Details

analyze239.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample64.0ms (1.4%)

Algorithm

1×

intervals

Results

38.0ms	77×	body	2048	valid
7.0ms	37×	body	1024	valid
6.0ms	42×	body	512	valid
3.0ms	75×	body	128	valid
2.0ms	23×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify182.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	364	12
1	364	12

prune2.0ms (0%)

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: 33.0b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 1 (cos.f64 x))
18.7b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
7×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
6×	`times-frac_binary64_85` `associate-/l*_binary64_24` `difference-of-squares_binary64_48`
5×	`add-cube-cbrt_binary64_114`
4×	`add-log-exp_binary64_118`
3×	`distribute-lft-out--_binary64_31` `cancel-sign-sub-inv_binary64_45`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `flip--_binary64_54` `flip3--_binary64_83` `associate-/l/_binary64_26` `pow1_binary64_140`
1×	`associate-/r*_binary64_23` `div-sub_binary64_84` `div-inv_binary64_76` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `diff-log_binary64_171` `clear-num_binary64_78` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

2 → 47

Calls

2 calls:

13.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

series83.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
21.0ms	(-.f64 1 (cos.f64 x))

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4925	715
1	4925	715

prune249.0ms (5.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	46	7	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	7	54

Merged error: 0.0b

Counts

54 → 7

Compiler

Compiled 3613 to 2395 computations (33.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.3b	(+.f64 1 (cos.f64 x))
18.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
24×	`*-un-lft-identity_binary64_79`
22×	`times-frac_binary64_85`
16×	`add-sqr-sqrt_binary64_101`
14×	`add-cube-cbrt_binary64_114`
12×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
11×	`associate-/l*_binary64_24` `pow1_binary64_140`
7×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
6×	`associate-/r/_binary64_25` `add-log-exp_binary64_118`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_53` `div-inv_binary64_76` `flip3-+_binary64_82`
3×	`associate-l_binary64_20` `div-sub_binary64_84` `sqr-sin-a_binary64_227` `swap-sqr_binary64_46` `associate-r_binary64_19`
2×	`sin-mult_binary64_234` `clear-num_binary64_78` `associate-/l/_binary64_26` `frac-2neg_binary64_90`
1×	`sum-log_binary64_170` `+-commutative_binary64_9` `pow-prod-up_binary64_149` `unswap-sqr_binary64_47` `pow-sqr_binary64_52` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `pow-plus_binary64_142` `pow2_binary64_160`

Counts

4 → 111

Calls

4 calls:

12.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
9.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series254.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
89.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
26.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4973	1781
1	4973	1781

prune211.0ms (4.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 0b

Counts

130 → 8

Compiler

Compiled 3644 to 2156 computations (40.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_101`
22×	`times-frac_binary64_85`
21×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
19×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
13×	`associate-l_binary64_20`
6×	`associate-/r*_binary64_23` `cbrt-undiv_binary64_113` `div-exp_binary64_130`
5×	`pow1_binary64_140`
4×	`associate-/l*_binary64_24` `tan-quot_binary64_238` `cbrt-unprod_binary64_112` `prod-exp_binary64_128`
3×	`div-inv_binary64_76` `add-log-exp_binary64_118` `associate-/l/_binary64_26` `associate-r_binary64_19`
2×	`frac-times_binary64_89` `associate-l/_binary64_22` `associate-r/_binary64_21` `unswap-sqr_binary64_47` `clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`*-commutative_binary64_10` `pow-prod-down_binary64_150`

Counts

3 → 87

Calls

3 calls:

9.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
9.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
4.0ms	(/.f64 (sin.f64 x) x)

series336.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

154.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
148.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
34.0ms	(/.f64 (sin.f64 x) x)

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4937	1539
1	4937	1539

prune111.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Merged error: 0b

Counts

104 → 8

Compiler

Compiled 2037 to 1116 computations (45.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.2b	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_101`
22×	`times-frac_binary64_85`
21×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
19×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
13×	`associate-r_binary64_19`
6×	`associate-/r*_binary64_23` `cbrt-undiv_binary64_113` `div-exp_binary64_130`
5×	`pow1_binary64_140`
4×	`associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128`
3×	`associate-l_binary64_20` `div-inv_binary64_76` `add-log-exp_binary64_118`
2×	`associate-*r/_binary64_21` `unswap-sqr_binary64_47` `clear-num_binary64_78` `associate-/l/_binary64_26` `frac-2neg_binary64_90`
1×	`tan-quot_binary64_238` `*-commutative_binary64_10` `pow-prod-down_binary64_150`

Counts

3 → 84

Calls

3 calls:

9.0ms	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
7.0ms	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

series401.0ms (8.9%)

Counts

3 → 9

Calls

3 calls:

165.0ms	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
147.0ms	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
89.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

simplify99.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4934	1640
1	4934	1640

prune90.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	94	7	101

Merged error: 0b

Counts

101 → 7

Compiler

Compiled 1695 to 1030 computations (39.2% saved)

regimes17.0ms (0.4%)

Compiler: Compiled 90 to 67 computations (25.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample1.8s (39.9%)

Algorithm

1×

intervals

Results

833.0ms	1954×	body	2048	valid
234.0ms	1113×	body	1024	valid
207.0ms	1483×	body	512	valid
111.0ms	2570×	body	128	valid
74.0ms	768×	body	256	valid
52.0ms	112×	body	4096	valid

Compiler

Compiled 108 to 81 computations (25% saved)

Details

analyze239.0ms (5.3%)

sample64.0ms (1.4%)

simplify182.0ms (4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite20.0ms (0.5%)

series83.0ms (1.8%)

simplify61.0ms (1.4%)

prune249.0ms (5.5%)

localize11.0ms (0.2%)

rewrite40.0ms (0.9%)

series254.0ms (5.6%)

simplify64.0ms (1.4%)

prune211.0ms (4.7%)

localize9.0ms (0.2%)

rewrite33.0ms (0.7%)

series336.0ms (7.5%)

simplify84.0ms (1.9%)

prune111.0ms (2.5%)

localize9.0ms (0.2%)

rewrite28.0ms (0.6%)

series401.0ms (8.9%)

simplify99.0ms (2.2%)

prune90.0ms (2%)

regimes17.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (39.9%)

Profiling