Details

analyze140.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample44.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
1.0ms	8×	body	128	invalid
1.0ms	10×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify263.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune8.0ms (0.1%)

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

0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite330.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`add-sqr-sqrt_binary64_1123`
23×	`*-un-lft-identity_binary64_1101`
17×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
11×	`pow1_binary64_1162`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-l_binary64_1042`
8×	`associate-*l/_binary64_1044`
7×	`associate-r_binary64_1041`
6×	`flip3--_binary64_1105` `flip--_binary64_1076`
5×	`sqrt-prod_binary64_1117`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-/r*_binary64_1045` `frac-times_binary64_1111`
3×	`associate-/l*_binary64_1046` `pow-prod-down_binary64_1172` `flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`associate-/r/_binary64_1047` `sqrt-pow1_binary64_1119` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069` `associate-r/_binary64_1043` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `-commutative_binary64_1032`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `pow1/2_binary64_1181` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `distribute-lft-out_binary64_1052`

Counts

4 → 99

Calls

4 calls:

28.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
14.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
13.0ms	(*.f64 (-.f64 a 1/3) 9)
9.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 2373 to 1883 computations (20.6% saved)

series519.0ms (4.7%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

234.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
172.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
51.0ms	(*.f64 (-.f64 a 1/3) 9)
27.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 850 to 737 computations (13.3% saved)

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5010	2067

prune250.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	6	125

Error

0.0b

Counts

125 → 6

Compiler

Compiled 2497 to 1970 computations (21.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a 1/3)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
0.2b	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
0.3b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)

rewrite276.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`add-sqr-sqrt_binary64_1123`
20×	`*-un-lft-identity_binary64_1101`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-l_binary64_1042`
12×	`add-cube-cbrt_binary64_1136`
8×	`pow1_binary64_1162`
7×	`associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140` `sqrt-prod_binary64_1117` `flip3--_binary64_1105` `associate-*l/_binary64_1044` `flip--_binary64_1076`
4×	`sqrt-div_binary64_1118` `frac-times_binary64_1111`
3×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `times-frac_binary64_1107` `associate-/l*_binary64_1046` `flip3-+_binary64_1104` `flip-+_binary64_1075` `cancel-sign-sub-inv_binary64_1067`
2×	`pow-prod-down_binary64_1172` `-commutative_binary64_1032` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r/_binary64_1047` `associate-r/_binary64_1043`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r*_binary64_1045` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `distribute-lft-out_binary64_1052` `diff-log_binary64_1193` `sub-neg_binary64_1094`

Counts

4 → 96

Calls

4 calls:

22.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
17.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
14.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
7.0ms	(-.f64 a 1/3)

Compiler

Compiled 2252 to 1796 computations (20.2% saved)

series512.0ms (4.6%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

236.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
179.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
38.0ms	(-.f64 a 1/3)
31.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)

Compiler

Compiled 870 to 759 computations (12.8% saved)

simplify119.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4930	1833
1	4930	1833

prune228.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	120	6	126

Error

0.0b

Counts

126 → 6

Compiler

Compiled 2351 to 1865 computations (20.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
0.3b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 1/3 rand))
0.3b	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
0.3b	(*.f64 1/3 rand)

rewrite511.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

60×	`add-sqr-sqrt_binary64_1123`
56×	`*-un-lft-identity_binary64_1101`
48×	`times-frac_binary64_1107`
40×	`add-cube-cbrt_binary64_1136`
38×	`associate-l_binary64_1042`
35×	`sqrt-prod_binary64_1117`
34×	`add-exp-log_binary64_1139`
22×	`add-cbrt-cube_binary64_1137`
15×	`pow1_binary64_1162`
14×	`prod-exp_binary64_1150`
8×	`cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `associate-/r*_binary64_1045`
7×	`associate-r_binary64_1041`
6×	`div-exp_binary64_1152`
5×	`pow-prod-down_binary64_1172` `flip3--_binary64_1105` `flip--_binary64_1076`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-/r/_binary64_1047` `frac-times_binary64_1111`
3×	`-commutative_binary64_1032` `pow-flip_binary64_1175` `1-exp_binary64_1145` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `associate-/l_binary64_1046` `associate-*l/_binary64_1044` `flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`unswap-sqr_binary64_1069` `div-inv_binary64_1098` `associate-*r/_binary64_1043`
1×	`inv-pow_binary64_1186` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`

Counts

4 → 157

Calls

4 calls:

31.0ms	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 1/3 rand))
17.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
13.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
7.0ms	(*.f64 1/3 rand)

