Details

analyze1.0s (15.2%)

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)

sample67.0ms (1%)

Algorithm

1×

intervals

Results

38.0ms	116×	body	1024	valid
9.0ms	43×	body	512	valid
5.0ms	68×	body	128	valid
3.0ms	25×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify88.0ms (1.3%)

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

Merged error: 12.6b

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 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
2.2b	(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	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))

series187.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

122.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
46.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
18.0ms	(cos.f64 (+.f64 a b))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5015	1258

prune66.0ms (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

Merged error: 0.2b

Counts

77 → 7

Compiler

Compiled 1276 to 295 computations (76.9% 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 (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))

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))

series467.0ms (6.9%)

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)))))
143.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
37.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
34.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5750	2593

prune121.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	9	117
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	113	11	124

Merged error: 0.0b

Counts

124 → 11

Compiler

Compiled 2977 to 595 computations (80% 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 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))

rewrite29.0ms (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)

series376.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

272.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
42.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
33.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
29.0ms	(*.f64 (sin.f64 b) r)

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5198	1471

prune83.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 0.0b

Counts

104 → 9

Compiler

Compiled 2142 to 508 computations (76.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
27.4b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_441`
19×	`associate-r_binary64_359`
16×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
14×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
11×	`pow1_binary64_480`
10×	`times-frac_binary64_425`
8×	`cbrt-prod_binary64_450`
6×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sin-mult_binary64_574` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `cube-div_binary64_448` `associate-/r/_binary64_365` `pow-unpow_binary64_496`
2×	`unpow-prod-down_binary64_498` `cbrt-div_binary64_451` `unpow3_binary64_485` `cube-mult_binary64_449` `rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `sqr-pow_binary64_391` `*-commutative_binary64_350` `cube-prod_binary64_447` `pow-pow_binary64_491`
1×	`pow1/3_binary64_501` `div-inv_binary64_416` `flip3--_binary64_423` `associate-*r/_binary64_361` `rem-cbrt-cube_binary64_443` `cos-mult_binary64_573` `pow-to-exp_binary64_488` `flip--_binary64_394` `div-exp_binary64_470` `frac-sub_binary64_428` `cbrt-undiv_binary64_453`

Counts

4 → 95

Calls

4 calls:

14.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
5.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))

series417.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

256.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))))
83.0ms	(pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)
41.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))
37.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4929	1891
1	4929	1891

prune98.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	106	10	116

Merged error: 0.0b

Counts

116 → 10

Compiler

Compiled 2632 to 801 computations (69.6% saved)

regimes463.0ms (6.9%)

Compiler: Compiled 4916 to 3175 computations (35.4% 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%)

sample2.8s (41.6%)

Algorithm

1×

intervals

Results

1.0s	3472×	body	1024	valid
283.0ms	1413×	body	512	valid
169.0ms	2313×	body	128	valid
121.0ms	203×	body	2048	valid
88.0ms	599×	body	256	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 953 to 619 computations (35% saved)

Details

analyze1.0s (15.2%)

sample67.0ms (1%)

simplify88.0ms (1.3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite22.0ms (0.3%)

series187.0ms (2.8%)

simplify69.0ms (1%)

prune66.0ms (1%)

localize13.0ms (0.2%)

rewrite40.0ms (0.6%)

series467.0ms (6.9%)

simplify79.0ms (1.2%)

prune121.0ms (1.8%)

localize13.0ms (0.2%)

rewrite29.0ms (0.4%)

series376.0ms (5.6%)

simplify58.0ms (0.9%)

prune83.0ms (1.2%)

localize16.0ms (0.2%)

rewrite36.0ms (0.5%)

series417.0ms (6.2%)

simplify90.0ms (1.3%)

prune98.0ms (1.5%)

regimes463.0ms (6.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (41.6%)

Profiling