Details

analyze33.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample79.0ms (1.3%)

Algorithm

1×

intervals

Results

25.0ms	52×	body	1024	valid
16.0ms	150×	body	128	valid
14.0ms	43×	body	512	valid
7.0ms	256×	pre	128	true
3.0ms	11×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify121.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.2b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (sin.f64 v))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
12×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `associate-r_binary64_18`
3×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`
1×	`flip-+_binary64_52` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `flip3-+_binary64_81`

Counts

3 → 59

Calls

3 calls:

6.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
4.0ms	(*.f64 e (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series217.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

136.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
43.0ms	(*.f64 e (sin.f64 v))
37.0ms	(*.f64 e (cos.f64 v))

simplify131.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4947	920
1	4947	920

prune112.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Error

0.0b

Counts

69 → 9

Compiler

Compiled 1222 to 505 computations (58.7% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (pow.f64 (cos.f64 v) 2))
0.1b	(*.f64 e (sin.f64 v))
0.2b	(pow.f64 (cos.f64 v) 2)

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_100`
14×	`associate-r_binary64_18` `add-exp-log_binary64_116`
13×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
10×	`add-cbrt-cube_binary64_114`
9×	`associate-l_binary64_19` `pow1_binary64_139`
7×	`unpow-prod-down_binary64_157`
6×	`unswap-sqr_binary64_46`
5×	`prod-exp_binary64_127`
4×	`add-log-exp_binary64_117`
3×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-unpow_binary64_155`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `pow-prod-down_binary64_149`
1×	`pow-pow_binary64_150`

Counts

4 → 81

Calls

4 calls:

12.0ms	(*.f64 e (pow.f64 (cos.f64 v) 2))
9.0ms	(*.f64 e (sin.f64 v))
8.0ms	(*.f64 e (cos.f64 v))
5.0ms	(pow.f64 (cos.f64 v) 2)

series128.0ms (2%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 e (pow.f64 (cos.f64 v) 2))
34.0ms	(*.f64 e (sin.f64 v))
29.0ms	(*.f64 e (cos.f64 v))
25.0ms	(pow.f64 (cos.f64 v) 2)

simplify116.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4937	793
1	4937	793

prune159.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	93	9	102

Error

0.0b

Counts

102 → 9

Compiler

Compiled 2471 to 1167 computations (52.8% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
0.2b	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_84`
57×	`add-sqr-sqrt_binary64_100`
55×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
16×	`associate-/r*_binary64_22`
12×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`div-inv_binary64_75` `associate-/l*_binary64_23`
5×	`pow1_binary64_139`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`associate-l_binary64_19` `add-log-exp_binary64_117` `associate-r_binary64_18`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `associate-/r/_binary64_24` `flip3-+_binary64_81`

Counts

3 → 117

Calls

3 calls:

13.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
11.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
8.0ms	(*.f64 e (cos.f64 v))

series281.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

123.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
106.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
52.0ms	(*.f64 e (cos.f64 v))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4954	3222
1	4954	3222

prune156.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	126	9	135

Error

Counts

135 → 9

Compiler

Compiled 2760 to 1142 computations (58.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.2b	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
0.2b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
0.3b	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite82.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_84`
47×	`add-sqr-sqrt_binary64_100`
41×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
28×	`sqrt-prod_binary64_94`
22×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
9×	`div-inv_binary64_75` `associate-r_binary64_18` `associate-/l*_binary64_23`
8×	`associate-/r*_binary64_22` `pow1_binary64_139`
7×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
6×	`associate-l_binary64_19`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127`
3×	`unswap-sqr_binary64_46`
2×	`*-commutative_binary64_9` `frac-2neg_binary64_89` `pow-prod-down_binary64_149` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`flip-+_binary64_52` `associate-/r/_binary64_24` `flip3-+_binary64_81`

Counts

4 → 135

Calls

4 calls:

21.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
16.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
11.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
8.0ms	(*.f64 e (cos.f64 v))

series368.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
106.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
61.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
30.0ms	(*.f64 e (cos.f64 v))

simplify170.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4954	3907
1	4954	3907

prune216.0ms (3.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	147	9	156

Error

Counts

156 → 9

Compiler

Compiled 3400 to 1224 computations (64% saved)

regimes307.0ms (4.9%)

Accuracy

Total 0.1b remaining (94.2%)

Threshold costs 0.1b (94.2%)

Compiler

Compiled 2146 to 1430 computations (33.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample3.3s (52.8%)

Algorithm

1×

intervals

Results

886.0ms	2016×	body	1024	valid
483.0ms	4520×	body	128	valid
308.0ms	981×	body	512	valid
217.0ms	8000×	pre	128	true
97.0ms	480×	body	256	valid
2.0ms	3×	body	2048	valid

Compiler

Compiled 717 to 478 computations (33.3% saved)

Details

analyze33.0ms (0.5%)

sample79.0ms (1.3%)

simplify121.0ms (1.9%)

prune3.0ms (0%)

localize13.0ms (0.2%)

rewrite18.0ms (0.3%)

series217.0ms (3.5%)

simplify131.0ms (2.1%)

prune112.0ms (1.8%)

localize26.0ms (0.4%)

rewrite48.0ms (0.8%)

series128.0ms (2%)

simplify116.0ms (1.9%)

prune159.0ms (2.5%)

localize17.0ms (0.3%)

rewrite42.0ms (0.7%)

series281.0ms (4.5%)

simplify91.0ms (1.5%)

prune156.0ms (2.5%)

localize22.0ms (0.3%)

rewrite82.0ms (1.3%)

series368.0ms (5.9%)

simplify170.0ms (2.7%)

prune216.0ms (3.4%)

regimes307.0ms (4.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.3s (52.8%)

Profiling