Details

analyze702.0ms (4.8%)

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)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	90×	body	128	nan
1.0ms	39×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

prune3.0ms (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

19.6b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

2.4b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.8b	(/.f64 A (*.f64 V l))
14.6b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite91.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

11.3b

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)

series354.0ms (2.4%)

Error

19.6b

Counts

3 → 30

Calls

3 calls:

157.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
113.0ms	(/.f64 A (*.f64 V l))
70.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Compiler

Compiled 1032 to 758 computations (26.6% saved)

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4894	1105
1	4894	1105

prune95.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	83	13	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	13	97

Error

11.3b

Counts

97 → 13

Compiler

Compiled 1253 to 363 computations (71% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b	(/.f64 V (/.f64 (cbrt.f64 A) l))
2.4b	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
2.4b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
14.6b	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

rewrite673.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

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` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `associate-/l*_binary64_1046`
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:

34.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
22.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
19.0ms	(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)

series748.0ms (5.1%)

Error

11.3b

Counts

4 → 39

Calls

4 calls:

330.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))
176.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
138.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
81.0ms	(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)

simplify169.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

502 → 502

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4992	12589
1	4992	12589

prune457.0ms (3.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	492	10	502
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	498	17	515

Error

2.8b

Counts

515 → 17

Compiler

Compiled 12001 to 2245 computations (81.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.5b	(/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l))
2.4b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))))
6.6b	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))

rewrite107.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

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` `associate-*r/_binary64_1043` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-r_binary64_1041` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r_binary64_1045` `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)))))
6.0ms	(/.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 A)

Compiler

Compiled 1859 to 386 computations (79.2% saved)

series1.5s (9.9%)

Error

2.3b

Counts

4 → 33

Calls

4 calls:

625.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))))
386.0ms	(/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l))
340.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 (cbrt.f64 V) l)))
73.0ms	(cbrt.f64 A)

Compiler

Compiled 2310 to 1803 computations (21.9% saved)

simplify106.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4972	1810
1	4972	1810

prune122.0ms (0.8%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	105	23	128

Error

2.3b

Counts

128 → 23

Compiler

Compiled 2621 to 838 computations (68% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
0.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l))
2.4b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))))
6.6b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))

rewrite265.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

61×	`add-sqr-sqrt_binary64_1123`
50×	`times-frac_binary64_1107`
46×	`cbrt-prod_binary64_1132`
32×	`associate-r_binary64_1041`
30×	`add-exp-log_binary64_1139`
28×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
19×	`add-cbrt-cube_binary64_1137`
14×	`pow1_binary64_1162`
13×	`associate-l_binary64_1042`
12×	`unswap-sqr_binary64_1069`
11×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
9×	`associate-*r/_binary64_1043`
7×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
6×	`sqrt-div_binary64_1118`
5×	`pow-prod-down_binary64_1172`
4×	`add-log-exp_binary64_1140`
3×	`frac-times_binary64_1111` `associate-*l/_binary64_1044`
2×	`sqrt-pow1_binary64_1119` `*-commutative_binary64_1032` `div-inv_binary64_1098`
1×	`pow1/2_binary64_1181` `sqrt-prod_binary64_1117` `pow1/3_binary64_1183`

Counts

4 → 123

Calls

4 calls:

25.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l))
17.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))))
12.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))
1.0ms	(cbrt.f64 A)

Compiler

Compiled 4487 to 733 computations (83.7% saved)

series1.5s (10.3%)

Error

2.3b

Counts

4 → 33

Calls

4 calls:

647.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))))
400.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l))
352.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (cbrt.f64 V)) (/.f64 (cbrt.f64 (cbrt.f64 A)) l)))
86.0ms	(cbrt.f64 A)

Compiler

Compiled 2391 to 1835 computations (23.3% saved)

simplify100.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5002	3259

prune169.0ms (1.1%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	150	6	156
Fresh	4	17	21
Picked	1	0	1
Done	1	0	1
Total	156	23	179

Error

0.3b

Counts

179 → 23

Compiler

Compiled 4062 to 1080 computations (73.4% saved)

regimes3.2s (22.1%)

Accuracy

Total 4.1b remaining (95.2%)

Threshold costs 0b (0%)

Compiler

Compiled 30153 to 20003 computations (33.7% saved)

bsearch72.0ms (0.5%)

Steps

Iters	Range		Point
10	-1.3337987288450902e-304	1.6341603030821176e-301	2.9757661883394e-311

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	100
1	38	100

Compiler

Compiled 120 to 64 computations (46.7% saved)

end0.0ms (0%)

sample4.1s (27.6%)

Algorithm

1×

intervals

Results

284.0ms	8000×	body	128	valid
102.0ms	3027×	body	128	nan
38.0ms	904×	body	128	invalid

Compiler

Compiled 3625 to 2402 computations (33.7% saved)

Details

analyze702.0ms (4.8%)

sample40.0ms (0.3%)

simplify12.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0%)

rewrite91.0ms (0.6%)

series354.0ms (2.4%)

simplify79.0ms (0.5%)

prune95.0ms (0.6%)

localize11.0ms (0.1%)

rewrite673.0ms (4.6%)

series748.0ms (5.1%)

simplify169.0ms (1.1%)

prune457.0ms (3.1%)

localize13.0ms (0.1%)

rewrite107.0ms (0.7%)

series1.5s (9.9%)

simplify106.0ms (0.7%)

prune122.0ms (0.8%)

localize17.0ms (0.1%)

rewrite265.0ms (1.8%)

series1.5s (10.3%)

simplify100.0ms (0.7%)

prune169.0ms (1.1%)

regimes3.2s (22.1%)

bsearch72.0ms (0.5%)

simplify13.0ms (0.1%)

end0.0ms (0%)

sample4.1s (27.6%)

Profiling