Details

analyze1.1s (16%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	56
1	66	56
0	3	3
1	3	3

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

34.0ms	112×	body	1024	valid
8.0ms	41×	body	512	valid
5.0ms	74×	body	128	valid
5.0ms	9×	body	2048	valid
3.0ms	20×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune3.0ms (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)

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)))
1.2b	(cos.f64 (+.f64 a b))

rewrite21.0ms (0.3%)

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:

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

series159.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

112.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
30.0ms	(*.f64 r (sin.f64 b))
17.0ms	(cos.f64 (+.f64 a b))

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5418	692

prune51.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Error

0.2b

Counts

57 → 8

Compiler

Compiled 844 to 236 computations (72% 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 a) (sin.f64 b)))
0.1b	(*.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))))

rewrite29.0ms (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))))
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))

series420.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

269.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
81.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
38.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
31.0ms	(*.f64 r (sin.f64 b))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4954	1592
1	4954	1592

prune94.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Error

0.1b

Counts

96 → 10

Compiler

Compiled 2118 to 433 computations (79.6% 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))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

rewrite39.0ms (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:

12.0ms	(.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))

series539.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

271.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
153.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
76.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
39.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	6088	2856

prune108.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	110	12	122

Error

0.0b

Counts

122 → 12

Compiler

Compiled 3078 to 620 computations (79.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 1 (-.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 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_457`
27×	`add-sqr-sqrt_binary64_441`
23×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359`
22×	`add-cbrt-cube_binary64_455`
18×	`times-frac_binary64_425`
14×	`prod-exp_binary64_468` `pow1_binary64_480`
8×	`cbrt-unprod_binary64_452` `associate-/r/_binary64_365`
7×	`associate-l_binary64_360`
6×	`div-exp_binary64_470`
5×	`pow-prod-down_binary64_490` `sin-mult_binary64_574`
4×	`add-log-exp_binary64_458` `cos-mult_binary64_573`
3×	`1-exp_binary64_463` `rec-exp_binary64_469` `-commutative_binary64_350` `associate-/r_binary64_363` `associate-/l*_binary64_364` `cbrt-undiv_binary64_453`
2×	`div-inv_binary64_416` `unswap-sqr_binary64_387` `flip3--_binary64_423` `flip--_binary64_394` `sub-div_binary64_426` `frac-sub_binary64_428`
1×	`clear-num_binary64_418` `inv-pow_binary64_504` `associate-*r/_binary64_361` `frac-2neg_binary64_430` `pow-flip_binary64_493` `un-div-inv_binary64_417`

Counts

4 → 114

Calls

4 calls:

13.0ms	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))
8.0ms	(/.f64 1 (-.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 r (sin.f64 b))

series459.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

264.0ms	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))
122.0ms	(/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
42.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
30.0ms	(*.f64 r (sin.f64 b))

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4970	2623
1	4970	2623

prune103.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	127	11	138

Error

0.0b

Counts

138 → 11

Compiler

Compiled 3026 to 616 computations (79.6% saved)

regimes387.0ms (5.4%)

Accuracy

Total 0.3b remaining (92.9%)

Threshold costs 0.3b (92.9%)

Compiler

Compiled 4656 to 2662 computations (42.8% 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%)

sample3.1s (43%)

Algorithm

1×

intervals

Results

1.2s	3543×	body	1024	valid
312.0ms	1397×	body	512	valid
163.0ms	2316×	body	128	valid
118.0ms	195×	body	2048	valid
82.0ms	549×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 1184 to 681 computations (42.5% saved)

Details

analyze1.1s (16%)

sample66.0ms (0.9%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite21.0ms (0.3%)

series159.0ms (2.2%)

simplify88.0ms (1.2%)

prune51.0ms (0.7%)

localize13.0ms (0.2%)

rewrite29.0ms (0.4%)

series420.0ms (5.9%)

simplify73.0ms (1%)

prune94.0ms (1.3%)

localize13.0ms (0.2%)

rewrite39.0ms (0.6%)

series539.0ms (7.6%)

simplify83.0ms (1.2%)

prune108.0ms (1.5%)

localize14.0ms (0.2%)

rewrite43.0ms (0.6%)

series459.0ms (6.5%)

simplify95.0ms (1.3%)

prune103.0ms (1.4%)

regimes387.0ms (5.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (43%)

Profiling