Details

analyze210.0ms (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)

sample61.0ms (1.2%)

Algorithm

1×

intervals

Results

25.0ms	65×	body	1024	valid
10.0ms	144×	body	128	valid
8.0ms	33×	body	512	valid
5.0ms	256×	pre	128	true
2.0ms	14×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify178.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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)

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))))
0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (sin.f64 v))

rewrite24.0ms (0.5%)

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

series315.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

173.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
72.0ms	(*.f64 e (cos.f64 v))
70.0ms	(*.f64 e (sin.f64 v))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5009	920

prune70.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	6	69

Merged error: 0.0b

Counts

69 → 6

Compiler

Compiled 1170 to 464 computations (60.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

10.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))
6.0ms	(/.f64 (sin.f64 v) (+.f64 1 (*.f64 e (cos.f64 v))))
5.0ms	(*.f64 e (cos.f64 v))

series360.0ms (7.2%)

Counts

3 → 9

Calls

3 calls:

177.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))
121.0ms	(/.f64 (sin.f64 v) (+.f64 1 (*.f64 e (cos.f64 v))))
62.0ms	(*.f64 e (cos.f64 v))

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4951	1715
1	4951	1715

prune86.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	90	6	96

Merged error: 0.0b

Counts

96 → 6

Compiler

Compiled 1774 to 769 computations (56.7% saved)

localize12.0ms (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))
0.2b	(*.f64 (sin.f64 v) (sqrt.f64 e))
0.3b	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))

rewrite38.0ms (0.8%)

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:

11.0ms	(/.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))

series452.0ms (9%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
90.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
70.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
60.0ms	(*.f64 e (cos.f64 v))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5084	1500

prune93.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	96	8	104

Merged error: 0.0b

Counts

104 → 8

Compiler

Compiled 2014 to 723 computations (64.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite45.0ms (0.9%)

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-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
8×	`associate-/r*_binary64` `pow1_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-r_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:

11.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sqrt.f64 e) (sin.f64 v))))
9.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sqrt.f64 e) (sin.f64 v)))
6.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series562.0ms (11.2%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sqrt.f64 e) (sin.f64 v))))
197.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sqrt.f64 e) (sin.f64 v)))
90.0ms	(*.f64 (sqrt.f64 e) (sin.f64 v))
55.0ms	(*.f64 e (cos.f64 v))

simplify111.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4952	3941
1	4952	3941

prune137.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	147	8	155

Merged error: 0.0b

Counts

155 → 8

Compiler

Compiled 3422 to 1215 computations (64.5% saved)

regimes39.0ms (0.8%)

Compiler: Compiled 280 to 194 computations (30.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample2.0s (39.1%)

Algorithm

1×

intervals

Results

785.0ms	2041×	body	1024	valid
328.0ms	4437×	body	128	valid
234.0ms	1023×	body	512	valid
154.0ms	8000×	pre	128	true
77.0ms	491×	body	256	valid
7.0ms	8×	body	2048	valid

Compiler

Compiled 164 to 116 computations (29.3% saved)

Details

analyze210.0ms (4.2%)

sample61.0ms (1.2%)

simplify178.0ms (3.5%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite24.0ms (0.5%)

series315.0ms (6.3%)

simplify62.0ms (1.2%)

prune70.0ms (1.4%)

localize10.0ms (0.2%)

rewrite28.0ms (0.6%)

series360.0ms (7.2%)

simplify68.0ms (1.3%)

prune86.0ms (1.7%)

localize12.0ms (0.2%)

rewrite38.0ms (0.8%)

series452.0ms (9%)

simplify62.0ms (1.2%)

prune93.0ms (1.9%)

localize12.0ms (0.2%)

rewrite45.0ms (0.9%)

series562.0ms (11.2%)

simplify111.0ms (2.2%)

prune137.0ms (2.7%)

regimes39.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (39.1%)

Profiling