Details

analyze459.0ms (8.9%)

Algorithm

1×

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

Compiler

Compiled 9 to 9 computations (0% saved)

sample27.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
3.0ms	96×	body	128	nan
1.0ms	27×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify168.0ms (3.2%)

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

Merged error: 20.1b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.4b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.6b	(/.f64 A (*.f64 V l))
15.7b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1123`
15×	`sqrt-prod_binary64_1117`
11×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
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×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sqrt-div_binary64_1118` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `associate-/r*_binary64_1045` `pow1/2_binary64_1181`

Counts

3 → 66

Calls

3 calls:

10.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

series192.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

100.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
56.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
35.0ms	(/.f64 A (*.f64 V l))

simplify91.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4937	857
1	4937	857

prune80.0ms (1.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	60	15	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	16	76

Merged error: 8.3b

Counts

76 → 16

Compiler

Compiled 1100 to 374 computations (66% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
4.0b	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
15.7b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

18.0ms	(.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))))
9.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))
1.0ms	(cbrt.f64 A)

series479.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt.f64 A)
137.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
97.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))
93.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l)))

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4920	1503
1	4920	1503

prune102.0ms (2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	113	5	118
Fresh	6	8	14
Picked	1	0	1
Done	0	1	1
Total	120	14	134

Merged error: 5.9b

Counts

134 → 14

Compiler

Compiled 2010 to 700 computations (65.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

1.4b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
5.6b	(*.f64 (/.f64 A V) (/.f64 1 l))
15.7b	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_1123`
27×	`add-exp-log_binary64_1139`
25×	`times-frac_binary64_1107`
21×	`*-un-lft-identity_binary64_1101`
19×	`add-cube-cbrt_binary64_1136`
17×	`add-cbrt-cube_binary64_1137` `associate-r_binary64_1041`
16×	`associate-l_binary64_1042`
10×	`pow1_binary64_1162`
9×	`prod-exp_binary64_1150`
8×	`sqrt-div_binary64_1118` `div-exp_binary64_1152`
7×	`associate-*r/_binary64_1043` `unswap-sqr_binary64_1069`
5×	`cbrt-unprod_binary64_1134`
4×	`cbrt-undiv_binary64_1135`
3×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `pow-prod-down_binary64_1172` `associate-*l/_binary64_1044` `un-div-inv_binary64_1099`
2×	`*-commutative_binary64_1032` `1-exp_binary64_1145` `sqrt-pow1_binary64_1119` `sqrt-prod_binary64_1117` `div-inv_binary64_1098` `rec-exp_binary64_1151`
1×	`pow1/2_binary64_1181`

Counts

3 → 95

Calls

3 calls:

12.0ms	(*.f64 (/.f64 A V) (/.f64 1 l))
10.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
6.0ms	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))

series201.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 A V) (/.f64 1 l))))
64.0ms	(sqrt.f64 (*.f64 (/.f64 A V) (/.f64 1 l)))
34.0ms	(*.f64 (/.f64 A V) (/.f64 1 l))

simplify103.0ms (2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4875	1146
1	4875	1146

prune75.0ms (1.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	104	14	118

Merged error: 5.9b

Counts

118 → 14

Compiler

Compiled 1475 to 568 computations (61.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.4b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
5.3b	(/.f64 (/.f64 A l) V)
15.7b	(sqrt.f64 (/.f64 (/.f64 A l) V))

rewrite53.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

213×	`times-frac_binary64_1107`
134×	`add-sqr-sqrt_binary64_1123`
117×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
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×	`rem-sqrt-square_binary64_1114` `add-log-exp_binary64_1140` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-l_binary64_1042` `associate-/r*_binary64_1045`
2×	`sqrt-div_binary64_1118`
1×	`-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `pow1/2_binary64_1181`

Counts

3 → 191

Calls

3 calls:

18.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
8.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
7.0ms	(/.f64 (/.f64 A l) V)

series204.0ms (4%)

Counts

3 → 9

Calls

3 calls:

103.0ms	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A l) V)))
63.0ms	(sqrt.f64 (/.f64 (/.f64 A l) V))
38.0ms	(/.f64 (/.f64 A l) V)

simplify111.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5768	3477

prune155.0ms (3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	190	10	200
Fresh	6	5	11
Picked	1	0	1
Done	1	1	2
Total	198	16	214

Merged error: 0.1b

Counts

214 → 16

Compiler

Compiled 3242 to 765 computations (76.4% saved)

regimes854.0ms (16.5%)

Compiler: Compiled 8352 to 6326 computations (24.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	35
1	16	35

end0.0ms (0%)

sample1.6s (30.9%)

Algorithm

1×

intervals

Results

287.0ms	8000×	body	128	valid
104.0ms	3002×	body	128	nan
30.0ms	890×	body	128	invalid

Compiler

Compiled 965 to 733 computations (24% saved)

Details

analyze459.0ms (8.9%)

sample27.0ms (0.5%)

simplify168.0ms (3.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite24.0ms (0.5%)

series192.0ms (3.7%)

simplify91.0ms (1.8%)

prune80.0ms (1.5%)

localize10.0ms (0.2%)

rewrite50.0ms (1%)

series479.0ms (9.3%)

simplify73.0ms (1.4%)

prune102.0ms (2%)

localize8.0ms (0.2%)

rewrite36.0ms (0.7%)

series201.0ms (3.9%)

simplify103.0ms (2%)

prune75.0ms (1.5%)

localize6.0ms (0.1%)

rewrite53.0ms (1%)

series204.0ms (4%)

simplify111.0ms (2.2%)

prune155.0ms (3%)

regimes854.0ms (16.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (30.9%)

Profiling