Details

analyze216.0ms (4.2%)

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)

sample52.0ms (1%)

Algorithm

1×

intervals

Results

17.0ms	61×	body	1024	valid
9.0ms	140×	body	128	valid
7.0ms	35×	body	512	valid
5.0ms	256×	pre	128	true
3.0ms	20×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify105.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune4.0ms (0.1%)

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

Merged error: 0.2b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize10.0ms (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))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

3 → 59

Calls

3 calls:

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

series170.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

99.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
43.0ms	(*.f64 e (sin.f64 v))
28.0ms	(*.f64 e (cos.f64 v))

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4947	920
1	4947	920

prune71.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	9	69

Merged error: 0.0b

Counts

69 → 9

Compiler

Compiled 1227 to 499 computations (59.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 117

Calls

3 calls:

8.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
6.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
5.0ms	(*.f64 e (cos.f64 v))

series195.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

92.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
69.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
33.0ms	(*.f64 e (cos.f64 v))

simplify89.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4954	3222
1	4954	3222

prune130.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	125	10	135

Merged error: 0.0b

Counts

135 → 10

Compiler

Compiled 2795 to 1162 computations (58.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
0.1b	(*.f64 e (cos.f64 v))
0.3b	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
0.3b	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
12×	`associate-l_binary64`
10×	`associate-r_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`sqrt-prod_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `times-frac_binary64` `div-exp_binary64` `-commutative_binary64`
2×	`associate-/r/_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
8.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series242.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
51.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
36.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
27.0ms	(*.f64 e (cos.f64 v))

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4981	1494
1	4981	1494

prune89.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	98	10	108

Merged error: 0.0b

Counts

108 → 10

Compiler

Compiled 2073 to 765 computations (63.1% saved)

localize14.0ms (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))) (sin.f64 v))
0.3b	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
0.3b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))

rewrite92.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`times-frac_binary64`
196×	`add-sqr-sqrt_binary64`
162×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
93×	`sqrt-prod_binary64`
86×	`associate-r_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-/r*_binary64` `div-inv_binary64`
11×	`unswap-sqr_binary64`
9×	`associate-l_binary64` `associate-/l*_binary64`
8×	`pow1_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`

Counts

4 → 274

Calls

4 calls:

34.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
10.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
6.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series374.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

159.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
119.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
67.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
29.0ms	(*.f64 e (cos.f64 v))

simplify145.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4965	8694
1	4965	8694

prune317.0ms (6.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	285	11	296

Merged error: 0.0b

Counts

296 → 11

Compiler

Compiled 7830 to 2919 computations (62.7% saved)

regimes258.0ms (5%)

Compiler: Compiled 2851 to 1858 computations (34.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample2.3s (44.6%)

Algorithm

1×

intervals

Results

551.0ms	1894×	body	1024	valid
318.0ms	4599×	body	128	valid
204.0ms	1014×	body	512	valid
144.0ms	8000×	pre	128	true
67.0ms	487×	body	256	valid
3.0ms	6×	body	2048	valid

Compiler

Compiled 944 to 618 computations (34.5% saved)

Details

analyze216.0ms (4.2%)

sample52.0ms (1%)

simplify105.0ms (2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite22.0ms (0.4%)

series170.0ms (3.3%)

simplify83.0ms (1.6%)

prune71.0ms (1.4%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series195.0ms (3.8%)

simplify89.0ms (1.7%)

prune130.0ms (2.5%)

localize10.0ms (0.2%)

rewrite38.0ms (0.7%)

series242.0ms (4.7%)

simplify81.0ms (1.6%)

prune89.0ms (1.7%)

localize14.0ms (0.3%)

rewrite92.0ms (1.8%)

series374.0ms (7.3%)

simplify145.0ms (2.8%)

prune317.0ms (6.2%)

regimes258.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (44.6%)

Profiling