Details

analyze75.0ms (1.7%)

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)

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid
0.0ms	6×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify153.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune6.0ms (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 (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.0b	(+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
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)))))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.7b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_100`
23×	`*-un-lft-identity_binary64_78`
17×	`add-cube-cbrt_binary64_113`
12×	`times-frac_binary64_84`
11×	`pow1_binary64_139`
10×	`add-cbrt-cube_binary64_114` `associate-l_binary64_19` `add-exp-log_binary64_116`
8×	`associate-*l/_binary64_21`
7×	`associate-r_binary64_18`
6×	`flip3--_binary64_82` `flip--_binary64_53`
5×	`sqrt-prod_binary64_94`
4×	`add-log-exp_binary64_117` `frac-times_binary64_88` `associate-/r*_binary64_22` `sqrt-div_binary64_95`
3×	`flip-+_binary64_52` `associate-/l*_binary64_23` `pow-prod-down_binary64_149` `flip3-+_binary64_81`
2×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `distribute-lft-out--_binary64_30` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47` `associate-/r/_binary64_24` `associate-r/_binary64_20`
1×	`distribute-lft-in_binary64_27` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `pow1/2_binary64_158`

Counts

4 → 99

Calls

8 calls:

14.0ms	(.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)
0.0ms	(-.f64 a 1/3)

series302.0ms (6.9%)

Counts

4 → 24

Calls

4 calls:

152.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
105.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
28.0ms	(*.f64 (-.f64 a 1/3) 9)
17.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 587 to 535 computations (8.9% saved)

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5010	2067

prune217.0ms (5%)

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

Counts

125 → 6

Compiler

Compiled 2491 to 1964 computations (21.2% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_100`
14×	`*-un-lft-identity_binary64_78`
12×	`pow1_binary64_139`
11×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94` `associate-l_binary64_19` `add-exp-log_binary64_116`
10×	`add-cube-cbrt_binary64_113` `sqrt-div_binary64_95`
9×	`add-log-exp_binary64_117`
8×	`associate-*l/_binary64_21`
7×	`flip3--_binary64_82` `flip--_binary64_53`
6×	`associate-*r/_binary64_20`
4×	`frac-add_binary64_86` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-+l+_binary64_11` `associate-r_binary64_18` `pow-prod-down_binary64_149`
3×	`cancel-sign-sub-inv_binary64_44`
2×	`*-commutative_binary64_9` `distribute-lft-out--_binary64_30` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47` `sum-log_binary64_169`
1×	`+-commutative_binary64_8` `associate-+l-_binary64_13` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `pow1/2_binary64_158` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 84

Calls

8 calls:

11.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
9.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
8.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
3.0ms	(sqrt.f64 (-.f64 a 1/3))
0.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))

series236.0ms (5.4%)

Counts

4 → 24

Calls

4 calls:

84.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
72.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
67.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
13.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 567 to 510 computations (10.1% saved)

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4885	1588
1	4885	1588

prune112.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	108	6	114

Error

Counts

114 → 6

Compiler

Compiled 1863 to 1429 computations (23.3% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_100`
14×	`*-un-lft-identity_binary64_78`
12×	`pow1_binary64_139`
11×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94` `associate-r_binary64_18` `add-exp-log_binary64_116`
10×	`add-cube-cbrt_binary64_113` `sqrt-div_binary64_95`
9×	`add-log-exp_binary64_117`
8×	`associate-*r/_binary64_20`
7×	`flip3--_binary64_82` `flip--_binary64_53`
6×	`associate-*l/_binary64_21`
4×	`associate-l_binary64_19` `frac-add_binary64_86` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-+l+_binary64_11` `pow-prod-down_binary64_149`
3×	`cancel-sign-sub-inv_binary64_44`
2×	`*-commutative_binary64_9` `distribute-lft-out--_binary64_30` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47` `sum-log_binary64_169`
1×	`+-commutative_binary64_8` `associate-+l-_binary64_13` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `pow1/2_binary64_158` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 84

Calls

8 calls:

8.0ms	(.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand)
8.0ms	(*.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))
8.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
3.0ms	(sqrt.f64 (-.f64 a 1/3))
0.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))

series203.0ms (4.7%)

Counts

4 → 21

Calls

4 calls:

95.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
77.0ms	(.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand)
17.0ms	(*.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))
13.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 489 to 445 computations (9% saved)

simplify104.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4872	1546
1	4872	1546

prune107.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	105	6	111

Error

Counts

111 → 6

Compiler

Compiled 1801 to 1390 computations (22.8% saved)

localize12.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.0b	(+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
0.1b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.3b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
0.7b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite72.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`sqrt-div_binary64_95`
32×	`frac-times_binary64_88`
26×	`add-sqr-sqrt_binary64_100`
24×	`*-un-lft-identity_binary64_78`
23×	`flip3--_binary64_82` `flip--_binary64_53`
18×	`add-cube-cbrt_binary64_113`
16×	`sqrt-prod_binary64_94` `associate-l_binary64_19` `associate-*r/_binary64_20`
14×	`associate-*l/_binary64_21` `pow1_binary64_139`
13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
12×	`flip-+_binary64_52` `times-frac_binary64_84` `flip3-+_binary64_81`
5×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `associate-r_binary64_18` `pow-prod-down_binary64_149`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-/r*_binary64_22`
3×	`associate-/l*_binary64_23`
2×	`*-commutative_binary64_9` `sqrt-pow1_binary64_96` `distribute-lft-out--_binary64_30` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47` `associate-/r/_binary64_24`
1×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `pow1/2_binary64_158`

Counts

4 → 134

Calls

8 calls:

22.0ms	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
16.0ms	(.f64 (sqrt.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)))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.0ms	(+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))

series438.0ms (10.1%)

Counts

4 → 27

Calls

4 calls:

180.0ms	(.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
145.0ms	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))))
96.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
17.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 834 to 744 computations (10.8% saved)

simplify82.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4954	4100
1	4954	4100

prune259.0ms (5.9%)

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

Counts

167 → 6

Compiler

Compiled 4313 to 3402 computations (21.1% saved)

regimes339.0ms (7.8%)

Accuracy

Total 0.1b remaining (98.1%)

Threshold costs 0.1b (98.1%)

Compiler

Compiled 2678 to 2402 computations (10.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	24
1	26	24

end1.0ms (0%)

Compiler: Compiled 16 to 15 computations (6.3% saved)

sample1.3s (30.2%)

Algorithm

1×

intervals

Results

459.0ms	8000×	body	128	valid
16.0ms	279×	body	128	invalid
15.0ms	292×	body	128	nan

Compiler

Compiled 693 to 623 computations (10.1% saved)

Pareto

Details

analyze75.0ms (1.7%)

sample31.0ms (0.7%)

simplify153.0ms (3.5%)

prune6.0ms (0.1%)

localize9.0ms (0.2%)

rewrite45.0ms (1%)

series302.0ms (6.9%)

simplify63.0ms (1.4%)

prune217.0ms (5%)

localize8.0ms (0.2%)

rewrite38.0ms (0.9%)

series236.0ms (5.4%)

simplify87.0ms (2%)

prune112.0ms (2.6%)

localize8.0ms (0.2%)

rewrite35.0ms (0.8%)

series203.0ms (4.7%)

simplify104.0ms (2.4%)

prune107.0ms (2.4%)

localize12.0ms (0.3%)

rewrite72.0ms (1.6%)

series438.0ms (10.1%)

simplify82.0ms (1.9%)

prune259.0ms (5.9%)

regimes339.0ms (7.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.3s (30.2%)

Profiling