Details

analyze408.0ms (3.9%)

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)

sample98.0ms (0.9%)

Algorithm

1×

intervals

Results

54.0ms	71×	body	2048	valid
13.0ms	38×	body	1024	valid
10.0ms	49×	body	512	valid
5.0ms	73×	body	128	valid
3.0ms	23×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify192.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12

prune3.0ms (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

Error

33.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

16.4b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
1.4b	(-.f64 1 (cos.f64 x))
1.4b	(-.f64 1 (cos.f64 x))
16.4b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_71` `add-sqr-sqrt_binary64_93`
7×	`add-cbrt-cube_binary64_107` `add-exp-log_binary64_109`
6×	`associate-/l*_binary64_16` `difference-of-squares_binary64_40` `times-frac_binary64_77`
5×	`add-cube-cbrt_binary64_106`
4×	`add-log-exp_binary64_110`
3×	`distribute-lft-out--_binary64_23` `cancel-sign-sub-inv_binary64_37`
2×	`flip--_binary64_46` `associate-/l/_binary64_18` `div-exp_binary64_122` `flip3--_binary64_75` `cbrt-undiv_binary64_105` `pow1_binary64_132`
1×	`associate-/r*_binary64_15` `clear-num_binary64_70` `div-sub_binary64_76` `div-inv_binary64_68` `prod-exp_binary64_120` `cbrt-unprod_binary64_104` `frac-2neg_binary64_82` `diff-log_binary64_163` `sub-neg_binary64_64`

Counts

2 → 47

Calls

4 calls:

14.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
7.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series77.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
23.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 96 to 80 computations (16.7% saved)

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4903	679
1	4903	679

prune184.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	45	8	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	8	54

Error

0.0b

Counts

54 → 8

Compiler

Compiled 742 to 396 computations (46.6% saved)

localize19.0ms (0.2%)

Local error

Found 8 expressions with local error:

16.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
0.3b	(+.f64 1 (cos.f64 x))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
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))
16.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite72.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_107` `add-exp-log_binary64_109`
24×	`*-un-lft-identity_binary64_71`
22×	`times-frac_binary64_77`
16×	`add-sqr-sqrt_binary64_93`
14×	`add-cube-cbrt_binary64_106`
12×	`div-exp_binary64_122` `cbrt-undiv_binary64_105`
11×	`associate-/l*_binary64_16` `pow1_binary64_132`
7×	`prod-exp_binary64_120` `cbrt-unprod_binary64_104`
6×	`associate-/r/_binary64_17` `add-log-exp_binary64_110`
5×	`associate-/r*_binary64_15` `distribute-lft-out_binary64_22`
4×	`div-inv_binary64_68` `flip-+_binary64_45` `flip3-+_binary64_74`
3×	`div-sub_binary64_76` `associate-r_binary64_11` `sqr-sin-a_binary64_219` `associate-l_binary64_12` `swap-sqr_binary64_38`
2×	`associate-/l/_binary64_18` `sin-mult_binary64_226` `clear-num_binary64_70` `frac-2neg_binary64_82`
1×	`pow-sqr_binary64_44` `pow2_binary64_152` `+-commutative_binary64_1` `unswap-sqr_binary64_39` `*-commutative_binary64_2` `pow-prod-up_binary64_141` `pow-prod-down_binary64_142` `pow-plus_binary64_134` `sum-log_binary64_162`

Counts

4 → 111

Calls

8 calls:

20.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
14.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
9.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
7.0ms	(+.f64 1 (cos.f64 x))
0.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))

series251.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
87.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
34.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
18.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 302 to 230 computations (23.8% saved)

simplify115.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5801	1709

prune203.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	126	5	131

Error

Counts

131 → 5

Compiler

Compiled 2093 to 1026 computations (51% saved)

localize17.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_93`
40×	`times-frac_binary64_77`
33×	`*-un-lft-identity_binary64_71` `add-cube-cbrt_binary64_106`
19×	`add-cbrt-cube_binary64_107` `add-exp-log_binary64_109`
13×	`associate-r_binary64_11` `associate-l_binary64_12`
6×	`associate-/r_binary64_15` `div-exp_binary64_122` `associate-/l_binary64_16` `cbrt-undiv_binary64_105`
5×	`pow1_binary64_132`
4×	`unswap-sqr_binary64_39` `div-inv_binary64_68` `prod-exp_binary64_120` `cbrt-unprod_binary64_104`
3×	`add-log-exp_binary64_110`
2×	`clear-num_binary64_70` `frac-2neg_binary64_82`
1×	`associate-/l/_binary64_18` `frac-times_binary64_81` `associate-l/_binary64_14` `-commutative_binary64_2` `tan-quot_binary64_230` `pow-prod-down_binary64_142` `associate-*r/_binary64_13`

