Details

analyze42.0ms (0.8%)

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 17 to 12 computations (29.4% saved)

sample81.0ms (1.6%)

Algorithm

1×

intervals

Results

33.0ms	65×	body	1024	valid
12.0ms	129×	body	128	valid
9.0ms	36×	body	512	valid
5.0ms	256×	pre	128	true
4.0ms	25×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	17
2	21	17
3	24	17
4	25	17
5	24	17

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))

Compiler

Compiled 26 to 18 computations (30.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite60.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 66

Calls

4 calls:

5.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
3.0ms	(*.f64 e (cos.f64 v))
3.0ms	(*.f64 e (sin.f64 v))
1.0ms	(sin.f64 v)

Compiler

Compiled 1123 to 406 computations (63.8% saved)

series79.0ms (1.6%)

Error

0.1b

Counts

4 → 30

Calls

4 calls:

34.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
14.0ms	(*.f64 e (sin.f64 v))
11.0ms	(*.f64 e (cos.f64 v))
7.0ms	(sin.f64 v)

Compiler

Compiled 1320 to 891 computations (32.5% saved)

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

403×	`associate-/r*_binary64`
343×	`unswap-sqr_binary64`
331×	`associate-*l/_binary64`
317×	`*-commutative_binary64`
246×	`associate-*r/_binary64`

Counts

96 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	1480
1	419	1314
2	1520	1295
3	4192	1295
4	5008	1295

prune46.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Error

0.0b

Counts

52 → 7

Alt Table

Status	Error	Program
	21.8b	(.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (*.f64 (cos.f64 v) e) 1))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))))
	34.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)) 3))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (.f64 (sin.f64 v) (cbrt.f64 e))) (+.f64 1 (.f64 e (cos.f64 v))))
	0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
▶	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 (cos.f64 v) e) 1)))

Compiler

Compiled 1065 to 531 computations (50.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite124.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

34×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
22×	`add-cbrt-cube_binary64`

Counts

4 → 109

Calls

4 calls:

9.0ms	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 (cos.f64 v) e) 1)))
5.0ms	(/.f64 1 (+.f64 (*.f64 (cos.f64 v) e) 1))
3.0ms	(*.f64 (cos.f64 v) e)
3.0ms	(*.f64 e (sin.f64 v))

Compiler

Compiled 2192 to 1013 computations (53.8% saved)

series95.0ms (1.9%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

34.0ms	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 (cos.f64 v) e) 1)))
16.0ms	(/.f64 1 (+.f64 (*.f64 (cos.f64 v) e) 1))
15.0ms	(*.f64 e (sin.f64 v))
12.0ms	(*.f64 (cos.f64 v) e)

Compiler

Compiled 1544 to 1045 computations (32.3% saved)

simplify102.0ms (2%)

Algorithm

1×	egg-herbie

Rules

918×	`times-frac_binary64`
532×	`associate-/l*_binary64`
322×	`cancel-sign-sub-inv_binary64`
245×	`associate-l_binary64`
204×	`associate-r_binary64`

Counts

143 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2427
1	480	2139
2	1653	2120
3	4637	2120
4	4994	2120

prune67.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	108	7	115

Error

0.0b

Counts

115 → 7

Alt Table

Status	Error	Program
	21.8b	(.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (*.f64 (cos.f64 v) e) 1))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))))
	34.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)) 3))
	0.4b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (.f64 (sin.f64 v) (cbrt.f64 e))) (+.f64 1 (.f64 e (cos.f64 v))))
▶	0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
✓	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 (cos.f64 v) e) 1)))

Compiler

Compiled 1639 to 808 computations (50.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sin.f64 v)
0.1b	(/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v))
0.1b	(*.f64 (cos.f64 v) e)
0.2b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))

rewrite141.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

84×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

4 → 124

Calls

4 calls:

8.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
5.0ms	(/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v))
3.0ms	(*.f64 (cos.f64 v) e)
1.0ms	(sin.f64 v)

Compiler

Compiled 2748 to 1134 computations (58.7% saved)

series95.0ms (1.9%)

Error

0.0b

Counts

4 → 33

Calls

4 calls:

34.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
27.0ms	(/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v))
11.0ms	(*.f64 (cos.f64 v) e)
5.0ms	(sin.f64 v)

Compiler

Compiled 1431 to 953 computations (33.4% saved)

simplify200.0ms (4%)

