Details

analyze742.0ms (6.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	84
1	60	84
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Symmetry

(sort V l)

Compiler

Compiled 9 to 9 computations (0% saved)

sample41.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	85×	body	128	nan
1.0ms	25×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	12
1	15	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

18.7b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.5b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
4.1b	(/.f64 A (*.f64 V l))
18.5b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite86.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

9.2b

Rules

16×	`add-sqr-sqrt_binary64_1123`
15×	`sqrt-prod_binary64_1117`
11×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-r_binary64_1041`
9×	`times-frac_binary64_1107`
6×	`pow1_binary64_1162`
3×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `associate-/l_binary64_1046` `associate-l*_binary64_1042`
2×	`sqrt-div_binary64_1118` `prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r_binary64_1045` `pow-prod-down_binary64_1172` `associate-r/_binary64_1043` `*-commutative_binary64_1032`

Counts

3 → 66

Calls

3 calls:

8.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
4.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Compiler

Compiled 937 to 244 computations (74% saved)

series330.0ms (2.7%)

Error

18.7b

Counts

3 → 30

Calls

3 calls:

150.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
101.0ms	(/.f64 A (*.f64 V l))
66.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Compiler

Compiled 1032 to 758 computations (26.6% saved)

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4894	1105
1	4894	1105

prune86.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Error

9.2b

Counts

97 → 12

Compiler

Compiled 1237 to 352 computations (71.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
2.0b	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
3.3b	(/.f64 V (/.f64 (cbrt.f64 A) l))
18.5b	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

rewrite602.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

849×	`times-frac_binary64_1107`
358×	`add-sqr-sqrt_binary64_1123`
331×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
157×	`sqrt-prod_binary64_1117`
146×	`cbrt-prod_binary64_1132`
93×	`associate-/r*_binary64_1045`
79×	`associate-r_binary64_1041`
32×	`add-exp-log_binary64_1139`
24×	`div-inv_binary64_1098`
23×	`add-cbrt-cube_binary64_1137`
15×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
8×	`associate-/r/_binary64_1047`
7×	`pow1_binary64_1162`
6×	`unswap-sqr_binary64_1069`
5×	`rem-sqrt-square_binary64_1114`
4×	`add-log-exp_binary64_1140` `associate-/l*_binary64_1046` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
3×	`associate-l_binary64_1042`
2×	`sqrt-div_binary64_1118` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `pow-prod-down_binary64_1172` `associate-r/_binary64_1043` `-commutative_binary64_1032`

Counts

4 → 463

Calls

4 calls:

37.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
18.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
18.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))
8.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))

Compiler

Compiled 12615 to 2772 computations (78% saved)

series716.0ms (5.9%)

Error

9.2b

Counts

4 → 39

Calls

4 calls:

326.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))
178.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
120.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
71.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

Compiler

Compiled 1588 to 1179 computations (25.8% saved)

simplify174.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

502 → 502

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4992	12589
1	4992	12589

prune426.0ms (3.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	493	9	502
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	498	16	514

Error

1.8b

Counts

514 → 16

Compiler

Compiled 12002 to 2235 computations (81.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 V)
1.5b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))))
2.2b	(/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l))
5.1b	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))

rewrite106.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

Rules

14×	`add-exp-log_binary64_1139` `add-sqr-sqrt_binary64_1123`
13×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
12×	`times-frac_binary64_1107` `cbrt-prod_binary64_1132`
11×	`add-cbrt-cube_binary64_1137`
10×	`pow1_binary64_1162` `sqrt-prod_binary64_1117`
6×	`associate-/l*_binary64_1046`
4×	`add-log-exp_binary64_1140` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
3×	`pow-prod-down_binary64_1172` `associate-l_binary64_1042`
2×	`sqrt-div_binary64_1118` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-*r/_binary64_1043`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r_binary64_1045` `associate-r_binary64_1041` `-commutative_binary64_1032` `pow1/3_binary64_1183`

