Details

analyze833.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

sample85.0ms

Algorithm

intervals

Results

43.0ms	108×	body	2560	valid
18.0ms	65×	body	1280	valid
11.0ms	40×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	19×	body	160	valid
0.0ms	5×	body	80	valid
0.0ms	1×	body	80	nan

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5044	14

prune2.0ms

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

Merged error: 0.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.1b	(.f64 5 (.f64 v v))
0.6b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `difference-of-squares_binary64`
6×	`associate-/r*_binary64`
4×	`difference-of-sqr-1_binary64`
3×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`acos-asin_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

3 → 71

Calls

3 calls:

9.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
6.0ms	(.f64 5 (.f64 v v))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

series15.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
4.0ms	(.f64 5 (.f64 v v))
4.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

simplify44.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4932	1195
1	4932	1195

prune78.0ms

Filtered

54 candidates to 80 candidates (-48.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Merged error: 0.6b

Counts

81 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4))
0.6b	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
2×	`add-log-exp_binary64` `associate-r/_binary64` `associate-l/_binary64`
1×	`flip3-+_binary64` `acos-asin_binary64` `associate-r_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

2 → 28

Calls

2 calls:

10.0ms	(.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4))
2.0ms	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))

series21.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4))
4.0ms	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))

simplify65.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4950	382
1	4950	382

prune31.0ms

Filtered

21 candidates to 34 candidates (-61.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Merged error: 0.6b

Counts

37 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))
1.0b	(sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
1.0b	(sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
1.0b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))) (sqrt.f64 (acos.f64 (+.f64 (.f64 v (*.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
8×	`swap-sqr_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`rem-sqrt-square_binary64`
1×	`cbrt-unprod_binary64` `acos-asin_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

2.0ms	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))
1.0ms	(sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
1.0ms	(sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
8.0ms	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))) (sqrt.f64 (acos.f64 (+.f64 (.f64 v (*.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))
12.0ms	(sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
12.0ms	(sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
6.0ms	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))) (sqrt.f64 (acos.f64 (+.f64 (.f64 v (*.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))))

simplify58.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5213	1280

prune81.0ms

Filtered

47 candidates to 95 candidates (-102.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Merged error: 0.5b

Counts

98 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
1.0b	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
1.0ms	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(.f64 (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
49.0ms	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
48.0ms	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
52.0ms	(cbrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))

simplify56.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4912	1672
1	4912	1672

prune112.0ms

Filtered

57 candidates to 85 candidates (-49.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	83	6	89

Merged error: 0.5b

Counts

89 → 6

regimes202.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	12
1	14	12

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	2949×	body	2560	valid
721.0ms	2548×	body	1280	valid
264.0ms	1255×	body	640	valid
91.0ms	605×	body	320	valid
43.0ms	423×	body	160	valid
15.0ms	220×	body	80	valid
0.0ms	4×	body	80	nan

Details

analyze833.0ms

sample85.0ms

simplify61.0ms

prune2.0ms

localize7.0ms

rewrite18.0ms

series15.0ms

simplify44.0ms

prune78.0ms

localize7.0ms

rewrite12.0ms

series21.0ms

simplify65.0ms

prune31.0ms

localize10.0ms

rewrite15.0ms

series34.0ms

simplify58.0ms

prune81.0ms

localize12.0ms

rewrite12.0ms

series215.0ms

simplify56.0ms

prune112.0ms

regimes202.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling