64 a)))))
122.0ms	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a))))
50.0ms	(*.f64 r (sin.f64 b))
41.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5913	1681

prune827.0ms (4.4%)

Pruning

104 alts after pruning (101 fresh and 3 done)

	Pruned	Kept	Total
New	54	34	88
Fresh	4	67	71
Picked	0	1	1
Done	0	2	2
Total	58	104	162

Merged error: 0.1b

Counts

162 → 104

Compiler

Compiled 4369 to 1725 computations (60.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 1 (*.f64 (sin.f64 b) (sin.f64 a)))))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.3b	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 1 (.f64 (sin.f64 b) (sin.f64 a))))))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_441`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`add-log-exp_binary64_458` `pow1_binary64_480`
6×	`associate-r_binary64_359` `associate-l_binary64_360`
3×	`times-frac_binary64_425` `sin-mult_binary64_574` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `frac-add_binary64_427` `unswap-sqr_binary64_387` `sum-log_binary64_510` `associate-r/_binary64_361` `cos-mult_binary64_573` `-commutative_binary64_350` `flip-+_binary64_393` `distribute-neg-frac_binary64_383` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `unsub-neg_binary64_413` `div-inv_binary64_416` `frac-2neg_binary64_430` `associate-+r-_binary64_353` `neg-log_binary64_512` `+-commutative_binary64_349` `associate-/l*_binary64_364` `neg-sub0_binary64_414`

Counts

4 → 76

Calls

4 calls:

10.0ms	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 1 (.f64 (sin.f64 b) (sin.f64 a))))))
7.0ms	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 1 (*.f64 (sin.f64 b) (sin.f64 a)))))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
4.0ms	(*.f64 r (sin.f64 b))

series464.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

275.0ms	(/.f64 (.f64 r (sin.f64 b)) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 1 (.f64 (sin.f64 b) (sin.f64 a))))))
103.0ms	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (neg.f64 (.f64 1 (*.f64 (sin.f64 b) (sin.f64 a)))))
47.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
39.0ms	(*.f64 r (sin.f64 b))

simplify102.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5565	1681

prune838.0ms (4.5%)

Pruning

125 alts after pruning (121 fresh and 4 done)

	Pruned	Kept	Total
New	65	23	88
Fresh	2	98	100
Picked	0	1	1
Done	0	3	3
Total	67	125	192

Merged error: 0.1b

Counts

192 → 125

Compiler

Compiled 2102 to 501 computations (76.2% saved)

regimes2.1s (11.3%)

Compiler: Compiled 17057 to 11178 computations (34.5% saved)

bsearch2.1s (11.2%)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample7.9s (41.8%)

Algorithm

1×

intervals

Results

1.5s	3599×	body	1024	valid
345.0ms	1266×	body	512	valid
212.0ms	2322×	body	128	valid
181.0ms	207×	body	2048	valid
118.0ms	606×	body	256	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 4410 to 2897 computations (34.3% saved)

Pareto

0.4036618115199209

Details

analyze1.5s (8%)

sample88.0ms (0.5%)

simplify120.0ms (0.6%)

prune5.0ms (0%)

localize14.0ms (0.1%)

rewrite17.0ms (0.1%)

series200.0ms (1.1%)

simplify89.0ms (0.5%)

prune182.0ms (1%)

localize26.0ms (0.1%)

rewrite58.0ms (0.3%)

series515.0ms (2.7%)

simplify94.0ms (0.5%)

prune812.0ms (4.3%)

localize14.0ms (0.1%)

rewrite31.0ms (0.2%)

series572.0ms (3%)

simplify81.0ms (0.4%)

prune827.0ms (4.4%)

localize16.0ms (0.1%)

rewrite34.0ms (0.2%)

series464.0ms (2.5%)

simplify102.0ms (0.5%)

prune838.0ms (4.5%)

regimes2.1s (11.3%)

bsearch2.1s (11.2%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample7.9s (41.8%)

Profiling