Details

analyze76.0ms (1.8%)

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)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	5×	body	128	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify157.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

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)

localize8.0ms (0.2%)

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))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_441`
23×	`*-un-lft-identity_binary64_419`
17×	`add-cube-cbrt_binary64_454`
12×	`times-frac_binary64_425`
11×	`pow1_binary64_480`
10×	`associate-l_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`associate-*l/_binary64_362`
7×	`associate-r_binary64_359`
6×	`flip3--_binary64_423` `flip--_binary64_394`
5×	`sqrt-prod_binary64_435`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `frac-times_binary64_429` `associate-/r*_binary64_363`
3×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `flip-+_binary64_393` `associate-/l*_binary64_364`
2×	`difference-of-squares_binary64_388` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `distribute-lft-out--_binary64_371` `associate-/r/_binary64_365` `-commutative_binary64_350` `sqrt-pow1_binary64_437`
1×	`clear-num_binary64_418` `distribute-rgt-in_binary64_369` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out_binary64_370` `distribute-lft-in_binary64_368` `frac-2neg_binary64_430` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 99

Calls

4 calls:

14.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
7.0ms	(/.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))

series279.0ms (6.6%)

Counts

4 → 24

Calls

4 calls:

131.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
102.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
26.0ms	(*.f64 (-.f64 a 1/3) 9)
20.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 587 to 535 computations (8.9% saved)

simplify64.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5010	2067

prune165.0ms (3.9%)

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 2494 to 1966 computations (21.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.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)

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_441`
20×	`*-un-lft-identity_binary64_419`
13×	`associate-l_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
12×	`add-cube-cbrt_binary64_454`
11×	`sqrt-prod_binary64_435`
9×	`pow1_binary64_480`
7×	`associate-r_binary64_359`
6×	`associate-*l/_binary64_362` `sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394`
4×	`add-log-exp_binary64_458` `frac-times_binary64_429`
3×	`flip3-+_binary64_422` `times-frac_binary64_425` `difference-of-squares_binary64_388` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `distribute-lft-out--_binary64_371` `flip-+_binary64_393` `associate-/l*_binary64_364`
2×	`pow-prod-down_binary64_490` `associate-r/_binary64_361` `associate-/r/_binary64_365` `-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `distribute-rgt-in_binary64_369` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out_binary64_370` `distribute-lft-in_binary64_368` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432`

Counts

4 → 97

Calls

4 calls:

14.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
8.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
7.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
3.0ms	(sqrt.f64 (-.f64 a 1/3))

series259.0ms (6.2%)

Counts

4 → 21

Calls

4 calls:

129.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
98.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
18.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
14.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 578 to 527 computations (8.8% saved)

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4934	1886
1	4934	1886

prune129.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Error

0.0b

Counts

124 → 6

Compiler

Compiled 2339 to 1858 computations (20.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(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)))

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64_441`
58×	`*-un-lft-identity_binary64_419`
50×	`times-frac_binary64_425`
41×	`sqrt-prod_binary64_435`
40×	`add-cube-cbrt_binary64_454`
33×	`associate-r_binary64_359`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `pow1_binary64_480`
8×	`associate-l_binary64_360` `associate-/r*_binary64_363`
6×	`sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `frac-times_binary64_429` `associate-/r/_binary64_365`
3×	`flip3-+_binary64_422` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `flip-+_binary64_393` `associate-/l_binary64_364`
2×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `div-inv_binary64_416` `-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `distribute-rgt-in_binary64_369` `pow1/2_binary64_499` `distribute-lft-in_binary64_368` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 146

Calls

4 calls:

15.0ms	(*.f64 rand (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))
8.0ms	(.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	(sqrt.f64 (-.f64 a 1/3))

series281.0ms (6.7%)

Counts

4 → 21

Calls

4 calls:

144.0ms	(.f64 (-.f64 a 1/3) (+.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)))
14.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 592 to 539 computations (9% saved)

simplify74.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4981	2798
1	4981	2798

prune202.0ms (4.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	167	6	173

Error

0.0b

Counts

173 → 6

Compiler

Compiled 3487 to 2807 computations (19.5% saved)

localize7.0ms (0.2%)

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 (sqrt.f64 (-.f64 a 1/3)) rand)))
0.3b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
0.6b	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
12×	`pow1_binary64_480`
11×	`associate-l_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `sqrt-prod_binary64_435`
10×	`sqrt-div_binary64_436` `add-cube-cbrt_binary64_454`
9×	`add-log-exp_binary64_458`
8×	`associate-*l/_binary64_362`
7×	`flip3--_binary64_423` `flip--_binary64_394`
6×	`associate-*r/_binary64_361`
4×	`pow-prod-down_binary64_490` `frac-add_binary64_427` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-+l+_binary64_352`
3×	`cancel-sign-sub-inv_binary64_385`
2×	`difference-of-squares_binary64_388` `unswap-sqr_binary64_387` `sum-log_binary64_510` `distribute-lft-out--_binary64_371` `*-commutative_binary64_350`
1×	`flip3-+_binary64_422` `sub-neg_binary64_412` `pow1/2_binary64_499` `associate-+l-_binary64_354` `flip-+_binary64_393` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

4 → 84

Calls

4 calls:

8.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
8.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
7.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series241.0ms (5.7%)

Counts

4 → 24

Calls

4 calls:

87.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
78.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
62.0ms	(*.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)

simplify83.0ms (2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4885	1588
1	4885	1588

prune105.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	108	6	114

Error

Counts

114 → 6

Compiler

Compiled 1774 to 1350 computations (23.9% saved)

regimes314.0ms (7.5%)

Accuracy

Total 0.1b remaining (97.7%)

Threshold costs 0.1b (97.7%)

Compiler

Compiled 3494 to 3098 computations (11.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	21
1	25	21

end0.0ms (0%)

sample1.5s (35.2%)

Algorithm

1×

intervals

Results

462.0ms	8000×	body	128	valid
15.0ms	261×	body	128	invalid
12.0ms	231×	body	128	nan

Compiler

Compiled 895 to 795 computations (11.2% saved)

Details

analyze76.0ms (1.8%)

sample22.0ms (0.5%)

simplify157.0ms (3.7%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite41.0ms (1%)

series279.0ms (6.6%)

simplify64.0ms (1.5%)

prune165.0ms (3.9%)

localize8.0ms (0.2%)

rewrite40.0ms (0.9%)

series259.0ms (6.2%)

simplify78.0ms (1.9%)

prune129.0ms (3.1%)

localize8.0ms (0.2%)

rewrite46.0ms (1.1%)

series281.0ms (6.7%)

simplify74.0ms (1.8%)

prune202.0ms (4.8%)

localize7.0ms (0.2%)

rewrite33.0ms (0.8%)

series241.0ms (5.7%)

simplify83.0ms (2%)

prune105.0ms (2.5%)

regimes314.0ms (7.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.5s (35.2%)

Profiling