Details

analyze794.0ms (15%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample36.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	204×	body	128	valid
5.0ms	256×	pre	128	true
5.0ms	18×	body	2048	valid
3.0ms	8×	body	4096	valid
2.0ms	10×	body	1024	valid
1.0ms	9×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

11.1b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
18.0b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_1101`
21×	`add-sqr-sqrt_binary64_1123`
20×	`add-cube-cbrt_binary64_1136`
18×	`times-frac_binary64_1107`
15×	`sqrt-prod_binary64_1117`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
5×	`pow1_binary64_1162`
4×	`flip3-+_binary64_1104` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
3×	`associate-/l*_binary64_1046`
2×	`sum-log_binary64_1192` `associate-/r/_binary64_1047` `+-commutative_binary64_1031`
1×	`rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`

Counts

4 → 79

Calls

4 calls:

13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
5.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

series131.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
32.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
29.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
26.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify90.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4921	2082
1	4921	2082

prune146.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	12	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Error

10.8b

Counts

92 → 12

Compiler

Compiled 2562 to 1688 computations (34.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
18.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
18.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1101`
8×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140`
6×	`pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
4×	`add-exp-log_binary64_1139` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
2×	`rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `+-commutative_binary64_1031` `pow1/2_binary64_1181`

Counts

4 → 54

Calls

4 calls:

17.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series135.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
40.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
27.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
27.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify109.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4841	1308
1	4841	1308

prune130.0ms (2.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	66	12	78

Error

10.8b

Counts

78 → 12

Compiler

Compiled 2891 to 1929 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
2.7b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
18.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1123`
24×	`associate-r_binary64_1041`
22×	`times-frac_binary64_1107`
21×	`*-un-lft-identity_binary64_1101`
19×	`add-cube-cbrt_binary64_1136`
14×	`sqrt-prod_binary64_1117`
13×	`add-exp-log_binary64_1139`
9×	`add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140`
7×	`pow1_binary64_1162`
5×	`unswap-sqr_binary64_1069`
4×	`prod-exp_binary64_1150` `flip3-+_binary64_1104` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
3×	`associate-l_binary64_1042`
2×	`cbrt-unprod_binary64_1134` `sum-log_binary64_1192` `associate-/r/_binary64_1047` `+-commutative_binary64_1031` `div-exp_binary64_1152`
1×	`-commutative_binary64_1032` `1-exp_binary64_1145` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-r/_binary64_1043` `div-inv_binary64_1098` `rec-exp_binary64_1151` `pow-prod-down_binary64_1172` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181` `un-div-inv_binary64_1099`

Counts

4 → 86

Calls

4 calls:

15.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
6.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
3.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))

series131.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
32.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
32.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
23.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5054	1934

prune142.0ms (2.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	98	12	110

Error

10.8b

Counts

110 → 12

Compiler

Compiled 2841 to 1946 computations (31.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.1b	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
18.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
18.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite63.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_1117`
58×	`add-sqr-sqrt_binary64_1123`
34×	`sqrt-pow1_binary64_1119`
29×	`pow1_binary64_1162`
28×	`sqrt-div_binary64_1118`
20×	`*-un-lft-identity_binary64_1101`
18×	`add-cube-cbrt_binary64_1136` `pow1/2_binary64_1181`
15×	`swap-sqr_binary64_1068`
10×	`rem-sqrt-square_binary64_1114`
9×	`pow-prod-up_binary64_1171` `flip3-+_binary64_1104` `associate-r_binary64_1041` `flip-+_binary64_1075` `associate-l_binary64_1042` `unswap-sqr_binary64_1069`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
4×	`frac-times_binary64_1111` `sqr-abs_binary64_1116`
2×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `rem-square-sqrt_binary64_1113` `sum-log_binary64_1192` `+-commutative_binary64_1031` `sqrt-unprod_binary64_1121` `pow2_binary64_1182`

Counts

4 → 129

Calls

4 calls:

25.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
10.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series127.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
29.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
26.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
26.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify104.0ms (2%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4925	2792
1	4925	2792

prune207.0ms (3.9%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	139	14	153

Error

10.8b

Counts

153 → 14

Compiler

Compiled 4182 to 2723 computations (34.9% saved)

regimes544.0ms (10.3%)

Accuracy

Total 0.3b remaining (2.1%)

Threshold costs 0.3b (2.1%)

Compiler

Compiled 7833 to 5956 computations (24% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	30
1	23	30

end0.0ms (0%)

sample2.0s (38.4%)

Algorithm

1×

intervals

Results

329.0ms	6122×	body	128	valid
199.0ms	722×	body	2048	valid
155.0ms	8000×	pre	128	true
107.0ms	501×	body	1024	valid
85.0ms	257×	body	4096	valid
40.0ms	258×	body	512	valid
15.0ms	140×	body	256	valid

Compiler

Compiled 1115 to 845 computations (24.2% saved)

Details

analyze794.0ms (15%)

sample36.0ms (0.7%)

simplify103.0ms (1.9%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

rewrite39.0ms (0.7%)

series131.0ms (2.5%)

simplify90.0ms (1.7%)

prune146.0ms (2.8%)

localize14.0ms (0.3%)

rewrite48.0ms (0.9%)

series135.0ms (2.6%)

simplify109.0ms (2.1%)

prune130.0ms (2.5%)

localize12.0ms (0.2%)

rewrite38.0ms (0.7%)

series131.0ms (2.5%)

simplify84.0ms (1.6%)

prune142.0ms (2.7%)

localize14.0ms (0.3%)

rewrite63.0ms (1.2%)

series127.0ms (2.4%)

simplify104.0ms (2%)

prune207.0ms (3.9%)

regimes544.0ms (10.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (38.4%)

Profiling