Details

analyze1.1s (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample125.0ms (1.8%)

Algorithm

1×

intervals

Results

77.0ms	140×	body	2048	valid
28.0ms	71×	body	1024	valid
5.0ms	18×	body	512	valid
2.0ms	12×	body	256	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify219.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4955	21
1	4955	21

prune4.0ms (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

0.6b

Counts

2 → 1

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.2b	(.f64 5 (.f64 v v))
0.6b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1123`
19×	`*-un-lft-identity_binary64_1101`
18×	`times-frac_binary64_1107`
15×	`add-cube-cbrt_binary64_1136`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`difference-of-squares_binary64_1070` `pow1_binary64_1162`
6×	`associate-/r*_binary64_1045`
4×	`difference-of-sqr-1_binary64_1071`
3×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `associate-/l_binary64_1046` `pow-prod-down_binary64_1172` `associate-l*_binary64_1042`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `acos-asin_binary64_1282` `associate-r*_binary64_1041` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069` `div-sub_binary64_1106`

Counts

3 → 71

Calls

3 calls:

17.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
11.0ms	(.f64 5 (.f64 v v))
2.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

series80.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

44.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
19.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
17.0ms	(.f64 5 (.f64 v v))

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4935	1788
1	4935	1788

prune123.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Error

0.6b

Counts

81 → 4

Compiler

Compiled 1813 to 1168 computations (35.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.0b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
0.2b	(.f64 5 (.f64 v v))
0.6b	(asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_1123`
23×	`*-un-lft-identity_binary64_1101`
19×	`times-frac_binary64_1107`
17×	`add-cube-cbrt_binary64_1136`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`difference-of-squares_binary64_1070`
9×	`pow1_binary64_1162`
6×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045`
4×	`difference-of-sqr-1_binary64_1071`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l_binary64_1046` `pow-prod-down_binary64_1172` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067`
2×	`associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `asin-acos_binary64_1281`
1×	`diff-log_binary64_1193` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `distribute-lft-out--_binary64_1053` `associate--r-_binary64_1040` `div-inv_binary64_1098` `associate-r*_binary64_1041` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069` `div-sub_binary64_1106`

Counts

4 → 89

Calls

4 calls:

12.0ms	(.f64 5 (.f64 v v))
10.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
9.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
2.0ms	(asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

series115.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
32.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
22.0ms	(.f64 5 (.f64 v v))
19.0ms	(asin.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4940	2579
1	4940	2579

prune167.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	101	4	105

Error

0.6b

Counts

105 → 4

Compiler

Compiled 2759 to 1808 computations (34.5% saved)

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 -1 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)))))
0.0b	(.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4))
0.6b	(asin.f64 (+.f64 -1 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4))))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1123`
8×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
7×	`*-un-lft-identity_binary64_1101`
5×	`add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `associate-l_binary64_1042` `cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-squares_binary64_1070` `associate-r/_binary64_1043` `asin-acos_binary64_1281` `associate-l/_binary64_1044`
1×	`diff-log_binary64_1193` `-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate--r-_binary64_1040` `times-frac_binary64_1107` `associate-r*_binary64_1041` `flip-+_binary64_1075`

Counts

3 → 46

Calls

3 calls:

22.0ms	(.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4))
14.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 -1 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)))))
2.0ms	(asin.f64 (+.f64 -1 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4))))

series160.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

93.0ms	(.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4))
55.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 -1 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)))))
12.0ms	(asin.f64 (+.f64 -1 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4))))

simplify125.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4928	1265
1	4928	1265

prune90.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	54	5	59

Error

0.6b

Counts

59 → 5

Compiler

Compiled 1394 to 1058 computations (24.1% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
1.0b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1123`
24×	`sqrt-prod_binary64_1117`
21×	`pow1_binary64_1162`
14×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
10×	`sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
8×	`swap-sqr_binary64_1068`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-r_binary64_1041` `associate-l_binary64_1042`
5×	`pow-prod-up_binary64_1171`
4×	`rem-sqrt-square_binary64_1114` `add-log-exp_binary64_1140` `unswap-sqr_binary64_1069`
3×	`pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `rem-square-sqrt_binary64_1113` `acos-asin_binary64_1282` `sqr-abs_binary64_1116` `sqrt-unprod_binary64_1121` `pow2_binary64_1182`

Counts

4 → 84

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
5.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
2.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
2.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))

series136.0ms (2%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
34.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
30.0ms	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
12.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5552	2247

prune166.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	94	7	101

Error

0.6b

Counts

101 → 7

Compiler

Compiled 2912 to 1840 computations (36.8% saved)

regimes231.0ms (3.3%)

Accuracy

Total 0.0b remaining (4%)

Threshold costs 0.0b (4%)

Compiler

Compiled 2782 to 2006 computations (27.9% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	83	28
1	83	28

end0.0ms (0%)

sample3.6s (52%)

Algorithm

1×

intervals

Results

1.7s	3981×	body	2048	valid
577.0ms	1971×	body	1024	valid
213.0ms	1021×	body	512	valid
73.0ms	517×	body	256	valid
40.0ms	508×	body	128	valid
1.0ms	2×	body	4096	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 623 to 453 computations (27.3% saved)

Details

analyze1.1s (15.5%)

sample125.0ms (1.8%)

simplify219.0ms (3.2%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite42.0ms (0.6%)

series80.0ms (1.2%)

simplify79.0ms (1.2%)

prune123.0ms (1.8%)

localize22.0ms (0.3%)

rewrite41.0ms (0.6%)

series115.0ms (1.7%)

simplify97.0ms (1.4%)

prune167.0ms (2.4%)

localize19.0ms (0.3%)

rewrite42.0ms (0.6%)

series160.0ms (2.3%)

simplify125.0ms (1.8%)

prune90.0ms (1.3%)

localize20.0ms (0.3%)

rewrite43.0ms (0.6%)

series136.0ms (2%)

simplify75.0ms (1.1%)

prune166.0ms (2.4%)

regimes231.0ms (3.3%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.6s (52%)

Profiling