Details

analyze216.0ms (3.7%)

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)

sample64.0ms (1.1%)

Algorithm

1×

intervals

Results

28.0ms	73×	body	1024	valid
9.0ms	124×	body	128	valid
8.0ms	34×	body	512	valid
6.0ms	256×	pre	128	true
4.0ms	25×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify180.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune5.0ms (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)

localize12.0ms (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))))
0.2b	(*.f64 e (cos.f64 v))
0.2b	(*.f64 e (sin.f64 v))

rewrite23.0ms (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:

7.0ms	(/.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))

series307.0ms (5.2%)

Counts

3 → 9

Calls

3 calls:

173.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
71.0ms	(*.f64 e (sin.f64 v))
63.0ms	(*.f64 e (cos.f64 v))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5009	920

prune75.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	10	69

Merged error: 0.0b

Counts

69 → 10

Compiler

Compiled 1224 to 501 computations (59.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(*.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 (0.5%)

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))
4.0ms	(*.f64 e (cos.f64 v))

series391.0ms (6.7%)

Counts

3 → 9

Calls

3 calls:

182.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
145.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
64.0ms	(*.f64 e (cos.f64 v))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4964	3208
1	4964	3208

prune135.0ms (2.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	123	13	136

Merged error: 0.0b

Counts

136 → 13

Compiler

Compiled 2825 to 1195 computations (57.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite49.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
9.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series567.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
200.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
92.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
54.0ms	(*.f64 e (cos.f64 v))

simplify113.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4940	3913
1	4940	3913

prune159.0ms (2.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	4	6	10
Picked	1	0	1
Done	0	2	2
Total	149	11	160

Merged error: 0b

Counts

160 → 11

Compiler

Compiled 3564 to 1336 computations (62.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.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)))

rewrite96.0ms (1.6%)

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:

36.0ms	(.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))
5.0ms	(*.f64 e (cos.f64 v))

series702.0ms (12%)

Counts

4 → 12

Calls

4 calls:

301.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
219.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
130.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
52.0ms	(*.f64 e (cos.f64 v))

simplify147.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4955	8633
1	4955	8633

prune326.0ms (5.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	285	1	286
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	287	10	297

Merged error: 0b

Counts

297 → 10

Compiler

Compiled 7792 to 2907 computations (62.7% saved)

regimes72.0ms (1.2%)

Compiler: Compiled 533 to 380 computations (28.7% 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%)

sample2.0s (34.1%)

Algorithm

1×

intervals

Results

745.0ms	1982×	body	1024	valid
333.0ms	4473×	body	128	valid
245.0ms	1007×	body	512	valid
159.0ms	8000×	pre	128	true
88.0ms	533×	body	256	valid
4.0ms	5×	body	2048	valid

Compiler

Compiled 195 to 141 computations (27.7% saved)

Details

analyze216.0ms (3.7%)

sample64.0ms (1.1%)

simplify180.0ms (3.1%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite23.0ms (0.4%)

series307.0ms (5.2%)

simplify61.0ms (1%)

prune75.0ms (1.3%)

localize10.0ms (0.2%)

rewrite31.0ms (0.5%)

series391.0ms (6.7%)

simplify86.0ms (1.5%)

prune135.0ms (2.3%)

localize12.0ms (0.2%)

rewrite49.0ms (0.8%)

series567.0ms (9.7%)

simplify113.0ms (1.9%)

prune159.0ms (2.7%)

localize12.0ms (0.2%)

rewrite96.0ms (1.6%)

series702.0ms (12%)

simplify147.0ms (2.5%)

prune326.0ms (5.6%)

regimes72.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (34.1%)

Profiling