Details

analyze1.0s (14.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample59.0ms (0.9%)

Algorithm

1×

intervals

Results

17.0ms	199×	body	128	valid
9.0ms	24×	body	1024	valid
5.0ms	61×	body	128	invalid
5.0ms	18×	body	512	valid
4.0ms	10×	body	1024	invalid
3.0ms	15×	body	256	valid
3.0ms	10×	body	512	invalid
1.0ms	9×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify171.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4891	24
1	4891	24

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 24.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.2b	(.f64 (.f64 x (pow.f64 s 2)) x)
6.3b	(*.f64 x (pow.f64 s 2))
17.3b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log_binary64`
82×	`prod-exp_binary64`
34×	`add-cbrt-cube_binary64`
18×	`pow-to-exp_binary64` `add-sqr-sqrt_binary64` `pow-exp_binary64`
16×	`cbrt-unprod_binary64` `div-exp_binary64`
12×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
7×	`unpow-prod-down_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64`
3×	`unpow2_binary64` `sqr-pow_binary64` `associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `cos-2_binary64`

Counts

4 → 119

Calls

4 calls:

12.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
10.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
6.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
6.0ms	(*.f64 x (pow.f64 s 2))

series347.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
108.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
50.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
49.0ms	(*.f64 x (pow.f64 s 2))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4973	2214
1	4973	2214

prune400.0ms (5.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 1.7b

Counts

132 → 11

Compiler

Compiled 7344 to 4570 computations (37.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(cos.f64 (*.f64 2 x))
0.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
4.2b	(.f64 s (.f64 c x))
4.2b	(.f64 s (.f64 c x))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`pow1_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`pow-prod-down_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/l*_binary64` `times-frac_binary64`
2×	`associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `cos-2_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 66

Calls

4 calls:

5.0ms	(.f64 s (.f64 c x))
5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
5.0ms	(.f64 s (.f64 c x))
2.0ms	(cos.f64 (*.f64 2 x))

series317.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
52.0ms	(.f64 s (.f64 c x))
51.0ms	(.f64 s (.f64 c x))
13.0ms	(cos.f64 (*.f64 2 x))

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5046	1049

prune491.0ms (7.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	77	12	89

Merged error: 1.2b

Counts

89 → 12

Compiler

Compiled 9453 to 5805 computations (38.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(cos.f64 (*.f64 x 2))
0.8b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
4.2b	(.f64 s (.f64 c x))
4.2b	(.f64 s (.f64 c x))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`associate-r_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 70

Calls

4 calls:

6.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
4.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
2.0ms	(cos.f64 (*.f64 x 2))

series225.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
53.0ms	(.f64 s (.f64 c x))
51.0ms	(.f64 s (.f64 c x))
10.0ms	(cos.f64 (*.f64 x 2))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5369	1235

prune267.0ms (3.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	81	13	94

Merged error: 1.2b

Counts

94 → 13

Compiler

Compiled 5393 to 2965 computations (45% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (.f64 (cos.f64 x) (cos.f64 x)) (pow.f64 (.f64 s (*.f64 c x)) 2))
1.9b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 (.f64 s (*.f64 c x)) 2))
4.2b	(.f64 s (.f64 c x))
4.2b	(.f64 s (.f64 c x))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-exp-log_binary64`
28×	`prod-exp_binary64`
24×	`add-cbrt-cube_binary64`
20×	`div-exp_binary64`
14×	`pow1_binary64`
12×	`associate-/r*_binary64` `times-frac_binary64` `pow-exp_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`cbrt-unprod_binary64`
6×	`pow-prod-down_binary64` `associate-l_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64`
2×	`associate-/l/_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`
1×	`cos-mult_binary64` `div-sub_binary64` `sin-mult_binary64` `sqr-sin-a_binary64`

Counts

4 → 109

Calls

4 calls:

9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 (.f64 s (*.f64 c x)) 2))
8.0ms	(/.f64 (.f64 (cos.f64 x) (cos.f64 x)) (pow.f64 (.f64 s (*.f64 c x)) 2))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))

series424.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 (.f64 s (*.f64 c x)) 2))
157.0ms	(/.f64 (.f64 (cos.f64 x) (cos.f64 x)) (pow.f64 (.f64 s (*.f64 c x)) 2))
51.0ms	(.f64 s (.f64 c x))
46.0ms	(.f64 s (.f64 c x))

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5009	1936

prune230.0ms (3.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	121	13	134

Merged error: 1.0b

Counts

134 → 13

Compiler

Compiled 5484 to 2275 computations (58.5% saved)

regimes123.0ms (1.8%)

Compiler: Compiled 1436 to 924 computations (35.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	15	28

end0.0ms (0%)

sample2.2s (33.1%)

Algorithm

1×

intervals

Results

701.0ms	6095×	body	128	valid
360.0ms	929×	body	1024	valid
173.0ms	643×	body	512	valid
165.0ms	1846×	body	128	invalid
85.0ms	224×	body	1024	invalid
58.0ms	330×	body	256	valid
56.0ms	225×	body	512	invalid
24.0ms	146×	body	256	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 391 to 253 computations (35.3% saved)

Details

analyze1.0s (14.9%)

sample59.0ms (0.9%)

simplify171.0ms (2.5%)

prune3.0ms (0%)

localize18.0ms (0.3%)

rewrite47.0ms (0.7%)

series347.0ms (5.1%)

simplify86.0ms (1.3%)

prune400.0ms (5.9%)

localize11.0ms (0.2%)

rewrite24.0ms (0.4%)

series317.0ms (4.7%)

simplify53.0ms (0.8%)

prune491.0ms (7.3%)

localize11.0ms (0.2%)

rewrite22.0ms (0.3%)

series225.0ms (3.3%)

simplify74.0ms (1.1%)

prune267.0ms (3.9%)

localize16.0ms (0.2%)

rewrite42.0ms (0.6%)

series424.0ms (6.3%)

simplify59.0ms (0.9%)

prune230.0ms (3.4%)

regimes123.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (33.1%)

Profiling