Details

analyze1.0s (12.9%)

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)

sample70.0ms (0.9%)

Algorithm

1×

intervals

Results

39.0ms	118×	body	1024	valid
11.0ms	51×	body	512	valid
5.0ms	65×	body	128	valid
3.0ms	6×	body	2048	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune2.0ms (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

Error

15.4b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
3.3b	(cos.f64 (+.f64 a b))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_441`
19×	`*-un-lft-identity_binary64_419` `times-frac_binary64_425` `add-cube-cbrt_binary64_454`
13×	`associate-r_binary64_359`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`pow1_binary64_480`
3×	`add-log-exp_binary64_458` `associate-l_binary64_360` `associate-/r_binary64_363` `associate-/l_binary64_364`
2×	`div-inv_binary64_416` `unswap-sqr_binary64_387` `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` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430`

Counts

3 → 67

Calls

3 calls:

8.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
5.0ms	(cos.f64 (+.f64 a b))
5.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))

series182.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

110.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
51.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
20.0ms	(cos.f64 (+.f64 a b))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5015	1258

prune73.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Error

0.2b

Counts

77 → 11

Compiler

Compiled 1344 to 338 computations (74.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_441`
22×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
20×	`associate-r_binary64_359`
19×	`times-frac_binary64_425`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`associate-/r/_binary64_365` `pow1_binary64_480`
7×	`sin-mult_binary64_574`
6×	`add-log-exp_binary64_458` `cos-mult_binary64_573` `associate-l_binary64_360`
3×	`unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip3--_binary64_423` `flip--_binary64_394` `associate-/r_binary64_363` `sub-div_binary64_426` `frac-sub_binary64_428` `associate-/l_binary64_364`
2×	`pow-prod-down_binary64_490` `div-inv_binary64_416` `*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `associate-*r/_binary64_361` `frac-2neg_binary64_430` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 100

Calls

4 calls:

13.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series539.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

267.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
145.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
83.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
44.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5825	2752

prune130.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Error

0.0b

Counts

123 → 13

Compiler

Compiled 3056 to 601 computations (80.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_441`
29×	`*-un-lft-identity_binary64_419`
19×	`add-cube-cbrt_binary64_454`
18×	`times-frac_binary64_425`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`associate-/r*_binary64_363`
6×	`add-log-exp_binary64_458` `pow1_binary64_480`
5×	`difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371`
4×	`associate-/l*_binary64_364`
3×	`associate-r_binary64_359` `associate-l_binary64_360` `cancel-sign-sub-inv_binary64_385` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip3--_binary64_423` `associate-/r/_binary64_365` `cos-mult_binary64_573` `frac-2neg_binary64_430` `flip--_binary64_394`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `*-commutative_binary64_350` `diff-log_binary64_511` `associate-/l/_binary64_366`

Counts

4 → 94

Calls

4 calls:

9.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
8.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
5.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series439.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
95.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
74.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
36.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5009	2353

prune102.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Error

0.0b

Counts

119 → 11

Compiler

Compiled 2492 to 544 computations (78.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 a))
0.2b	(/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))
0.2b	(/.f64 r (-.f64 (/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 a)))
0.2b	(/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b))))

rewrite66.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`times-frac_binary64_425`
72×	`add-sqr-sqrt_binary64_441`
57×	`*-un-lft-identity_binary64_419`
37×	`add-cube-cbrt_binary64_454`
32×	`add-exp-log_binary64_457`
20×	`add-cbrt-cube_binary64_455`
17×	`associate-/r*_binary64_363`
15×	`difference-of-squares_binary64_388` `div-exp_binary64_470`
12×	`div-inv_binary64_416`
10×	`distribute-lft-out--_binary64_371`
9×	`associate-/l*_binary64_364`
8×	`associate-/r/_binary64_365` `cbrt-undiv_binary64_453`
6×	`add-log-exp_binary64_458`
5×	`cos-mult_binary64_573` `pow1_binary64_480`
4×	`prod-exp_binary64_468`
3×	`clear-num_binary64_418` `1-exp_binary64_463` `rec-exp_binary64_469` `frac-2neg_binary64_430` `cancel-sign-sub-inv_binary64_385`
2×	`cbrt-unprod_binary64_452` `flip3--_binary64_423` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `inv-pow_binary64_504` `pow-flip_binary64_493` `diff-log_binary64_511`

Counts

4 → 150

Calls

4 calls:

20.0ms	(/.f64 r (-.f64 (/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 a)))
18.0ms	(-.f64 (/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 a))
8.0ms	(/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b))))
6.0ms	(/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))

series487.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(/.f64 r (-.f64 (/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 a)))
97.0ms	(-.f64 (/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))) (sin.f64 a))
80.0ms	(/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b)))
69.0ms	(/.f64 1 (/.f64 (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b))))

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4928	3976
1	4928	3976

prune126.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	163	10	173

Error

0.0b

Counts

173 → 10

Compiler

Compiled 3527 to 799 computations (77.3% saved)

regimes699.0ms (8.8%)

Accuracy

Total 0.3b remaining (95.3%)

Threshold costs 0.3b (95.3%)

Compiler

Compiled 8186 to 4979 computations (39.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample3.4s (43.2%)

Algorithm

1×

intervals

Results

1.0s	3515×	body	1024	valid
284.0ms	1405×	body	512	valid
160.0ms	2250×	body	128	valid
126.0ms	209×	body	2048	valid
89.0ms	621×	body	256	valid
0.0ms	2×	body	256	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 1627 to 991 computations (39.1% saved)

Details

analyze1.0s (12.9%)

sample70.0ms (0.9%)

simplify97.0ms (1.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite22.0ms (0.3%)

series182.0ms (2.3%)

simplify73.0ms (0.9%)

prune73.0ms (0.9%)

localize13.0ms (0.2%)

rewrite42.0ms (0.5%)

series539.0ms (6.8%)

simplify82.0ms (1%)

prune130.0ms (1.6%)

localize12.0ms (0.2%)

rewrite34.0ms (0.4%)

series439.0ms (5.5%)

simplify66.0ms (0.8%)

prune102.0ms (1.3%)

localize13.0ms (0.2%)

rewrite66.0ms (0.8%)

series487.0ms (6.1%)

simplify95.0ms (1.2%)

prune126.0ms (1.6%)

regimes699.0ms (8.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.4s (43.2%)

Profiling