Details

analyze395.0ms (4.9%)

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 (0.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan
0.0ms	7×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune5.0ms (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)

localize12.0ms (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)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.6b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite232.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`pow-prod-down_binary64_1172` `associate-/l*_binary64_1046` `flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`sqrt-pow1_binary64_1119` `associate-/r/_binary64_1047` `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×	`pow1/2_binary64_1181` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `distribute-lft-out_binary64_1052`

Counts

4 → 99

Calls

4 calls:

23.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(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)

Compiler

Compiled 2373 to 1883 computations (20.6% saved)

series396.0ms (4.9%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

175.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
142.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
39.0ms	(*.f64 (-.f64 a 1/3) 9)
18.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 850 to 737 computations (13.3% saved)

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5010	2067

prune185.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Error

Counts

125 → 8

Compiler

Compiled 2554 to 2019 computations (20.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite133.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`*-un-lft-identity_binary64_1101`
14×	`add-sqr-sqrt_binary64_1123`
12×	`pow1_binary64_1162`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`add-cube-cbrt_binary64_1136` `sqrt-prod_binary64_1117`
8×	`associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-r/_binary64_1043` `associate-l*_binary64_1042`
4×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`distribute-lft-out_binary64_1052`
2×	`*-commutative_binary64_1032` `unswap-sqr_binary64_1069`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 73

Calls

4 calls:

16.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
11.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
3.0ms	(sqrt.f64 (+.f64 -1/3 a))
3.0ms	(+.f64 -1/3 a)

Compiler

Compiled 1358 to 1046 computations (23% saved)

series244.0ms (3%)

Error

Counts

4 → 21

Calls

4 calls:

104.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
85.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
21.0ms	(+.f64 -1/3 a)
18.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 753 to 630 computations (16.3% saved)

simplify107.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4904	922
1	4904	922

prune117.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	94	8	102

Error

Counts

102 → 8

Compiler

Compiled 1563 to 1207 computations (22.8% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite736.0ms (9.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

330×	`times-frac_binary64_1107`
233×	`*-un-lft-identity_binary64_1101`
188×	`sqrt-prod_binary64_1117`
182×	`add-sqr-sqrt_binary64_1123`
177×	`add-cube-cbrt_binary64_1136`
30×	`associate-/l*_binary64_1046`
27×	`distribute-lft-out_binary64_1052`
18×	`sqrt-div_binary64_1118`
16×	`associate-/r/_binary64_1047`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
12×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
9×	`div-inv_binary64_1098`
7×	`pow1_binary64_1162`
5×	`associate-l_binary64_1042`
4×	`div-exp_binary64_1152` `add-log-exp_binary64_1140` `cbrt-undiv_binary64_1135` `frac-times_binary64_1111` `associate-r_binary64_1041`
3×	`flip3--_binary64_1105` `flip--_binary64_1076`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-l/_binary64_1044` `associate-r/_binary64_1043`
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` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 302

Calls

4 calls:

60.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
14.0ms	(/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))
6.0ms	(/.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
3.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 8545 to 6746 computations (21.1% saved)

series402.0ms (5%)

Error

Counts

4 → 24

Calls

4 calls:

177.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))))
99.0ms	(/.f64 (/.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (sqrt.f64 9))
82.0ms	(/.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
14.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 994 to 863 computations (13.2% saved)

simplify146.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4986	7703
1	4986	7703

prune626.0ms (7.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	326	0	326
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	326	8	334

Error

Counts

334 → 8

Compiler

Compiled 7779 to 5987 computations (23% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite122.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`*-un-lft-identity_binary64_1101`
12×	`pow1_binary64_1162` `add-sqr-sqrt_binary64_1123`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`associate-r_binary64_1041`
9×	`add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
8×	`sqrt-prod_binary64_1117`
4×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `associate-l_binary64_1042` `sqrt-div_binary64_1118`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192`
2×	`-commutative_binary64_1032` `associate-r/_binary64_1043`
1×	`unswap-sqr_binary64_1069` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-+r+_binary64_1033` `+-commutative_binary64_1031`

Counts

4 → 72

Calls

4 calls:

8.0ms	(.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))
6.0ms	(*.f64 1/3 rand)
5.0ms	(+.f64 -1/3 (+.f64 a (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))))
3.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 1379 to 1071 computations (22.3% saved)

series253.0ms (3.1%)

Error

Counts

4 → 21

Calls

4 calls:

120.0ms	(+.f64 -1/3 (+.f64 a (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))))
85.0ms	(.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))
18.0ms	(*.f64 1/3 rand)
14.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 663 to 573 computations (13.6% saved)

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5142	1093

prune103.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	93	8	101

Error

Counts

101 → 8

Compiler

Compiled 1418 to 1091 computations (23.1% saved)

regimes686.0ms (8.5%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Compiler

Compiled 6506 to 5806 computations (10.8% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	18
1	25	18

end0.0ms (0%)

sample2.8s (35.3%)

Algorithm

1×

intervals

Results

551.0ms	8000×	body	128	valid
17.0ms	284×	body	128	nan
16.0ms	244×	body	128	invalid

Compiler

Compiled 1646 to 1470 computations (10.7% saved)

Details

analyze395.0ms (4.9%)

sample26.0ms (0.3%)

simplify82.0ms (1%)

prune5.0ms (0.1%)

localize12.0ms (0.1%)

rewrite232.0ms (2.9%)

series396.0ms (4.9%)

simplify74.0ms (0.9%)

prune185.0ms (2.3%)

localize8.0ms (0.1%)

rewrite133.0ms (1.7%)

series244.0ms (3%)

simplify107.0ms (1.3%)

prune117.0ms (1.5%)

localize22.0ms (0.3%)

rewrite736.0ms (9.2%)

series402.0ms (5%)

simplify146.0ms (1.8%)

prune626.0ms (7.8%)

localize10.0ms (0.1%)

rewrite122.0ms (1.5%)

series253.0ms (3.1%)

simplify78.0ms (1%)

prune103.0ms (1.3%)

regimes686.0ms (8.5%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.8s (35.3%)

Profiling