Compiler

Compiled 4083 to 3390 computations (17% saved)

series527.0ms (4.8%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

246.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 1/3 rand))))
192.0ms	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 1/3 rand))
34.0ms	(*.f64 1/3 rand)
30.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 832 to 729 computations (12.4% saved)

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4950	2697
1	4950	2697

prune411.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	178	6	184

Error

0.0b

Counts

184 → 6

Compiler

Compiled 3783 to 3095 computations (18.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))
0.1b	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))
0.2b	(/.f64 rand (.f64 (sqrt.f64 (sqrt.f64 (+.f64 -3 (.f64 a 9)))) (sqrt.f64 (sqrt.f64 (+.f64 -3 (*.f64 a 9))))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 -3 (.f64 a 9)))) (sqrt.f64 (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))

rewrite625.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

76×	`sqrt-prod_binary64_1117`
60×	`add-sqr-sqrt_binary64_1123`
52×	`sqrt-div_binary64_1118`
34×	`sqrt-pow1_binary64_1119`
29×	`pow1_binary64_1162`
20×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
18×	`pow1/2_binary64_1181`
15×	`swap-sqr_binary64_1068`
14×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`rem-sqrt-square_binary64_1114`
9×	`pow-prod-up_binary64_1171` `unswap-sqr_binary64_1069` `associate-l_binary64_1042` `associate-r_binary64_1041`
8×	`frac-times_binary64_1111` `associate-/r/_binary64_1047`
5×	`pow-prod-down_binary64_1172` `pow-sqr_binary64_1074`
4×	`add-log-exp_binary64_1140` `sqr-abs_binary64_1116` `associate-l/_binary64_1044` `associate-r/_binary64_1043`
3×	`times-frac_binary64_1107` `associate-/l*_binary64_1046`
2×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`pow2_binary64_1182` `pow-plus_binary64_1164` `sqrt-unprod_binary64_1121` `rem-square-sqrt_binary64_1113` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r_binary64_1045`

Counts

4 → 146

Calls

4 calls:

30.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 -3 (.f64 a 9)))) (sqrt.f64 (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))
27.0ms	(/.f64 rand (.f64 (sqrt.f64 (sqrt.f64 (+.f64 -3 (.f64 a 9)))) (sqrt.f64 (sqrt.f64 (+.f64 -3 (*.f64 a 9))))))
6.0ms	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))
5.0ms	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))

Compiler

Compiled 5021 to 4245 computations (15.5% saved)

series300.0ms (2.7%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

192.0ms	(/.f64 rand (.f64 (sqrt.f64 (sqrt.f64 (+.f64 -3 (.f64 a 9)))) (sqrt.f64 (sqrt.f64 (+.f64 -3 (*.f64 a 9))))))
30.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 -3 (.f64 a 9)))) (sqrt.f64 (sqrt.f64 (+.f64 -3 (*.f64 a 9)))))
29.0ms	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))
27.0ms	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))

Compiler

Compiled 784 to 672 computations (14.3% saved)

simplify155.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5027	2236

prune367.0ms (3.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	161	6	167

Error

0.0b

Counts

167 → 6

Compiler

Compiled 3819 to 3143 computations (17.7% saved)

regimes1.0s (9.2%)

Accuracy

Total 0.1b remaining (97.6%)

Threshold costs 0.1b (97.6%)

Compiler

Compiled 6422 to 5718 computations (11% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms (0%)

sample4.2s (37.7%)

Algorithm

1×

intervals

Results

820.0ms	8000×	body	128	valid
30.0ms	255×	body	128	nan
28.0ms	280×	body	128	invalid

Compiler

Compiled 1629 to 1451 computations (10.9% saved)

Details

analyze140.0ms (1.3%)

sample44.0ms (0.4%)

simplify263.0ms (2.4%)

prune8.0ms (0.1%)

localize16.0ms (0.1%)

rewrite330.0ms (3%)

series519.0ms (4.7%)

simplify111.0ms (1%)

prune250.0ms (2.3%)

localize17.0ms (0.1%)

rewrite276.0ms (2.5%)

series512.0ms (4.6%)

simplify119.0ms (1.1%)

prune228.0ms (2.1%)

localize19.0ms (0.2%)

rewrite511.0ms (4.6%)

series527.0ms (4.8%)

simplify101.0ms (0.9%)

prune411.0ms (3.7%)

localize25.0ms (0.2%)

rewrite625.0ms (5.6%)

series300.0ms (2.7%)

simplify155.0ms (1.4%)

prune367.0ms (3.3%)

regimes1.0s (9.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.2s (37.7%)

Profiling