Details

analyze723.0ms (9.6%)

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)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	94×	body	128	nan
1.0ms	30×	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

22.4b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

2.3b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.5b	(/.f64 A (*.f64 V l))
15.8b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite88.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

11.6b

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:

14.0ms	(.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)

series332.0ms (4.4%)

Error

22.4b

Counts

3 → 30

Calls

3 calls:

148.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
102.0ms	(/.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 (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4894	1105
1	4894	1105

prune81.0ms (1.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	83	13	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	14	97

Error

11.6b

Counts

97 → 14

Compiler

Compiled 1256 to 361 computations (71.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
2.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
3.2b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
15.8b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

rewrite141.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

6.7b

Rules

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

Counts

4 → 106

Calls

4 calls:

18.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
12.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
8.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms	(cbrt.f64 A)

Compiler

Compiled 2506 to 501 computations (80% saved)

series447.0ms (5.9%)

Error

11.6b

Counts

4 → 33

Calls

4 calls:

155.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
125.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
77.0ms	(cbrt.f64 A)
74.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

Compiler

Compiled 1252 to 940 computations (24.9% saved)

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5074	1761

prune105.0ms (1.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	139	14	153

Error

6.6b

Counts

153 → 14

Compiler

Compiled 2212 to 697 computations (68.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

2.3b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
4.1b	(/.f64 (/.f64 A V) l)
15.8b	(sqrt.f64 (/.f64 (/.f64 A V) l))

rewrite207.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

213×	`times-frac_binary64_1107`
134×	`add-sqr-sqrt_binary64_1123`
117×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
89×	`sqrt-prod_binary64_1117`
46×	`associate-r_binary64_1041`
13×	`div-inv_binary64_1098` `associate-/l*_binary64_1046`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
6×	`pow1_binary64_1162`
4×	`unswap-sqr_binary64_1069`
3×	`add-log-exp_binary64_1140` `rem-sqrt-square_binary64_1114` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r_binary64_1045` `associate-l*_binary64_1042`
2×	`sqrt-div_binary64_1118`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `associate-r/_binary64_1043` `-commutative_binary64_1032`

Counts

3 → 191

Calls

3 calls:

18.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
7.0ms	(sqrt.f64 (/.f64 (/.f64 A V) l))
6.0ms	(/.f64 (/.f64 A V) l)

Compiler

Compiled 3504 to 961 computations (72.6% saved)

series317.0ms (4.2%)

Error

6.6b

Counts

3 → 30

Calls

3 calls:

141.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
94.0ms	(/.f64 (/.f64 A V) l)
69.0ms	(sqrt.f64 (/.f64 (/.f64 A V) l))

Compiler

Compiled 1032 to 758 computations (26.6% saved)

simplify128.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4917	3725
1	4917	3725

prune167.0ms (2.2%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	208	13	221
Fresh	6	5	11
Picked	1	0	1
Done	0	2	2
Total	215	20	235

Error

0.1b

Counts

235 → 20

Compiler

Compiled 3731 to 992 computations (73.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 V)
0.6b	(cbrt.f64 V)
0.6b	(cbrt.f64 l)
0.6b	(cbrt.f64 l)

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`cbrt-prod_binary64_1132`
8×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
4×	`pow1/3_binary64_1183` `pow1_binary64_1162` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt.f64 l)
1.0ms	(cbrt.f64 V)
1.0ms	(cbrt.f64 V)
1.0ms	(cbrt.f64 l)

Compiler

Compiled 1108 to 237 computations (78.6% saved)

series302.0ms (4%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt.f64 l)
73.0ms	(cbrt.f64 V)
72.0ms	(cbrt.f64 l)
69.0ms	(cbrt.f64 V)

Compiler

Compiled 852 to 540 computations (36.6% saved)

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4832	324
1	4832	324

prune50.0ms (0.7%)

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	2	15	17
Picked	0	1	1
Done	0	2	2
Total	53	23	76

Error

0.1b

Counts

76 → 23

Compiler

Compiled 1340 to 266 computations (80.1% saved)

regimes1.5s (19.8%)

Accuracy

Total 1.1b remaining (96%)

Threshold costs 0b (0%)

Compiler

Compiled 17704 to 12068 computations (31.8% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	35
1	16	35

Remove

(sort V l)

Compiler

Compiled 42 to 26 computations (38.1% saved)

end0.0ms (0%)

sample2.6s (34.1%)

Algorithm

1×

intervals

Results

289.0ms	8000×	body	128	valid
113.0ms	3054×	body	128	nan
37.0ms	836×	body	128	invalid

Compiler

Compiled 2067 to 1418 computations (31.4% saved)

Details

analyze723.0ms (9.6%)

sample38.0ms (0.5%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite88.0ms (1.2%)

series332.0ms (4.4%)

simplify79.0ms (1%)

prune81.0ms (1.1%)

localize10.0ms (0.1%)

rewrite141.0ms (1.9%)

series447.0ms (5.9%)

simplify76.0ms (1%)

prune105.0ms (1.4%)

localize6.0ms (0.1%)

rewrite207.0ms (2.7%)

series317.0ms (4.2%)

simplify128.0ms (1.7%)

prune167.0ms (2.2%)

localize14.0ms (0.2%)

rewrite52.0ms (0.7%)

series302.0ms (4%)

simplify82.0ms (1.1%)

prune50.0ms (0.7%)

regimes1.5s (19.8%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample2.6s (34.1%)

Profiling