Details

analyze1.6s (15.1%)

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)

sample99.0ms (0.9%)

Algorithm

1×

intervals

Results

51.0ms	108×	body	1024	valid
17.0ms	50×	body	512	valid
8.0ms	70×	body	128	valid
6.0ms	24×	body	256	valid
3.0ms	4×	body	2048	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify150.0ms (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)

localize9.0ms (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))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_100`
19×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84` `*-un-lft-identity_binary64_78`
13×	`associate-r_binary64_18`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`pow1_binary64_139`
3×	`associate-l_binary64_19` `add-log-exp_binary64_117` `associate-/l_binary64_23` `associate-/r_binary64_22`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75` `unswap-sqr_binary64_46`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `pow-prod-down_binary64_149` `cos-sum_binary64_212` `associate-r/_binary64_20` `clear-num_binary64_77`

Counts

3 → 67

Calls

3 calls:

14.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
9.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
8.0ms	(cos.f64 (+.f64 a b))

series252.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

132.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
90.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
30.0ms	(cos.f64 (+.f64 a b))

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5015	1258

prune128.0ms (1.2%)

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)

localize27.0ms (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))))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_100`
24×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
23×	`associate-r_binary64_18`
19×	`times-frac_binary64_84`
15×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`pow1_binary64_139`
9×	`associate-l_binary64_19`
8×	`associate-/r/_binary64_24`
5×	`sin-mult_binary64_233` `cos-mult_binary64_232`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
3×	`-commutative_binary64_9` `associate-/l_binary64_23` `associate-/r*_binary64_22` `pow-prod-down_binary64_149`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-sub_binary64_87` `flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `sub-div_binary64_85`
1×	`frac-2neg_binary64_89` `associate-*r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 105

Calls

4 calls:

12.0ms	(.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 (cos.f64 a) (cos.f64 b))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series666.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

350.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
228.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
53.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
34.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify99.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5750	2593

prune154.0ms (1.4%)

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)

localize26.0ms (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))))

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_100`
15×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
10×	`pow1_binary64_139`
9×	`associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-/r/_binary64_24`
3×	`-commutative_binary64_9` `times-frac_binary64_84` `associate-/r_binary64_22` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `sin-mult_binary64_233` `cos-mult_binary64_232`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
1×	`frac-sub_binary64_87` `flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `associate-/l*_binary64_23` `clear-num_binary64_77` `sub-div_binary64_85`

Counts

4 → 81

Calls

4 calls:

17.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
9.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
8.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
8.0ms	(*.f64 (sin.f64 b) r)

series616.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

472.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
62.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
46.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
36.0ms	(*.f64 (sin.f64 b) r)

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5198	1471

prune89.0ms (0.8%)

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 (0.1%)

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)))))

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_100`
24×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
23×	`associate-r_binary64_18`
19×	`times-frac_binary64_84`
15×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`pow1_binary64_139`
9×	`associate-l_binary64_19`
8×	`associate-/r/_binary64_24`
5×	`sin-mult_binary64_233` `cos-mult_binary64_232`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
3×	`-commutative_binary64_9` `associate-/l_binary64_23` `associate-/r*_binary64_22` `pow-prod-down_binary64_149`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-sub_binary64_87` `flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `sub-div_binary64_85`
1×	`frac-2neg_binary64_89` `associate-*r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 105

Calls

4 calls:

12.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
9.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
8.0ms	(/.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))

series1.0s (9.4%)

Counts

4 → 12

Calls

4 calls:

484.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
400.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
71.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
56.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5661	2608

prune113.0ms (1%)

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)

regimes774.0ms (7.2%)

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%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample4.4s (41.1%)

Algorithm

1×

intervals

Results

1.6s	3512×	body	1024	valid
433.0ms	1366×	body	512	valid
258.0ms	2341×	body	128	valid
165.0ms	188×	body	2048	valid
138.0ms	593×	body	256	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 1243 to 755 computations (39.3% saved)

Details

analyze1.6s (15.1%)

sample99.0ms (0.9%)

simplify150.0ms (1.4%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite40.0ms (0.4%)

series252.0ms (2.3%)

simplify97.0ms (0.9%)

prune128.0ms (1.2%)

localize27.0ms (0.2%)

rewrite47.0ms (0.4%)

series666.0ms (6.2%)

simplify99.0ms (0.9%)

prune154.0ms (1.4%)

localize26.0ms (0.2%)

rewrite53.0ms (0.5%)

series616.0ms (5.7%)

simplify105.0ms (1%)

prune89.0ms (0.8%)

localize13.0ms (0.1%)

rewrite53.0ms (0.5%)

series1.0s (9.4%)

simplify106.0ms (1%)

prune113.0ms (1%)

regimes774.0ms (7.2%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample4.4s (41.1%)

Profiling