Algorithm

1×	egg-herbie

Rules

507×	`associate-/r/_binary64`
480×	`associate-/r*_binary64`
422×	`associate-*l/_binary64`
388×	`associate-/l/_binary64`
259×	`cancel-sign-sub-inv_binary64`

Counts

157 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	3932
1	649	3698
2	2110	3667
3	4557	3667
4	4868	3667
5	4976	3667
6	4951	3667

prune104.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	132	8	140

Error

0.0b

Counts

140 → 8

Alt Table

Status	Error	Program
	34.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)) 3))
	30.4b	(/.f64 (/.f64 e (sqrt.f64 (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v)))) (sqrt.f64 (/.f64 (+.f64 (.f64 (cos.f64 v) e) 1) (sin.f64 v))))
	21.8b	(.f64 (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (sqrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (*.f64 (cos.f64 v) e) 1))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))))
▶	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
✓	0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
✓	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 (cos.f64 v) e) 1)))
	1.1b	(.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 e)) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (cbrt.f64 (sin.f64 v)))))

Compiler

Compiled 2778 to 1215 computations (56.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite139.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

66×	`times-frac_binary64`
47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
28×	`sqrt-prod_binary64`

Counts

4 → 135

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
6.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
3.0ms	(*.f64 e (cos.f64 v))

Compiler

Compiled 3107 to 1067 computations (65.7% saved)

series108.0ms (2.1%)

Error

Counts

4 → 33

Calls

4 calls:

37.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
28.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
15.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
12.0ms	(*.f64 e (cos.f64 v))

Compiler

Compiled 1845 to 1217 computations (34% saved)

simplify193.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

685×	`associate-/r/_binary64`
279×	`cancel-sign-sub-inv_binary64`
239×	`associate-r_binary64`
193×	`associate-l_binary64`
154×	`*-commutative_binary64`

Counts

168 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	4705
1	731	4101
2	2686	4070
3	4480	4070
4	4939	4070
5	4933	4070

prune84.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	133	8	141

Error

Counts

141 → 8

Alt Table

Status	Error	Program
	34.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)) 3))
	30.4b	(/.f64 (/.f64 e (sqrt.f64 (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v)))) (sqrt.f64 (/.f64 (+.f64 (.f64 (cos.f64 v) e) 1) (sin.f64 v))))
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
	0.9b	(.f64 (.f64 (sin.f64 v) (fabs.f64 (cbrt.f64 e))) (/.f64 (sqrt.f64 (cbrt.f64 e)) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sqrt.f64 e))))
	0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
	0.1b	(.f64 (.f64 e (sin.f64 v)) (/.f64 1 (+.f64 (*.f64 (cos.f64 v) e) 1)))
	0.5b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 e)) (+.f64 (.f64 e (cos.f64 v)) 1)) (.f64 (.f64 (sin.f64 v) (sqrt.f64 e)) (sqrt.f64 (sqrt.f64 e))))
	1.1b	(.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 e)) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (cbrt.f64 (sin.f64 v)))))

Compiler

Compiled 2264 to 918 computations (59.5% saved)

regimes620.0ms (12.3%)

Accuracy

Total 0.1b remaining (84.1%)

Threshold costs 0.1b (84.1%)

Compiler

Compiled 12779 to 7943 computations (37.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	15	17
2	14	17

end0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample2.5s (49.9%)

Algorithm

1×

intervals

Results

1.1s	2011×	body	1024	valid
415.0ms	4463×	body	128	valid
283.0ms	1018×	body	512	valid
169.0ms	8000×	pre	128	true
96.0ms	503×	body	256	valid
6.0ms	5×	body	2048	valid

Compiler

Compiled 188 to 124 computations (34% saved)

Details

analyze42.0ms (0.8%)

sample81.0ms (1.6%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite60.0ms (1.2%)

series79.0ms (1.6%)

simplify79.0ms (1.6%)

prune46.0ms (0.9%)

localize10.0ms (0.2%)

rewrite124.0ms (2.5%)

series95.0ms (1.9%)

simplify102.0ms (2%)

prune67.0ms (1.3%)

localize8.0ms (0.2%)

rewrite141.0ms (2.8%)

series95.0ms (1.9%)

simplify200.0ms (4%)

prune104.0ms (2.1%)

localize12.0ms (0.2%)

rewrite139.0ms (2.8%)

series108.0ms (2.1%)

simplify193.0ms (3.9%)

prune84.0ms (1.7%)

regimes620.0ms (12.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.5s (49.9%)

Profiling