Details

analyze1.0s (8.9%)

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)

sample72.0ms (0.6%)

Algorithm

1×

intervals

Results

32.0ms	106×	body	1024	valid
16.0ms	52×	body	512	valid
5.0ms	71×	body	128	valid
3.0ms	23×	body	256	valid
2.0ms	4×	body	2048	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify92.0ms (0.8%)

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

14.2b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize12.0ms (0.1%)

Local error

Found 6 expressions with local error:

3.0b	(cos.f64 (+.f64 a b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
0.2b	(*.f64 r (sin.f64 b))
0.2b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
3.0b	(cos.f64 (+.f64 a b))

rewrite16.0ms (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

6 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))
0.0ms	(*.f64 r (sin.f64 b))
0.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

series407.0ms (3.5%)

Counts

3 → 33

Calls

3 calls:

292.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
70.0ms	(*.f64 r (sin.f64 b))
44.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 824 to 642 computations (22.1% saved)

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4937	1166
1	4937	1166

prune88.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	8	81

Error

0.2b

Counts

81 → 8

Compiler

Compiled 1207 to 347 computations (71.3% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite30.0ms (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

8 calls:

9.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms	(*.f64 r (sin.f64 b))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series962.0ms (8.3%)

Counts

4 → 43

Calls

4 calls:

612.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
161.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
102.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
87.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1390 to 1021 computations (26.5% saved)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5174	2227

prune163.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	11	119
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	116	11	127

Error

0.1b

Counts

127 → 11

Compiler

Compiled 2756 to 640 computations (76.8% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite41.0ms (0.4%)

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

8 calls:

13.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
8.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
5.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series1.2s (10.4%)

Counts

4 → 44

Calls

4 calls:

610.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
333.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
159.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
102.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

Compiler

Compiled 1530 to 1110 computations (27.5% saved)

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4969	3613
1	4969	3613

prune165.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	143	12	155

Error

0.1b

Counts

155 → 12

Compiler

Compiled 3681 to 859 computations (76.7% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite34.0ms (0.3%)

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

8 calls:

9.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
7.0ms	(-.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))
4.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series1.0s (8.6%)

Counts

4 → 44

Calls

4 calls:

561.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
181.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
163.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
97.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

Compiler

Compiled 1231 to 954 computations (22.5% saved)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4973	3006
1	4973	3006

prune129.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	139	11	150

Error

0.0b

Counts

150 → 11

Compiler

Compiled 2670 to 537 computations (79.9% saved)

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	529	2118
1	529	2118

regimes495.0ms (4.3%)

Compiler: Compiled 5139 to 3507 computations (31.8% saved)

bsearch0.0ms (0%)

regimes410.0ms (3.5%)

Compiler: Compiled 1374 to 1230 computations (10.5% saved)

bsearch0.0ms (0%)

regimes194.0ms (1.7%)

Compiler: Compiled 1246 to 1142 computations (8.3% saved)

bsearch0.0ms (0%)

regimes141.0ms (1.2%)

Compiler: Compiled 774 to 758 computations (2.1% saved)

bsearch0.0ms (0%)

regimes123.0ms (1.1%)

Compiler: Compiled 640 to 634 computations (0.9% saved)

bsearch0.0ms (0%)

regimes58.0ms (0.5%)

Compiler: Compiled 234 to 264 computations (-12.8% saved)

bsearch0.0ms (0%)

regimes54.0ms (0.5%)

Compiler: Compiled 207 to 240 computations (-15.9% saved)

bsearch0.0ms (0%)

regimes104.0ms (0.9%)

Compiler: Compiled 180 to 216 computations (-20% saved)

bsearch58.0ms (0.5%)

Steps

Iters	Range		Point
9	4.7108576861351374e-21	1.2174788082581859e-15	1.2018833323933556e-15
6	-752701015.3286803	-47100768.39577524	-48148899.43532421

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes101.0ms (0.9%)

Compiler: Compiled 153 to 192 computations (-25.5% saved)

bsearch81.0ms (0.7%)

Steps

Iters	Range		Point
9	4.7108576861351374e-21	1.2174788082581859e-15	1.2018833323933556e-15
10	-1.0323682737881521e-06	-9.629081624821127e-17	-1.0168394498600097e-06

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes94.0ms (0.8%)

Compiler: Compiled 132 to 171 computations (-29.5% saved)

bsearch76.0ms (0.7%)

Steps

Iters	Range		Point
9	4.7108576861351374e-21	1.2174788082581859e-15	1.2018833323933556e-15
10	-1.0323682737881521e-06	-9.629081624821127e-17	-1.0168394498600097e-06

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes82.0ms (0.7%)

Compiler: Compiled 90 to 129 computations (-43.3% saved)

bsearch81.0ms (0.7%)

Steps

Iters	Range		Point
10	5.607460290547805e-15	0.01370526432397266	6.432466860921704e-05
10	-2.783093503206085	-4.0863092004357396e-11	-9.457761768289544e-06

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes36.0ms (0.3%)

Compiler: Compiled 69 to 108 computations (-56.5% saved)

bsearch0.0ms (0%)

regimes30.0ms (0.3%)

Compiler: Compiled 51 to 90 computations (-76.5% saved)

bsearch0.0ms (0%)

regimes27.0ms (0.2%)

Compiler: Compiled 33 to 72 computations (-118.2% saved)

bsearch0.0ms (0%)

regimes24.0ms (0.2%)

Accuracy

Total 0.3b remaining (94.9%)

Threshold costs 0.3b (94.9%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch13.0ms (0.1%)

Compiler: Compiled 224 to 161 computations (28.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	112	310
1	112	310

end0.0ms (0%)

sample3.5s (29.9%)

Algorithm

1×

intervals

Results

1.0s	3497×	body	1024	valid
265.0ms	1329×	body	512	valid
173.0ms	2339×	body	128	valid
128.0ms	209×	body	2048	valid
92.0ms	626×	body	256	valid
1.0ms	2×	body	1024	invalid
0.0ms	2×	body	512	invalid

Compiler

Compiled 1466 to 1031 computations (29.7% saved)

Pareto

0.4470739905057487

Details

analyze1.0s (8.9%)

sample72.0ms (0.6%)

simplify92.0ms (0.8%)

prune2.0ms (0%)

localize12.0ms (0.1%)

rewrite16.0ms (0.1%)

series407.0ms (3.5%)

simplify88.0ms (0.8%)

prune88.0ms (0.8%)

localize13.0ms (0.1%)

rewrite30.0ms (0.3%)

series962.0ms (8.3%)

simplify76.0ms (0.6%)

prune163.0ms (1.4%)

localize13.0ms (0.1%)

rewrite41.0ms (0.4%)

series1.2s (10.4%)

simplify82.0ms (0.7%)

prune165.0ms (1.4%)

localize13.0ms (0.1%)

rewrite34.0ms (0.3%)

series1.0s (8.6%)

simplify96.0ms (0.8%)

prune129.0ms (1.1%)

simplify32.0ms (0.3%)

regimes495.0ms (4.3%)

bsearch0.0ms (0%)

regimes410.0ms (3.5%)

bsearch0.0ms (0%)

regimes194.0ms (1.7%)

bsearch0.0ms (0%)

regimes141.0ms (1.2%)

bsearch0.0ms (0%)

regimes123.0ms (1.1%)

bsearch0.0ms (0%)

regimes58.0ms (0.5%)

bsearch0.0ms (0%)

regimes54.0ms (0.5%)

bsearch0.0ms (0%)

regimes104.0ms (0.9%)

bsearch58.0ms (0.5%)

regimes101.0ms (0.9%)

bsearch81.0ms (0.7%)

regimes94.0ms (0.8%)

bsearch76.0ms (0.7%)

regimes82.0ms (0.7%)

bsearch81.0ms (0.7%)

regimes36.0ms (0.3%)

bsearch0.0ms (0%)

regimes30.0ms (0.3%)

bsearch0.0ms (0%)

regimes27.0ms (0.2%)

bsearch0.0ms (0%)

regimes24.0ms (0.2%)

bsearch13.0ms (0.1%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.5s (29.9%)

Profiling