Details

analyze1.3s (11.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	56
1	66	56
0	3	3
1	3	3

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

Symmetry

Compiler

Compiled 10 to 9 computations (10% saved)

sample66.0ms (0.6%)

Algorithm

1×

intervals

Results

30.0ms	109×	body	1024	valid
9.0ms	46×	body	512	valid
5.0ms	9×	body	2048	valid
5.0ms	74×	body	128	valid
3.0ms	18×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify7.0ms (0.1%)

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

15.1b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.3b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
3.7b	(cos.f64 (+.f64 a b))

rewrite77.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`add-sqr-sqrt_binary64_441`
7×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
5×	`pow1_binary64_480`
3×	`add-log-exp_binary64_458` `times-frac_binary64_425` `associate-/r_binary64_363` `associate-l_binary64_360` `associate-r*_binary64_359`
2×	`prod-exp_binary64_468` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `cbrt-unprod_binary64_452`
1×	`cos-sum_binary64_553` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l_binary64_364` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `-commutative_binary64_350`

Counts

3 → 47

Calls

3 calls:

14.0ms	(cos.f64 (+.f64 a b))
10.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
8.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 725 to 158 computations (78.2% saved)

series428.0ms (3.8%)

Error

13.5b

Counts

3 → 34

Calls

3 calls:

282.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
67.0ms	(*.f64 r (sin.f64 b))
43.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1416 to 851 computations (39.9% saved)

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5028	1388

prune88.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	70	11	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	11	82

Error

0.2b

Counts

82 → 11

Compiler

Compiled 1433 to 465 computations (67.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite112.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 76

Calls

4 calls:

9.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
5.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
4.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1946 to 307 computations (84.2% saved)

series929.0ms (8.2%)

Error

0.1b

Counts

4 → 47

Calls

4 calls:

567.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
142.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
112.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
70.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 2502 to 1389 computations (44.5% saved)

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4975	2535
1	4975	2535

prune127.0ms (1.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	114	9	123
Fresh	8	2	10
Picked	0	1	1
Done	0	0	0
Total	122	12	134

Error

0.0b

Counts

134 → 12

Compiler

Compiled 2936 to 731 computations (75.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite116.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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

Counts

4 → 94

Calls

4 calls:

11.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
8.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))
5.0ms	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))
4.0ms	(*.f64 (cos.f64 b) (cos.f64 a))

Compiler

Compiled 2167 to 410 computations (81.1% saved)

series1.0s (8.8%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

520.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
171.0ms	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))
162.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))
103.0ms	(*.f64 (cos.f64 b) (cos.f64 a))

Compiler

Compiled 2381 to 1409 computations (40.8% saved)

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4954	3459
1	4954	3459

prune135.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	4	6	10
Picked	1	0	1
Done	0	1	1
Total	146	11	157

Error

0.0b

Counts

157 → 11

Compiler

Compiled 3230 to 829 computations (74.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite201.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

120×	`times-frac_binary64_425`
112×	`add-sqr-sqrt_binary64_441`
77×	`*-un-lft-identity_binary64_419`
67×	`add-cube-cbrt_binary64_454`
23×	`associate-/r*_binary64_363`
15×	`difference-of-squares_binary64_388`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`associate-/l*_binary64_364`
7×	`div-inv_binary64_416`
6×	`add-log-exp_binary64_458`
5×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `distribute-lft-out--_binary64_371`
4×	`pow1_binary64_480`
3×	`frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/r/_binary64_365` `cancel-sign-sub-inv_binary64_385`
2×	`flip3--_binary64_423` `flip--_binary64_394`
1×	`diff-log_binary64_511` `sub-neg_binary64_412`

Counts

4 → 160

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a))
19.0ms	(/.f64 r (-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a)))
7.0ms	(/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a)))
4.0ms	(/.f64 (sin.f64 b) (cos.f64 a))

Compiler

Compiled 4003 to 778 computations (80.6% saved)

series1.0s (8.9%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

505.0ms	(/.f64 r (-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a)))
173.0ms	(-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a))
171.0ms	(/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a)))
124.0ms	(/.f64 (sin.f64 b) (cos.f64 a))

Compiler

Compiled 2397 to 1418 computations (40.8% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5224	5683

prune156.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	211	11	222

Error

0.0b

Counts

222 → 11

Compiler

Compiled 4763 to 981 computations (79.4% saved)

regimes939.0ms (8.3%)

Accuracy

Total 0.3b remaining (95.8%)

Threshold costs 0.3b (95.8%)

Compiler

Compiled 11010 to 6678 computations (39.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	26
1	44	26

Removed

()

end0.0ms (0%)

sample4.3s (38.2%)

Algorithm

1×

intervals

Results

1.0s	3517×	body	1024	valid
291.0ms	1381×	body	512	valid
168.0ms	2349×	body	128	valid
129.0ms	205×	body	2048	valid
78.0ms	548×	body	256	valid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 2745 to 1671 computations (39.1% saved)

Details

analyze1.3s (11.1%)

sample66.0ms (0.6%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite77.0ms (0.7%)

series428.0ms (3.8%)

simplify55.0ms (0.5%)

prune88.0ms (0.8%)

localize13.0ms (0.1%)

rewrite112.0ms (1%)

series929.0ms (8.2%)

simplify72.0ms (0.6%)

prune127.0ms (1.1%)

localize12.0ms (0.1%)

rewrite116.0ms (1%)

series1.0s (8.8%)

simplify95.0ms (0.8%)

prune135.0ms (1.2%)

localize12.0ms (0.1%)

rewrite201.0ms (1.8%)

series1.0s (8.9%)

simplify83.0ms (0.7%)

prune156.0ms (1.4%)

regimes939.0ms (8.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.3s (38.2%)

Profiling