Details

analyze31.0ms

Algorithm

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

sample77.0ms

Algorithm

intervals

Results

29.0ms	61×	body	1280	valid
12.0ms	39×	body	640	valid
9.0ms	131×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	20×	body	320	valid
1.0ms	5×	body	160	valid

simplify748.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	23	17
1	23	17

prune19.0ms

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

localize32.0ms

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))
0.2b	(*.f64 e (sin.f64 v))

rewrite33.0ms

Algorithm

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:

12.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
7.0ms	(*.f64 e (cos.f64 v))
11.0ms	(*.f64 e (sin.f64 v))

series222.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
37.0ms	(*.f64 e (cos.f64 v))
61.0ms	(*.f64 e (sin.f64 v))

simplify91.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5261	920

prune383.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 0.0b

Counts

69 → 7

localize17.0ms

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

rewrite21.0ms

Algorithm

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:

5.0ms	(/.f64 (sin.f64 v) (+.f64 1 (*.f64 e (cos.f64 v))))
4.0ms	(*.f64 e (cos.f64 v))
9.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))

series241.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/.f64 (sin.f64 v) (+.f64 1 (*.f64 e (cos.f64 v))))
42.0ms	(*.f64 e (cos.f64 v))
136.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 1 (.f64 e (cos.f64 v)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5014	1715

prune601.0ms

Filtered

68 candidates to 90 candidates (-32.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	88	9	97

Merged error: 0.0b

Counts

97 → 9

localize29.0ms

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

Algorithm

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

series239.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(*.f64 e (cos.f64 v))
68.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
143.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))

simplify150.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5380	3218

prune838.0ms

Filtered

101 candidates to 126 candidates (-24.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	127	8	135

Merged error: 0.0b

Counts

135 → 8

localize18.0ms

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)))

rewrite31.0ms

Algorithm

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))))
4.0ms	(*.f64 e (cos.f64 v))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
7.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
42.0ms	(*.f64 e (cos.f64 v))
87.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
71.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))

simplify100.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5035	1528

prune27.0ms

Filtered: 72 candidates to 98 candidates (-36.1%)

Details

analyze31.0ms

sample77.0ms

simplify748.0ms

prune19.0ms

localize32.0ms

rewrite33.0ms

series222.0ms

simplify91.0ms

prune383.0ms

localize17.0ms

rewrite21.0ms

series241.0ms

simplify59.0ms

prune601.0ms

localize29.0ms

rewrite42.0ms

series239.0ms

simplify150.0ms

prune838.0ms

localize18.0ms

rewrite31.0ms

series330.0ms

simplify100.0ms

prune27.0ms

Profiling