Details

analyze1.6s (5.7%)

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
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 (0.3%)

Algorithm

1×

intervals

Results

45.0ms	106×	body	1024	valid
12.0ms	40×	body	512	valid
8.0ms	88×	body	128	valid
7.0ms	9×	body	2048	valid
3.0ms	13×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify167.0ms (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)

localize16.0ms (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)))
2.8b	(cos.f64 (+.f64 a b))

rewrite48.0ms (0.2%)

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:

17.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
10.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
10.0ms	(cos.f64 (+.f64 a b))

series343.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

205.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
101.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
36.0ms	(cos.f64 (+.f64 a b))

simplify117.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5015	1258

prune405.0ms (1.5%)

Pruning

49 alts after pruning (48 fresh and 1 done)

	Pruned	Kept	Total
New	28	48	76
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	49	77

Merged error: 0.3b

Counts

77 → 49

Compiler

Compiled 2037 to 746 computations (63.4% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(-.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 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 a) (sin.f64 b))

rewrite41.0ms (0.1%)

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))

series722.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

380.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
167.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
100.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
75.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify97.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5825	2752

prune1.1s (3.9%)

Pruning

104 alts after pruning (102 fresh and 2 done)

	Pruned	Kept	Total
New	50	62	112
Fresh	7	40	47
Picked	0	1	1
Done	0	1	1
Total	57	104	161

Merged error: 0.1b

Counts

161 → 104

Compiler

Compiled 5268 to 1771 computations (66.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.1%)

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:

11.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.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))
5.0ms	(*.f64 (sin.f64 b) r)

series666.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

463.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
87.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
73.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
43.0ms	(*.f64 (sin.f64 b) r)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5161	1643

prune1.0s (3.8%)

Pruning

137 alts after pruning (134 fresh and 3 done)

	Pruned	Kept	Total
New	45	43	88
Fresh	10	91	101
Picked	0	1	1
Done	0	2	2
Total	55	137	192

Merged error: 0.1b

Counts

192 → 137

Compiler

Compiled 5365 to 2238 computations (58.3% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite61.0ms (0.2%)

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:

15.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
11.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
10.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

series1.1s (3.9%)

Counts

4 → 12

Calls

4 calls:

508.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
388.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
120.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
51.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify153.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5438	2802

prune1.1s (4.1%)

Pruning

183 alts after pruning (179 fresh and 4 done)

	Pruned	Kept	Total
New	57	55	112
Fresh	9	124	133
Picked	0	1	1
Done	0	3	3
Total	66	183	249

Merged error: 0.1b

Counts

249 → 183

Compiler

Compiled 2743 to 426 computations (84.5% saved)

regimes4.4s (16%)

Compiler: Compiled 34582 to 20219 computations (41.5% saved)

bsearch4.1s (14.7%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	26
1	61	26

end0.0ms (0%)

sample10.2s (36.7%)

Algorithm

1×

intervals

Results

1.4s	3599×	body	1024	valid
335.0ms	1266×	body	512	valid
212.0ms	2322×	body	128	valid
161.0ms	207×	body	2048	valid
116.0ms	606×	body	256	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 6873 to 4014 computations (41.6% saved)

Pareto

Details

analyze1.6s (5.7%)

sample88.0ms (0.3%)

simplify167.0ms (0.6%)

prune5.0ms (0%)

localize16.0ms (0.1%)

rewrite48.0ms (0.2%)

series343.0ms (1.2%)

simplify117.0ms (0.4%)

prune405.0ms (1.5%)

localize13.0ms (0%)

rewrite41.0ms (0.1%)

series722.0ms (2.6%)

simplify97.0ms (0.4%)

prune1.1s (3.9%)

localize15.0ms (0.1%)

rewrite35.0ms (0.1%)

series666.0ms (2.4%)

simplify71.0ms (0.3%)

prune1.0s (3.8%)

localize23.0ms (0.1%)

rewrite61.0ms (0.2%)

series1.1s (3.9%)

simplify153.0ms (0.6%)

prune1.1s (4.1%)

regimes4.4s (16%)

bsearch4.1s (14.7%)

simplify5.0ms (0%)

end0.0ms (0%)

sample10.2s (36.7%)

Profiling