Counts

4 → 78

Calls

4 calls:

10.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))))
5.0ms	(/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l))
5.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))
1.0ms	(cbrt.f64 V)

Compiler

Compiled 1859 to 404 computations (78.3% saved)

series1.4s (11.4%)

Error

1.2b

Counts

4 → 33

Calls

4 calls:

609.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))))
354.0ms	(/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l))
317.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))
71.0ms	(cbrt.f64 V)

Compiler

Compiled 2310 to 1805 computations (21.9% saved)

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4937	1812
1	4937	1812

prune112.0ms (0.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	109	18	127

Error

1.3b

Counts

127 → 18

Compiler

Compiled 2569 to 806 computations (68.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 V)
0.6b	(cbrt.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)))
1.5b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))))
5.1b	(sqrt.f64 (.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))

rewrite93.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

12×	`pow1_binary64_1162`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`associate-*r/_binary64_1043`
6×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `sqrt-div_binary64_1118` `*-un-lft-identity_binary64_1101`
4×	`add-log-exp_binary64_1140` `pow-prod-down_binary64_1172` `cbrt-prod_binary64_1132`
3×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `associate-l_binary64_1042`
2×	`sqrt-pow1_binary64_1119` `frac-times_binary64_1111` `associate-*l/_binary64_1044` `pow1/3_binary64_1183`
1×	`pow1/2_binary64_1181` `sqrt-prod_binary64_1117` `associate-r_binary64_1041` `*-commutative_binary64_1032`

Counts

4 → 55

Calls

4 calls:

14.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))))
9.0ms	(sqrt.f64 (.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))
4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)))
1.0ms	(cbrt.f64 V)

Compiler

Compiled 1859 to 291 computations (84.3% saved)

series1.2s (9.5%)

Error

1.2b

Counts

4 → 27

Calls

4 calls:

598.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))))
333.0ms	(sqrt.f64 (.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))
118.0ms	(cbrt.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)))
79.0ms	(cbrt.f64 V)

Compiler

Compiled 2028 to 1539 computations (24.1% saved)

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5020	1928

prune77.0ms (0.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	81	19	100

Error

0.4b

Counts

100 → 19

Compiler

Compiled 2200 to 464 computations (78.9% saved)

regimes2.3s (19%)

Accuracy

Total 2.6b remaining (90.4%)

Threshold costs 0b (0%)

Compiler

Compiled 22463 to 15298 computations (31.9% saved)

bsearch69.0ms (0.6%)

Steps

Iters	Range		Point
10	-6.0155462135221084e-307	9.807687794802345e-301	3.1183793200646e-310

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	109
1	43	109

Compiler

Compiled 130 to 72 computations (44.6% saved)

end0.0ms (0%)

sample3.3s (27.4%)

Algorithm

1×

intervals

Results

316.0ms	8000×	body	128	valid
108.0ms	3001×	body	128	nan
38.0ms	896×	body	128	invalid

Compiler

Compiled 2708 to 1843 computations (31.9% saved)

Details

analyze742.0ms (6.1%)

sample41.0ms (0.3%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite86.0ms (0.7%)

series330.0ms (2.7%)

simplify79.0ms (0.6%)

prune86.0ms (0.7%)

localize11.0ms (0.1%)

rewrite602.0ms (5%)

series716.0ms (5.9%)

simplify174.0ms (1.4%)

prune426.0ms (3.5%)

localize14.0ms (0.1%)

rewrite106.0ms (0.9%)

series1.4s (11.4%)

simplify91.0ms (0.7%)

prune112.0ms (0.9%)

localize19.0ms (0.2%)

rewrite93.0ms (0.8%)

series1.2s (9.5%)

simplify68.0ms (0.6%)

prune77.0ms (0.6%)

regimes2.3s (19%)

bsearch69.0ms (0.6%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample3.3s (27.4%)

Profiling