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

sample78.0ms

Algorithm

intervals

Results

62.0ms	183×	body	1280	valid
7.0ms	42×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	8×	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: 25.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2.0)
2.9b	(+.f64 (-.f64 (exp.f64 x) 2.0) (exp.f64 (neg.f64 x)))

rewrite15.0ms

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:

5.0ms	(-.f64 (exp.f64 x) 2.0)
9.0ms	(+.f64 (-.f64 (exp.f64 x) 2.0) (exp.f64 (neg.f64 x)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify63.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4890	441
1	4890	441

prune57.0ms

Filtered

29 candidates to 39 candidates (-34.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	32	7	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	7	40

Merged error: 25.6b

Counts

40 → 7

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 (neg.f64 x)) 2.0)
3.0b	(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

8.0ms	(-.f64 (exp.f64 (neg.f64 x)) 2.0)
9.0ms	(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2.0))

series11.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(-.f64 (exp.f64 (neg.f64 x)) 2.0)
7.0ms	(+.f64 (exp.f64 x) (-.f64 (exp.f64 (neg.f64 x)) 2.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4888	381
1	4888	381

prune51.0ms

Filtered

27 candidates to 35 candidates (-29.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	30	5	35
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	34	8	42

Merged error: 25.6b

Counts

42 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (exp.f64 x) (+.f64 2.0 (+.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 2.0 3)) (exp.f64 x))))
0.1b	(pow.f64 (exp.f64 x) 3)
0.1b	(pow.f64 (exp.f64 x) 3)
3.1b	(+.f64 (.f64 2.0 2.0) (.f64 (exp.f64 x) (+.f64 2.0 (+.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 2.0 3)) (exp.f64 x)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
8×	`pow1_binary64` `pow-pow_binary64` `add-cbrt-cube_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `associate-r_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `exp-prod_binary64`
5×	`distribute-lft-out_binary64` `add-exp-log_binary64`
3×	`associate-l_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-cube-cbrt_binary64` `flip-+_binary64` `associate-+r+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

28.0ms	(*.f64 (exp.f64 x) (+.f64 2.0 (+.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 2.0 3)) (exp.f64 x))))
4.0ms	(pow.f64 (exp.f64 x) 3)
4.0ms	(pow.f64 (exp.f64 x) 3)
5.0ms	(+.f64 (.f64 2.0 2.0) (.f64 (exp.f64 x) (+.f64 2.0 (+.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 2.0 3)) (exp.f64 x)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 (exp.f64 x) (+.f64 2.0 (+.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 2.0 3)) (exp.f64 x))))
7.0ms	(pow.f64 (exp.f64 x) 3)
7.0ms	(pow.f64 (exp.f64 x) 3)
21.0ms	(+.f64 (.f64 2.0 2.0) (.f64 (exp.f64 x) (+.f64 2.0 (+.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 2.0 3)) (exp.f64 x)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4902	1084
1	4902	1084

prune143.0ms

Filtered

66 candidates to 102 candidates (-54.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Merged error: 0.1b

Counts

110 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (exp.f64 x) 3)
0.1b	(*.f64 11.083333333333334 (pow.f64 x 4))
0.1b	(/.f64 (+.f64 (.f64 11.083333333333334 (pow.f64 x 4)) (.f64 (.f64 x x) (+.f64 7.0 (.f64 x 11.0)))) (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 2.0 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2.0)))))
0.2b	(.f64 (.f64 x x) (+.f64 7.0 (*.f64 x 11.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
10×	`pow1_binary64` `associate-r_binary64`
9×	`times-frac_binary64`
7×	`unpow-prod-down_binary64`
6×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow-unpow_binary64` `associate-/r_binary64` `sqr-pow_binary64` `cube-prod_binary64` `associate-/l_binary64` `flip-+_binary64` `exp-prod_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-exp_binary64` `-commutative_binary64`
1×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 105

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 x) 3)
8.0ms	(*.f64 11.083333333333334 (pow.f64 x 4))
20.0ms	(/.f64 (+.f64 (.f64 11.083333333333334 (pow.f64 x 4)) (.f64 (.f64 x x) (+.f64 7.0 (.f64 x 11.0)))) (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 2.0 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2.0)))))
9.0ms	(.f64 (.f64 x x) (+.f64 7.0 (*.f64 x 11.0)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(pow.f64 (exp.f64 x) 3)
6.0ms	(*.f64 11.083333333333334 (pow.f64 x 4))
29.0ms	(/.f64 (+.f64 (.f64 11.083333333333334 (pow.f64 x 4)) (.f64 (.f64 x x) (+.f64 7.0 (.f64 x 11.0)))) (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 2.0 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2.0)))))
14.0ms	(.f64 (.f64 x x) (+.f64 7.0 (*.f64 x 11.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5111	2026

prune156.0ms

Filtered

79 candidates to 117 candidates (-48.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 0.1b

Counts

121 → 6

regimes45.0ms

Accuracy

48.7% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 1.1b

bsearch14.0ms

Steps

Iters	Range		Point
8	-0.014288197670302222	-1.137816725132413e-05	-0.0005096403824734452

simplify12.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	457	139
1	457	139

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.8s	5708×	body	1280	valid
206.0ms	1196×	body	640	valid
66.0ms	601×	body	320	valid
22.0ms	315×	body	160	valid
6.0ms	180×	body	80	valid
0.0ms	2×	body	80	invalid

Details

analyze4.0ms

sample78.0ms

simplify48.0ms

prune2.0ms

localize6.0ms

rewrite15.0ms

series9.0ms

simplify63.0ms

prune57.0ms

localize6.0ms

rewrite18.0ms

series11.0ms

simplify47.0ms

prune51.0ms

localize17.0ms

rewrite44.0ms

series50.0ms

simplify59.0ms

prune143.0ms

localize18.0ms

rewrite44.0ms

series57.0ms

simplify55.0ms

prune156.0ms

regimes45.0ms

bsearch14.0ms

simplify12.0ms

end0.0ms

sample2.2s

Profiling