Details

analyze14.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	1.6%	48.5%	9
50.4%	1.2%	48.5%	10
50.4%	1.2%	48.5%	11
50.4%	1.1%	48.6%	12
50.4%	1%	48.6%	13
50.5%	0.9%	48.6%	14

Compiler

Compiled 14 to 8 computations (42.9% saved)

sample58.0ms (1.6%)

Algorithm

1×

intervals

Results

35.0ms	131×	body	1024	valid
8.0ms	58×	body	512	valid
3.0ms	11×	body	2048	valid
3.0ms	35×	body	256	valid
1.0ms	21×	body	128	valid

Compiler

Compiled 27 to 16 computations (40.7% saved)

simplify168.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4797	22
1	4797	22

prune2.0ms (0.1%)

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

59.2b

Counts

2 → 1

Compiler

Compiled 26 to 14 computations (46.2% saved)

localize7.0ms (0.2%)

Local error

Found 6 expressions with local error:

7.1b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
1.0b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
1.0b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
7.1b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_1101`
31×	`add-sqr-sqrt_binary64_1123`
30×	`times-frac_binary64_1107`
17×	`add-cube-cbrt_binary64_1136`
8×	`distribute-lft-out_binary64_1052` `cosh-undef_binary64_1295`
7×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140` `distribute-lft-out--_binary64_1053` `sinh-undef_binary64_1294`
6×	`associate-/l*_binary64_1046`
5×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
3×	`pow1_binary64_1162` `cancel-sign-sub-inv_binary64_1067`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `clear-num_binary64_1100` `tanh-undef_binary64_1296` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `div-sub_binary64_1106`

Counts

3 → 89

Calls

6 calls:

13.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
6.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
5.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

series134.0ms (3.7%)

Counts

3 → 18

Calls

3 calls:

79.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
32.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
23.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 342 to 252 computations (26.3% saved)

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5039	2484

prune90.0ms (2.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	3	108

Error

Counts

108 → 3

Compiler

Compiled 2089 to 413 computations (80.2% saved)

localize2.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(tanh.f64 x)
0.0b	(tanh.f64 x)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`tanh-def-b_binary64_1289` `tanh-def-a_binary64_1288` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137` `tanh-def-c_binary64_1290`

Counts

1 → 10

Calls

2 calls:

1.0ms	(tanh.f64 x)
0.0ms	(tanh.f64 x)

series61.0ms (1.7%)

Counts

1 → 6

Calls

1 calls:

61.0ms

(tanh.f64 x)

Compiler

Compiled 92 to 82 computations (10.9% saved)

simplify36.0ms (1%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4965	163
1	4965	163

prune13.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Error

Counts

19 → 3

Compiler

Compiled 147 to 87 computations (40.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 (sinh.f64 x) (cosh.f64 x))
1.0b	(/.f64 (sinh.f64 x) (cosh.f64 x))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `times-frac_binary64_1107`
3×	`add-exp-log_binary64_1139` `associate-/l_binary64_1046` `add-cbrt-cube_binary64_1137` `associate-/r_binary64_1045`
1×	`add-log-exp_binary64_1140` `frac-2neg_binary64_1112` `pow1_binary64_1162` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `div-inv_binary64_1098` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `sinh-def_binary64_1286` `cosh-def_binary64_1287`

Counts

1 → 29

Calls

2 calls:

4.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
0.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))

series111.0ms (3.1%)

Counts

1 → 6

Calls

1 calls:

111.0ms

(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 96 to 70 computations (27.1% saved)

simplify84.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4892	490
1	4892	490

prune32.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	36	2	38

Error

Counts

38 → 2

Compiler

Compiled 382 to 122 computations (68.1% saved)

localize7.0ms (0.2%)

Local error

Found 6 expressions with local error:

1.0b	(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x))))
0.8b	(/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x)))
0.0b	(/.f64 1 (sqrt.f64 (cosh.f64 x)))
0.0b	(/.f64 1 (sqrt.f64 (cosh.f64 x)))
0.8b	(/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x)))
1.0b	(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x))))

rewrite50.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-sqr-sqrt_binary64_1123`
94×	`times-frac_binary64_1107`
65×	`*-un-lft-identity_binary64_1101`
59×	`add-cube-cbrt_binary64_1136`
53×	`sqrt-prod_binary64_1117`
31×	`add-exp-log_binary64_1139`
23×	`associate-r_binary64_1041` `associate-l_binary64_1042`
19×	`add-cbrt-cube_binary64_1137`
15×	`unswap-sqr_binary64_1069`
12×	`associate-/r*_binary64_1045`
11×	`div-exp_binary64_1152`
8×	`prod-exp_binary64_1150`
7×	`pow1_binary64_1162`
6×	`associate-/l*_binary64_1046` `cbrt-undiv_binary64_1135`
4×	`cbrt-unprod_binary64_1134` `div-inv_binary64_1098` `associate-/r/_binary64_1047` `sqrt-div_binary64_1118` `cosh-def_binary64_1287`
3×	`1-exp_binary64_1145` `add-log-exp_binary64_1140` `rec-exp_binary64_1151` `pow-flip_binary64_1175`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`inv-pow_binary64_1186` `-commutative_binary64_1032` `frac-times_binary64_1111` `sqrt-pow1_binary64_1119` `associate-/l/_binary64_1048` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `associate-*l/_binary64_1044` `sinh-def_binary64_1286` `pow1/2_binary64_1181`

Counts

3 → 172

Calls

6 calls:

21.0ms	(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x))))
5.0ms	(/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x)))
4.0ms	(/.f64 1 (sqrt.f64 (cosh.f64 x)))
0.0ms	(/.f64 1 (sqrt.f64 (cosh.f64 x)))
0.0ms	(/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x)))

series344.0ms (9.6%)

Counts

3 → 18

Calls

3 calls:

145.0ms	(/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x)))
112.0ms	(*.f64 (/.f64 1 (sqrt.f64 (cosh.f64 x))) (/.f64 (sinh.f64 x) (sqrt.f64 (cosh.f64 x))))
87.0ms	(/.f64 1 (sqrt.f64 (cosh.f64 x)))

Compiler

Compiled 418 to 336 computations (19.6% saved)

simplify76.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5029	3277

prune137.0ms (3.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	190	2	192

Error

Counts

192 → 2

Compiler

Compiled 3264 to 897 computations (72.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	200
1	68	200

regimes49.0ms (1.4%)

Compiler: Compiled 304 to 191 computations (37.2% saved)

bsearch0.0ms (0%)

regimes15.0ms (0.4%)

Compiler: Compiled 6 to 9 computations (-50% saved)

bsearch12.0ms (0.3%)

Steps

Iters	Range		Point
7	0.694616828524831	51.00029292517128	0.9975721750512928

Compiler

Compiled 1 to 1 computations (0% saved)

regimes12.0ms (0.3%)

Accuracy

Total 0.0b remaining (87.3%)

Threshold costs 0.0b (87.3%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch38.0ms (1.1%)

Steps

Iters	Range		Point
9	3.935028535732182e-160	1.407343869546793e-150	1.0964452542503893e-154

Compiler

Compiled 16 to 16 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	20
1	12	20

end0.0ms (0%)

sample1.9s (52.7%)

Algorithm

1×

intervals

Results

1.0s	3899×	body	1024	valid
260.0ms	1904×	body	512	valid
117.0ms	416×	body	2048	valid
83.0ms	981×	body	256	valid
39.0ms	800×	body	128	valid
0.0ms	4×	body	128	overflowed

Compiler

Compiled 146 to 98 computations (32.9% saved)

Pareto

0.02192624252139631

Details

analyze14.0ms (0.4%)

sample58.0ms (1.6%)

simplify168.0ms (4.7%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite32.0ms (0.9%)

series134.0ms (3.7%)

simplify87.0ms (2.4%)

prune90.0ms (2.5%)

localize2.0ms (0.1%)

rewrite2.0ms (0%)

series61.0ms (1.7%)

simplify36.0ms (1%)

prune13.0ms (0.4%)

localize4.0ms (0.1%)

rewrite6.0ms (0.2%)

series111.0ms (3.1%)

simplify84.0ms (2.3%)

prune32.0ms (0.9%)

localize7.0ms (0.2%)

rewrite50.0ms (1.4%)

series344.0ms (9.6%)

simplify76.0ms (2.1%)

prune137.0ms (3.8%)

simplify5.0ms (0.1%)

regimes49.0ms (1.4%)

bsearch0.0ms (0%)

regimes15.0ms (0.4%)

bsearch12.0ms (0.3%)

regimes12.0ms (0.3%)

bsearch38.0ms (1.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.9s (52.7%)

Profiling