Details

analyze1.0s (14.7%)

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)

sample60.0ms (0.8%)

Algorithm

1×

intervals

Results

30.0ms	108×	body	1024	valid
10.0ms	50×	body	512	valid
5.0ms	70×	body	128	valid
3.0ms	24×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify96.0ms (1.4%)

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

13.9b

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 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
3.9b	(cos.f64 (+.f64 a b))

rewrite21.0ms (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))))
4.0ms	(cos.f64 (+.f64 a b))
4.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))

series181.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

111.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
54.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
16.0ms	(cos.f64 (+.f64 a b))

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5015	1258

prune70.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Error

0.1b

Counts

77 → 7

Compiler

Compiled 1300 to 298 computations (77.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_441`
24×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
23×	`associate-r_binary64_359`
19×	`times-frac_binary64_425`
15×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`pow1_binary64_480`
9×	`associate-l_binary64_360`
8×	`associate-/r/_binary64_365`
5×	`sin-mult_binary64_574` `cos-mult_binary64_573`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `-commutative_binary64_350` `associate-/r_binary64_363` `associate-/l*_binary64_364`
2×	`div-inv_binary64_416` `flip3--_binary64_423` `flip--_binary64_394` `sub-div_binary64_426` `div-exp_binary64_470` `frac-sub_binary64_428` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `associate-*r/_binary64_361` `frac-2neg_binary64_430`

Counts

4 → 105

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

series476.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
148.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
39.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
36.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5750	2593

prune124.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Error

Counts

124 → 12

Compiler

Compiled 3073 to 619 computations (79.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_441`
15×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
12×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
10×	`pow1_binary64_480`
9×	`associate-r_binary64_359` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365`
3×	`pow-prod-down_binary64_490` `times-frac_binary64_425` `unswap-sqr_binary64_387` `sin-mult_binary64_574` `cos-mult_binary64_573` `-commutative_binary64_350` `associate-/r_binary64_363`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip--_binary64_394` `sub-div_binary64_426` `frac-sub_binary64_428` `associate-/l*_binary64_364`

Counts

4 → 81

Calls

4 calls:

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

series390.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

289.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
38.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
34.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
29.0ms	(*.f64 (sin.f64 b) r)

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5198	1471

prune86.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Error

Counts

105 → 11

Compiler

Compiled 2237 to 540 computations (75.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_441`
24×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
23×	`associate-r_binary64_359`
19×	`times-frac_binary64_425`
15×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`pow1_binary64_480`
9×	`associate-l_binary64_360`
8×	`associate-/r/_binary64_365`
5×	`sin-mult_binary64_574` `cos-mult_binary64_573`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `-commutative_binary64_350` `associate-/r_binary64_363` `associate-/l*_binary64_364`
2×	`div-inv_binary64_416` `flip3--_binary64_423` `flip--_binary64_394` `sub-div_binary64_426` `div-exp_binary64_470` `frac-sub_binary64_428` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `associate-*r/_binary64_361` `frac-2neg_binary64_430`

Counts

4 → 105

Calls

4 calls:

13.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
7.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
4.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series570.0ms (8%)

Counts

4 → 12

Calls

4 calls:

286.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
212.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
38.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
33.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5661	2608

prune94.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Error

Counts

128 → 10

Compiler

Compiled 2788 to 458 computations (83.6% saved)

regimes534.0ms (7.5%)

Accuracy

Total 0.3b remaining (92.2%)

Threshold costs 0.3b (92.2%)

Compiler

Compiled 6286 to 3800 computations (39.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample2.9s (40.8%)

Algorithm

1×

intervals

Results

1.0s	3512×	body	1024	valid
269.0ms	1366×	body	512	valid
172.0ms	2341×	body	128	valid
105.0ms	188×	body	2048	valid
81.0ms	593×	body	256	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 1243 to 755 computations (39.3% saved)

Details

analyze1.0s (14.7%)

sample60.0ms (0.8%)

simplify96.0ms (1.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite21.0ms (0.3%)

series181.0ms (2.5%)

simplify71.0ms (1%)

prune70.0ms (1%)

localize13.0ms (0.2%)

rewrite40.0ms (0.6%)

series476.0ms (6.7%)

simplify82.0ms (1.2%)

prune124.0ms (1.7%)

localize13.0ms (0.2%)

rewrite30.0ms (0.4%)

series390.0ms (5.5%)

simplify62.0ms (0.9%)

prune86.0ms (1.2%)

localize13.0ms (0.2%)

rewrite41.0ms (0.6%)

series570.0ms (8%)

simplify86.0ms (1.2%)

prune94.0ms (1.3%)

regimes534.0ms (7.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (40.8%)

Profiling