Details

analyze1.0s (14.4%)

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)

sample66.0ms (0.9%)

Algorithm

1×

intervals

Results

32.0ms	107×	body	1024	valid
10.0ms	50×	body	512	valid
7.0ms	13×	body	2048	valid
5.0ms	67×	body	128	valid
3.0ms	19×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify100.0ms (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

Merged error: 13.0b

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))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.4b	(cos.f64 (+.f64 a b))

rewrite17.0ms (0.2%)

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

3 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))

series162.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

116.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
30.0ms	(*.f64 r (sin.f64 b))
16.0ms	(cos.f64 (+.f64 a b))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5418	692

prune53.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

Compiler

Compiled 862 to 248 computations (71.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.4%)

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:

9.0ms	(/.f64 (.f64 r (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))
4.0ms	(*.f64 r (sin.f64 b))

series403.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

260.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
76.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
38.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
29.0ms	(*.f64 r (sin.f64 b))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4954	1592
1	4954	1592

prune96.0ms (1.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	83	14	97

Merged error: 0.0b

Counts

97 → 14

Compiler

Compiled 2230 to 492 computations (77.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite45.0ms (0.6%)

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 b) (sin.f64 a)))))
11.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

series527.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
150.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
74.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
36.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	6088	2856

prune116.0ms (1.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	111	15	126

Merged error: 0.0b

Counts

126 → 15

Compiler

Compiled 3166 to 670 computations (78.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_441`
28×	`*-un-lft-identity_binary64_419`
20×	`add-cube-cbrt_binary64_454`
18×	`times-frac_binary64_425`
15×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`associate-/r*_binary64_363` `pow1_binary64_480`
6×	`associate-r_binary64_359` `associate-l_binary64_360`
4×	`difference-of-squares_binary64_388` `add-log-exp_binary64_458` `distribute-lft-out--_binary64_371` `associate-/l*_binary64_364`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `sin-mult_binary64_574` `associate-/r/_binary64_365` `*-commutative_binary64_350` `frac-2neg_binary64_430`
1×	`flip3--_binary64_423` `cos-mult_binary64_573` `flip--_binary64_394` `associate-/l/_binary64_366`

Counts

4 → 97

Calls

4 calls:

9.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
6.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series382.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
82.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
39.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
36.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5165	2126

prune123.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	111	13	124

Merged error: 0.0b

Counts

124 → 13

Compiler

Compiled 4747 to 484 computations (89.8% saved)

regimes557.0ms (7.9%)

Compiler: Compiled 4808 to 2870 computations (40.3% 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%)

sample3.0s (41.8%)

Algorithm

1×

intervals

Results

1.1s	3537×	body	1024	valid
285.0ms	1317×	body	512	valid
164.0ms	2285×	body	128	valid
127.0ms	216×	body	2048	valid
93.0ms	645×	body	256	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 1222 to 733 computations (40% saved)

Details

analyze1.0s (14.4%)

sample66.0ms (0.9%)

simplify100.0ms (1.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite17.0ms (0.2%)

series162.0ms (2.3%)

simplify84.0ms (1.2%)

prune53.0ms (0.8%)

localize13.0ms (0.2%)

rewrite31.0ms (0.4%)

series403.0ms (5.7%)

simplify74.0ms (1%)

prune96.0ms (1.4%)

localize13.0ms (0.2%)

rewrite45.0ms (0.6%)

series527.0ms (7.5%)

simplify84.0ms (1.2%)

prune116.0ms (1.6%)

localize18.0ms (0.3%)

rewrite39.0ms (0.5%)

series382.0ms (5.4%)

simplify74.0ms (1%)

prune123.0ms (1.7%)

regimes557.0ms (7.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.0s (41.8%)

Profiling