Details

analyze349.0ms (4.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2024	42
1	2024	42
0	2	2
1	2	2

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)

sample26.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	8×	body	128	nan
0.0ms	7×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune4.0ms (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)

localize9.0ms (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)))

rewrite191.0ms (2.6%)

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:

15.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 2373 to 1883 computations (20.6% saved)

series321.0ms (4.4%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

147.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
108.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
28.0ms	(*.f64 (-.f64 a 1/3) 9)
16.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 850 to 737 computations (13.3% saved)

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5010	2067

prune159.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Error

Counts

125 → 5

Compiler

Compiled 2460 to 1933 computations (21.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite921.0ms (12.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

372×	`times-frac_binary64_1107`
246×	`*-un-lft-identity_binary64_1101`
244×	`add-sqr-sqrt_binary64_1123`
218×	`sqrt-prod_binary64_1117`
190×	`add-cube-cbrt_binary64_1136`
33×	`associate-/l*_binary64_1046`
26×	`difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053`
16×	`sqrt-div_binary64_1118` `associate-/r/_binary64_1047`
14×	`associate-/r*_binary64_1045`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
11×	`flip3--_binary64_1105` `flip--_binary64_1076`
9×	`div-inv_binary64_1098`
6×	`pow1_binary64_1162` `add-log-exp_binary64_1140`
5×	`associate-l_binary64_1042`
4×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip3-+_binary64_1104` `frac-times_binary64_1111` `flip-+_binary64_1075` `associate-r_binary64_1041`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `distribute-lft-out_binary64_1052`
1×	`associate-/l/_binary64_1048` `pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `*-commutative_binary64_1032` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 323

Calls

4 calls:

60.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
55.0ms	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
16.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 9333 to 7319 computations (21.6% saved)

series474.0ms (6.5%)

Error

Counts

4 → 30

Calls

4 calls:

150.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
115.0ms	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
101.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
88.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 1179 to 1029 computations (12.7% saved)

simplify133.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

353 → 353

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4959	8777
1	4959	8777

prune561.0ms (7.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	352	1	353
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	353	5	358

Error

Counts

358 → 5

Compiler

Compiled 8493 to 6479 computations (23.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a 1/3))
0.0b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
0.3b	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.4b	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))

rewrite129.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-sqr-sqrt_binary64_1123`
14×	`-un-lft-identity_binary64_1101` `associate-r/_binary64_1043`
12×	`pow1_binary64_1162`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-prod_binary64_1117`
10×	`add-cube-cbrt_binary64_1136` `sqrt-div_binary64_1118`
9×	`add-log-exp_binary64_1140` `associate-r_binary64_1041`
7×	`flip3--_binary64_1105` `flip--_binary64_1076`
6×	`associate-l_binary64_1042`
4×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `frac-add_binary64_1109` `associate-+l+_binary64_1034`
3×	`cancel-sign-sub-inv_binary64_1067`
2×	`*-commutative_binary64_1032` `unswap-sqr_binary64_1069` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `sum-log_binary64_1192`
1×	`diff-log_binary64_1193` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-+l-_binary64_1036` `sub-neg_binary64_1094` `+-commutative_binary64_1031` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
8.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
8.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
3.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 1785 to 1369 computations (23.3% saved)

series263.0ms (3.6%)

Error

Counts

4 → 24

Calls

4 calls:

89.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
81.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
67.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
12.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 788 to 671 computations (14.8% saved)

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4934	1567
1	4934	1567

prune107.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	108	5	113

Error

Counts

113 → 5

Compiler

Compiled 1803 to 1374 computations (23.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
0.2b	(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
0.4b	(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

rewrite260.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

65×	`add-sqr-sqrt_binary64_1123`
55×	`*-un-lft-identity_binary64_1101`
50×	`times-frac_binary64_1107`
39×	`add-cube-cbrt_binary64_1136`
36×	`sqrt-prod_binary64_1117`
33×	`associate-r_binary64_1041`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`pow1_binary64_1162` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `associate-/r_binary64_1045` `associate-l*_binary64_1042`
6×	`add-log-exp_binary64_1140`
5×	`flip3--_binary64_1105` `flip--_binary64_1076`
4×	`sqrt-div_binary64_1118` `associate-/r/_binary64_1047` `unswap-sqr_binary64_1069` `flip3-+_binary64_1104` `frac-times_binary64_1111` `flip-+_binary64_1075`
3×	`associate-/l_binary64_1046` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `associate-r/_binary64_1043`
2×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `div-inv_binary64_1098` `pow-prod-down_binary64_1172` `-commutative_binary64_1032` `associate-l/_binary64_1044`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 140

Calls

4 calls:

17.0ms	(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
9.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
7.0ms	(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))
3.0ms	(+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))

Compiler

Compiled 3491 to 2840 computations (18.6% saved)

series404.0ms (5.6%)

Error

Counts

4 → 27

Calls

4 calls:

144.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))
118.0ms	(+.f64 1 (*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))
103.0ms	(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
20.0ms	(/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 1015 to 889 computations (12.4% saved)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4981	2962
1	4981	2962

prune212.0ms (2.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	167	5	172

Error

Counts

172 → 5

Compiler

Compiled 3405 to 2737 computations (19.6% saved)

regimes449.0ms (6.2%)

Accuracy

Total 0.1b remaining (98.9%)

Threshold costs 0.1b (98.9%)

Compiler

Compiled 5394 to 4694 computations (13% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	21
1	25	21

end0.0ms (0%)

sample2.0s (27%)

Algorithm

1×

intervals

Results

471.0ms	8000×	body	128	valid
17.0ms	265×	body	128	nan
14.0ms	249×	body	128	invalid

Compiler

Compiled 1370 to 1194 computations (12.8% saved)

Details

analyze349.0ms (4.8%)

sample26.0ms (0.4%)

simplify73.0ms (1%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite191.0ms (2.6%)

series321.0ms (4.4%)

simplify68.0ms (0.9%)

prune159.0ms (2.2%)

localize10.0ms (0.1%)

rewrite921.0ms (12.7%)

series474.0ms (6.5%)

simplify133.0ms (1.8%)

prune561.0ms (7.7%)

localize7.0ms (0.1%)

rewrite129.0ms (1.8%)

series263.0ms (3.6%)

simplify73.0ms (1%)

prune107.0ms (1.5%)

localize9.0ms (0.1%)

rewrite260.0ms (3.6%)

series404.0ms (5.6%)

simplify74.0ms (1%)

prune212.0ms (2.9%)

regimes449.0ms (6.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (27%)

Profiling