Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

sample75.0ms

Algorithm

intervals

Results

60.0ms	184×	body	1280	valid
6.0ms	39×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	7×	body	80	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5718	8

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: 31.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2.0)
2.6b	(+.f64 (-.f64 (exp.f64 x) 2.0) (exp.f64 (neg.f64 x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
4×	`frac-add_binary64` `add-sqr-sqrt_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `pow1_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-diff_binary64` `distribute-lft-out--_binary64` `exp-neg_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

2 → 33

Calls

2 calls:

4.0ms	(-.f64 (exp.f64 x) 2.0)
8.0ms	(+.f64 (-.f64 (exp.f64 x) 2.0) (exp.f64 (neg.f64 x)))

series8.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(-.f64 (exp.f64 x) 2.0)
6.0ms	(+.f64 (-.f64 (exp.f64 x) 2.0) (exp.f64 (neg.f64 x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5310	423

prune51.0ms

Filtered

28 candidates to 39 candidates (-39.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	4	40

Merged error: 0.0b

Counts

40 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64` `add-exp-log_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
6×	`associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+r+_binary64`

Counts

4 → 74

Calls

4 calls:

8.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
5.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
5.0ms	(*.f64 1/360 (pow.f64 x 6))
5.0ms	(*.f64 1/12 (pow.f64 x 4))

series37.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
17.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
5.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify60.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5022	849

prune84.0ms

Filtered

55 candidates to 86 candidates (-56.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2.0)
0.0b	(-.f64 (exp.f64 x) 2.0)
0.0b	(pow.f64 (exp.f64 x) -2)
2.2b	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2.0) (-.f64 (exp.f64 x) 2.0)) (pow.f64 (exp.f64 x) -2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`sub-neg_binary64` `pow1_binary64` `difference-of-squares_binary64`
4×	`pow-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `exp-prod_binary64`
2×	`sqr-pow_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64`
1×	`pow-to-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-exp_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(-.f64 (exp.f64 x) 2.0)
4.0ms	(-.f64 (exp.f64 x) 2.0)
3.0ms	(pow.f64 (exp.f64 x) -2)
14.0ms	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2.0) (-.f64 (exp.f64 x) 2.0)) (pow.f64 (exp.f64 x) -2))

series29.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(-.f64 (exp.f64 x) 2.0)
2.0ms	(-.f64 (exp.f64 x) 2.0)
6.0ms	(pow.f64 (exp.f64 x) -2)
18.0ms	(-.f64 (*.f64 (-.f64 (exp.f64 x) 2.0) (-.f64 (exp.f64 x) 2.0)) (pow.f64 (exp.f64 x) -2))

simplify70.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4986	668
1	4986	668

prune74.0ms

Filtered

55 candidates to 74 candidates (-34.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Merged error: 0.0b

Counts

79 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
0.0b	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
0.0b	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
4.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 x) 2.0)) (cbrt.f64 (-.f64 (exp.f64 x) 2.0))) (cbrt.f64 (-.f64 (exp.f64 x) 2.0))) (exp.f64 (neg.f64 x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

114×	`cbrt-div_binary64`
57×	`flip3--_binary64` `flip--_binary64`
56×	`frac-times_binary64`
52×	`frac-add_binary64`
28×	`associate-*l/_binary64`
26×	`neg-sub0_binary64` `exp-diff_binary64` `exp-neg_binary64`
16×	`associate-*r/_binary64`
15×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 108

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
4.0ms	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
4.0ms	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
23.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 x) 2.0)) (cbrt.f64 (-.f64 (exp.f64 x) 2.0))) (cbrt.f64 (-.f64 (exp.f64 x) 2.0))) (exp.f64 (neg.f64 x)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
22.0ms	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
18.0ms	(cbrt.f64 (-.f64 (exp.f64 x) 2.0))
7.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 x) 2.0)) (cbrt.f64 (-.f64 (exp.f64 x) 2.0))) (cbrt.f64 (-.f64 (exp.f64 x) 2.0))) (exp.f64 (neg.f64 x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4905	4003
1	4905	4003

prune90.0ms

Filtered

62 candidates to 120 candidates (-93.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	121	4	125

Merged error: 0.0b

Counts

125 → 4

regimes31.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.8s	5607×	body	1280	valid
227.0ms	1280×	body	640	valid
70.0ms	635×	body	320	valid
21.0ms	298×	body	160	valid
7.0ms	180×	body	80	valid
0.0ms	2×	body	80	invalid

Details

analyze4.0ms

sample75.0ms

simplify48.0ms

prune2.0ms

localize6.0ms

rewrite13.0ms

series8.0ms

simplify62.0ms

prune51.0ms

localize9.0ms

rewrite26.0ms

series37.0ms

simplify60.0ms

prune84.0ms

localize10.0ms

rewrite27.0ms

series29.0ms

simplify70.0ms

prune74.0ms

localize11.0ms

rewrite44.0ms

series66.0ms

simplify82.0ms

prune90.0ms

regimes31.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling