Details

analyze231.0ms (4.5%)

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)

sample56.0ms (1.1%)

Algorithm

1×

intervals

Results

29.0ms	66×	body	2048	valid
9.0ms	45×	body	1024	valid
6.0ms	53×	body	512	valid
3.0ms	72×	body	128	valid
1.0ms	3×	body	4096	valid
1.0ms	17×	body	256	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify113.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	366	12
1	366	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

Error

34.8b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

16.4b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
1.6b	(-.f64 1 (cos.f64 x))
1.6b	(-.f64 1 (cos.f64 x))
16.4b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
7×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`times-frac_binary64_84` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`add-cube-cbrt_binary64_113`
4×	`add-log-exp_binary64_117`
3×	`distribute-lft-out--_binary64_30` `cancel-sign-sub-inv_binary64_44`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `flip--_binary64_53` `associate-/l/_binary64_25` `pow1_binary64_139`
1×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83` `sub-neg_binary64_71`

Counts

2 → 47

Calls

4 calls:

8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series49.0ms (1%)

Counts

2 → 8

Calls

2 calls:

33.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
17.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 130 to 109 computations (16.2% saved)

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4996	705
1	4996	705

prune97.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	46	9	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	9	56

Error

0.0b

Counts

56 → 9

Compiler

Compiled 803 to 432 computations (46.2% saved)

localize10.0ms (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))
0.4b	(+.f64 1 (cos.f64 x))
0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.4b	(+.f64 1 (cos.f64 x))
16.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
24×	`*-un-lft-identity_binary64_78`
22×	`times-frac_binary64_84`
16×	`add-sqr-sqrt_binary64_100`
14×	`add-cube-cbrt_binary64_113`
12×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
11×	`associate-/l*_binary64_23` `pow1_binary64_139`
7×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
6×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29`
4×	`flip-+_binary64_52` `div-inv_binary64_75` `flip3-+_binary64_81`
3×	`associate-l_binary64_19` `swap-sqr_binary64_45` `associate-r_binary64_18` `sqr-sin-a_binary64_226` `div-sub_binary64_83`
2×	`frac-2neg_binary64_89` `sin-mult_binary64_233` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`+-commutative_binary64_8` `pow2_binary64_159` `*-commutative_binary64_9` `pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `pow-plus_binary64_141` `sum-log_binary64_169`

Counts

4 → 111

Calls

8 calls:

11.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
8.0ms	(/.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))
0.0ms	(*.f64 (sin.f64 x) (sin.f64 x))

series168.0ms (3.3%)

Counts

4 → 16

Calls

4 calls:

76.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
53.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
25.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
13.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 383 to 295 computations (23% saved)

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4986	1758
1	4986	1758

prune124.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	130	6	136

Error

Counts

136 → 6

Compiler

Compiled 2171 to 1067 computations (50.9% saved)

localize9.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_100`
22×	`times-frac_binary64_84`
21×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
13×	`associate-l_binary64_19`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`tan-quot_binary64_237` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-/l*_binary64_23`
3×	`add-log-exp_binary64_117` `div-inv_binary64_75` `associate-r_binary64_18` `associate-/l/_binary64_25`
2×	`frac-2neg_binary64_89` `frac-times_binary64_88` `associate-l/_binary64_21` `unswap-sqr_binary64_46` `associate-r/_binary64_20` `clear-num_binary64_77`
1×	`*-commutative_binary64_9` `pow-prod-down_binary64_149`

Counts

3 → 87

Calls

6 calls:

8.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
8.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
4.0ms	(/.f64 (sin.f64 x) x)
0.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

series188.0ms (3.7%)

Counts

3 → 12

Calls

3 calls:

87.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
74.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
26.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 268 to 216 computations (19.4% saved)

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4982	1518
1	4982	1518

prune82.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	99	6	105

Error

Counts

105 → 6

Compiler

Compiled 1644 to 824 computations (49.9% saved)

localize8.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_100`
40×	`times-frac_binary64_84`
33×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
13×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/l_binary64_23` `associate-/r_binary64_22`
5×	`pow1_binary64_139`
4×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `div-inv_binary64_75` `unswap-sqr_binary64_46`
3×	`add-log-exp_binary64_117`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`tan-quot_binary64_237` `-commutative_binary64_9` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `associate-/l/_binary64_25`

Counts

3 → 105

Calls

6 calls:

11.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)
0.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

series159.0ms (3.1%)

Counts

3 → 12

Calls

3 calls:

74.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
55.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
29.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 271 to 219 computations (19.2% saved)

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4973	1929
1	4973	1929

prune96.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	117	6	123

Error

Counts

123 → 6

Compiler

Compiled 1986 to 1003 computations (49.5% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	273	779
1	273	779

regimes129.0ms (2.5%)

Compiler: Compiled 1125 to 822 computations (26.9% saved)

bsearch0.0ms (0%)

regimes69.0ms (1.4%)

Compiler: Compiled 206 to 170 computations (17.5% saved)

bsearch39.0ms (0.8%)

Steps

Iters	Range		Point
9	3.5167827464173845e-05	47669.887057392094	0.0054783708862614616
10	-162357.139483226	-7.126381145595913e-06	-0.0004457821252976667

Compiler

Compiled 1 to 1 computations (0% saved)

regimes71.0ms (1.4%)

Compiler: Compiled 184 to 154 computations (16.3% saved)

bsearch36.0ms (0.7%)

Steps

Iters	Range		Point
9	3.5167827464173845e-05	47669.887057392094	0.0054783708862614616
10	-162357.139483226	-7.126381145595913e-06	-0.005012177499423301

Compiler

Compiled 1 to 1 computations (0% saved)

regimes63.0ms (1.2%)

Compiler: Compiled 140 to 124 computations (11.4% saved)

bsearch40.0ms (0.8%)

Steps

Iters	Range		Point
9	3.5167827464173845e-05	47669.887057392094	0.0054783708862614616
10	-162357.139483226	-7.126381145595913e-06	-0.005012177499423301

Compiler

Compiled 1 to 1 computations (0% saved)

regimes55.0ms (1.1%)

Compiler: Compiled 84 to 80 computations (4.8% saved)

bsearch38.0ms (0.8%)

Steps

Iters	Range		Point
9	3.5167827464173845e-05	47669.887057392094	0.0054783708862614616
10	-162357.139483226	-7.126381145595913e-06	-0.005012177499423301

Compiler

Compiled 1 to 1 computations (0% saved)

regimes20.0ms (0.4%)

Compiler: Compiled 13 to 16 computations (-23.1% saved)

bsearch35.0ms (0.7%)

Steps

Iters	Range		Point
9	3.5167827464173845e-05	47669.887057392094	3.5071823034446923
10	-162357.139483226	-7.126381145595913e-06	-3.4968886079870694

Compiler

Compiled 1 to 1 computations (0% saved)

regimes18.0ms (0.4%)

Compiler: Compiled 6 to 10 computations (-66.7% saved)

bsearch56.0ms (1.1%)

Steps

Iters	Range		Point
10	6.680847411321486e+68	1.3481927354821352e+80	1.1081643599956554e+77
10	-1.1380318168474188e+82	-6.835077137307714e+69	-1.2257923376035007e+77

Compiler

Compiled 1 to 1 computations (0% saved)

regimes17.0ms (0.3%)

Accuracy

Total 0.1b remaining (98.4%)

Threshold costs 0.1b (98.4%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch65.0ms (1.3%)

Steps

Iters	Range		Point
10	6.680847411321486e+68	1.3481927354821352e+80	1.1081643599956554e+77
10	-1.1380318168474188e+82	-6.835077137307714e+69	-1.2257923376035007e+77

Compiler

Compiled 183 to 133 computations (27.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	104	247
1	104	247

end0.0ms (0%)

sample2.5s (49.8%)

Algorithm

1×

intervals

Results

876.0ms	1987×	body	2048	valid
355.0ms	1073×	body	1024	valid
189.0ms	1540×	body	512	valid
106.0ms	2554×	body	128	valid
62.0ms	738×	body	256	valid
43.0ms	108×	body	4096	valid

Compiler

Compiled 677 to 499 computations (26.3% saved)

Pareto

0.7876398180375468

Details

analyze231.0ms (4.5%)

sample56.0ms (1.1%)

simplify113.0ms (2.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite15.0ms (0.3%)

series49.0ms (1%)

simplify41.0ms (0.8%)

prune97.0ms (1.9%)

localize10.0ms (0.2%)

rewrite40.0ms (0.8%)

series168.0ms (3.3%)

simplify80.0ms (1.6%)

prune124.0ms (2.4%)

localize9.0ms (0.2%)

rewrite26.0ms (0.5%)

series188.0ms (3.7%)

simplify72.0ms (1.4%)

prune82.0ms (1.6%)

localize8.0ms (0.2%)

rewrite29.0ms (0.6%)

series159.0ms (3.1%)

simplify78.0ms (1.5%)

prune96.0ms (1.9%)

simplify13.0ms (0.3%)

regimes129.0ms (2.5%)

bsearch0.0ms (0%)

regimes69.0ms (1.4%)

bsearch39.0ms (0.8%)

regimes71.0ms (1.4%)

bsearch36.0ms (0.7%)

regimes63.0ms (1.2%)

bsearch40.0ms (0.8%)

regimes55.0ms (1.1%)

bsearch38.0ms (0.8%)

regimes20.0ms (0.4%)

bsearch35.0ms (0.7%)

regimes18.0ms (0.4%)

bsearch56.0ms (1.1%)

regimes17.0ms (0.3%)

bsearch65.0ms (1.3%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.5s (49.8%)

Profiling