Counts

3 → 105

Calls

6 calls:

19.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
8.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
7.0ms	(/.f64 (sin.f64 x) x)
0.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))

series255.0ms (2.4%)

Counts

3 → 10

Calls

3 calls:

125.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
85.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
45.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 240 to 192 computations (20% saved)

simplify141.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4967	1909
1	4967	1909

prune165.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	115	5	120

Error

Counts

120 → 5

Compiler

Compiled 2019 to 1031 computations (48.9% saved)

localize20.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 x (sin.f64 x))
0.1b	(/.f64 1 (/.f64 x (sin.f64 x)))
0.1b	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 1 (/.f64 x (sin.f64 x)))
0.2b	(/.f64 x (sin.f64 x))

rewrite114.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`times-frac_binary64_77`
137×	`add-sqr-sqrt_binary64_93`
108×	`*-un-lft-identity_binary64_71`
104×	`add-cube-cbrt_binary64_106`
64×	`add-exp-log_binary64_109`
44×	`associate-l_binary64_12`
34×	`add-cbrt-cube_binary64_107`
30×	`div-exp_binary64_122`
19×	`associate-/r*_binary64_15`
14×	`cbrt-undiv_binary64_105` `prod-exp_binary64_120`
13×	`associate-r_binary64_11`
12×	`div-inv_binary64_68`
10×	`unswap-sqr_binary64_39`
9×	`associate-/l*_binary64_16`
7×	`pow1_binary64_132`
6×	`rec-exp_binary64_121` `cbrt-unprod_binary64_104` `1-exp_binary64_115`
4×	`add-log-exp_binary64_110`
3×	`clear-num_binary64_70` `frac-2neg_binary64_82`
2×	`associate-/r/_binary64_17`
1×	`associate-/l/_binary64_18` `inv-pow_binary64_156` `frac-times_binary64_81` `associate-l/_binary64_14` `-commutative_binary64_2` `tan-quot_binary64_230` `pow-prod-down_binary64_142` `associate-*r/_binary64_13` `pow-flip_binary64_145`

Counts

4 → 230

Calls

8 calls:

43.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
11.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))
8.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
6.0ms	(/.f64 x (sin.f64 x))
0.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

series345.0ms (3.3%)

Counts

4 → 14

Calls

4 calls:

130.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
99.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
65.0ms	(/.f64 x (sin.f64 x))
50.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))

Compiler

Compiled 352 to 286 computations (18.8% saved)

simplify216.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4959	4295
1	4959	4295

prune409.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	244	5	249

Error

Counts

249 → 5

Compiler

Compiled 4707 to 2355 computations (50% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	198	738
1	198	738

regimes215.0ms (2.1%)

Accuracy

Total 0.1b remaining (98.1%)

Threshold costs 0.1b (98.1%)

Compiler

Compiled 1021 to 736 computations (27.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample6.7s (64.3%)

Algorithm

1×

intervals

Results

1.7s	2053×	body	2048	valid
407.0ms	1084×	body	1024	valid
347.0ms	1524×	body	512	valid
177.0ms	2501×	body	128	valid
112.0ms	746×	body	256	valid
71.0ms	92×	body	4096	valid

Compiler

Compiled 1383 to 995 computations (28.1% saved)

Pareto

0.11204778269340229

Details

analyze408.0ms (3.9%)

sample98.0ms (0.9%)

simplify192.0ms (1.8%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite28.0ms (0.3%)

series77.0ms (0.7%)

simplify106.0ms (1%)

prune184.0ms (1.8%)

localize19.0ms (0.2%)

rewrite72.0ms (0.7%)

series251.0ms (2.4%)

simplify115.0ms (1.1%)

prune203.0ms (1.9%)

localize17.0ms (0.2%)

rewrite49.0ms (0.5%)

series255.0ms (2.4%)

simplify141.0ms (1.4%)

prune165.0ms (1.6%)

localize20.0ms (0.2%)

rewrite114.0ms (1.1%)

series345.0ms (3.3%)

simplify216.0ms (2.1%)

prune409.0ms (3.9%)

simplify22.0ms (0.2%)

regimes215.0ms (2.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.7s (64.3%)

Profiling