Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample63.0ms

Algorithm

intervals

Results

36.0ms	75×	body	1280	valid
14.0ms	61×	body	640	valid
4.0ms	31×	body	320	valid
2.0ms	78×	body	80	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	4
1	6	4

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: 41.6b

Counts

2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

2.6b	(log.f64 (+.f64 1 x))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `log-prod_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `log-pow_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

1 → 15

Calls

1 calls:

3.0ms

(log.f64 (+.f64 1 x))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(log.f64 (+.f64 1 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4968	137
1	4968	137

prune21.0ms

Filtered

13 candidates to 18 candidates (-38.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	2	19

Merged error: 0.0b

Counts

19 → 2

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 x (+.f64 -1/2 (.f64 x 1/3)))
0.0b	(.f64 x (+.f64 1 (.f64 x (+.f64 -1/2 (*.f64 x 1/3)))))
0.3b	(*.f64 x 1/3)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l*_binary64`
4×	`associate-*r/_binary64`
3×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64`

Counts

3 → 62

Calls

3 calls:

6.0ms	(.f64 x (+.f64 -1/2 (.f64 x 1/3)))
8.0ms	(.f64 x (+.f64 1 (.f64 x (+.f64 -1/2 (*.f64 x 1/3)))))
4.0ms	(*.f64 x 1/3)

series12.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(.f64 x (+.f64 -1/2 (.f64 x 1/3)))
4.0ms	(.f64 x (+.f64 1 (.f64 x (+.f64 -1/2 (*.f64 x 1/3)))))
2.0ms	(*.f64 x 1/3)

simplify51.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5469	611

prune66.0ms

Filtered

50 candidates to 71 candidates (-42.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	70	3	73

Merged error: 0.0b

Counts

73 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/3) -1/2))))
0.0b	(.f64 x (+.f64 (.f64 x 1/3) -1/2))
0.0b	(.f64 x (.f64 x (+.f64 (*.f64 x 1/3) -1/2)))
0.3b	(*.f64 x 1/3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `distribute-lft-in_binary64` `associate-l*_binary64` `distribute-rgt-in_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-+r+_binary64`
3×	`flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/3) -1/2))))
7.0ms	(.f64 x (+.f64 (.f64 x 1/3) -1/2))
9.0ms	(.f64 x (.f64 x (+.f64 (*.f64 x 1/3) -1/2)))
4.0ms	(*.f64 x 1/3)

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/3) -1/2))))
6.0ms	(.f64 x (+.f64 (.f64 x 1/3) -1/2))
10.0ms	(.f64 x (.f64 x (+.f64 (*.f64 x 1/3) -1/2)))
2.0ms	(*.f64 x 1/3)

simplify56.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4941	798
1	4941	798

prune67.0ms

Filtered

57 candidates to 91 candidates (-59.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	91	3	94

Merged error: 0.0b

Counts

94 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/3)
0.3b	(*.f64 x 1/3)
0.3b	(*.f64 x 1/3)
9.5b	(/.f64 (+.f64 x (.f64 (pow.f64 x 3) (.f64 (+.f64 (.f64 x 1/3) -1/2) (-.f64 1/2 (.f64 x 1/3))))) (-.f64 1 (.f64 x (+.f64 -1/2 (.f64 x 1/3)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(*.f64 x 1/3)
4.0ms	(*.f64 x 1/3)
4.0ms	(*.f64 x 1/3)
8.0ms	(/.f64 (+.f64 x (.f64 (pow.f64 x 3) (.f64 (+.f64 (.f64 x 1/3) -1/2) (-.f64 1/2 (.f64 x 1/3))))) (-.f64 1 (.f64 x (+.f64 -1/2 (.f64 x 1/3)))))

series14.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(*.f64 x 1/3)
2.0ms	(*.f64 x 1/3)
2.0ms	(*.f64 x 1/3)
8.0ms	(/.f64 (+.f64 x (.f64 (pow.f64 x 3) (.f64 (+.f64 (.f64 x 1/3) -1/2) (-.f64 1/2 (.f64 x 1/3))))) (-.f64 1 (.f64 x (+.f64 -1/2 (.f64 x 1/3)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5942	1466

prune120.0ms

Filtered

66 candidates to 97 candidates (-47.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	97	3	100

Merged error: 0.0b

Counts

100 → 3

regimes88.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.7b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	21
1	21	21

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	2276×	body	1280	valid
389.0ms	1715×	body	640	valid
99.0ms	825×	body	320	valid
71.0ms	2746×	body	80	valid
30.0ms	438×	body	160	valid

Details

analyze3.0ms

sample63.0ms

simplify5.0ms

prune2.0ms

localize3.0ms

rewrite4.0ms

series3.0ms

simplify42.0ms

prune21.0ms

localize7.0ms

rewrite20.0ms

series12.0ms

simplify51.0ms

prune66.0ms

localize7.0ms

rewrite26.0ms

series22.0ms

simplify56.0ms

prune67.0ms

localize15.0ms

rewrite24.0ms

series14.0ms

simplify64.0ms

prune120.0ms

regimes88.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling