Details

analyze892.0ms (8.5%)

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)

sample42.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	87×	body	128	nan
1.0ms	38×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify8.0ms (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

18.3b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

2.4b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.2b	(/.f64 A (*.f64 V l))
13.4b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite124.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

10.4b

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)

series410.0ms (3.9%)

Error

18.3b

Counts

3 → 30

Calls

3 calls:

189.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
137.0ms	(/.f64 A (*.f64 V l))
71.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Compiler

Compiled 1032 to 758 computations (26.6% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4894	1105
1	4894	1105

prune91.0ms (0.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	81	15	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	15	97

Error

10.4b

Counts

97 → 15

Compiler

Compiled 1303 to 385 computations (70.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
2.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
5.0b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
13.4b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

rewrite158.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

6.3b

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:

21.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
17.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
13.0ms	(.f64 c0 (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)

series591.0ms (5.6%)

Error

10.4b

Counts

4 → 33

Calls

4 calls:

186.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
179.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
120.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
84.0ms	(cbrt.f64 A)

Compiler

Compiled 1252 to 940 computations (24.9% saved)

simplify111.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5074	1761

prune127.0ms (1.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	5	9	14
Picked	0	1	1
Done	0	0	0
Total	140	14	154

Error

6.3b

Counts

154 → 14

Compiler

Compiled 2220 to 706 computations (68.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

2.4b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
5.4b	(/.f64 (/.f64 A V) l)
13.4b	(sqrt.f64 (/.f64 (/.f64 A V) l))

rewrite246.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

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)))
8.0ms	(sqrt.f64 (/.f64 (/.f64 A V) l))
6.0ms	(/.f64 (/.f64 A V) l)

Compiler

Compiled 3504 to 961 computations (72.6% saved)

series638.0ms (6.1%)

Error

6.3b

Counts

3 → 30

Calls

3 calls:

345.0ms	(sqrt.f64 (/.f64 (/.f64 A V) l))
152.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
129.0ms	(/.f64 (/.f64 A V) l)

Compiler

Compiled 1032 to 758 computations (26.6% saved)

simplify158.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4917	3725
1	4917	3725

prune195.0ms (1.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	208	13	221
Fresh	9	3	12
Picked	0	1	1
Done	1	0	1
Total	218	17	235

Error

0.1b

Counts

235 → 17

Compiler

Compiled 3692 to 970 computations (73.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 l)
0.5b	(cbrt.f64 l)
0.6b	(cbrt.f64 A)
0.6b	(cbrt.f64 A)

rewrite72.0ms (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:

2.0ms	(cbrt.f64 A)
2.0ms	(cbrt.f64 A)
2.0ms	(cbrt.f64 l)
2.0ms	(cbrt.f64 l)

Compiler

Compiled 1108 to 237 computations (78.6% saved)

series429.0ms (4.1%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt.f64 l)
105.0ms	(cbrt.f64 l)
96.0ms	(cbrt.f64 A)
86.0ms	(cbrt.f64 A)

Compiler

Compiled 852 to 540 computations (36.6% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4832	324
1	4832	324

prune61.0ms (0.6%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	2	13	15
Picked	0	1	1
Done	0	1	1
Total	54	19	73

Error

0.0b

Counts

73 → 19

Compiler

Compiled 1340 to 266 computations (80.1% saved)

regimes2.2s (21.4%)

Accuracy

Total 1.1b remaining (96.8%)

Threshold costs 0b (0%)

Compiler

Compiled 22037 to 15149 computations (31.3% saved)

bsearch0.0ms (0%)

simplify16.0ms (0.2%)

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%)

sample3.6s (34.6%)

Algorithm

1×

intervals

Results

347.0ms	8000×	body	128	valid
122.0ms	2984×	body	128	nan
44.0ms	886×	body	128	invalid

Compiler

Compiled 2573 to 1784 computations (30.7% saved)

Details

analyze892.0ms (8.5%)

sample42.0ms (0.4%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite124.0ms (1.2%)

series410.0ms (3.9%)

simplify108.0ms (1%)

prune91.0ms (0.9%)

localize22.0ms (0.2%)

rewrite158.0ms (1.5%)

series591.0ms (5.6%)

simplify111.0ms (1.1%)

prune127.0ms (1.2%)

localize6.0ms (0.1%)

rewrite246.0ms (2.3%)

series638.0ms (6.1%)

simplify158.0ms (1.5%)

prune195.0ms (1.9%)

localize14.0ms (0.1%)

rewrite72.0ms (0.7%)

series429.0ms (4.1%)

simplify108.0ms (1%)

prune61.0ms (0.6%)

regimes2.2s (21.4%)

bsearch0.0ms (0%)

simplify16.0ms (0.2%)

end0.0ms (0%)

sample3.6s (34.6%)

Profiling