Details

analyze66.0ms

Algorithm: search

sample31.0ms

Algorithm

intervals

Results

10.0ms	228×	body	80	valid
9.0ms	17×	body	640	valid
3.0ms	4×	body	1280	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	80	invalid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	5

prune3.0ms

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: 0.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(log (+ 1.0 (exp x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `log-div` `associate--l+`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
5.0ms	(- (log (+ 1.0 (exp x))) (* x y))
4.0ms	(log (+ 1.0 (exp x)))

series21.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(+ 1.0 (exp x))
9.0ms	(- (log (+ 1.0 (exp x))) (* x y))
10.0ms	(log (+ 1.0 (exp x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune87.0ms

Filtered

40 candidates to 54 candidates (-35.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0.3b

Counts

55 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ 1.0 (exp x)))
0.7b	(cbrt (+ 1.0 (exp x)))
0.7b	(cbrt (+ 1.0 (exp x)))
0.7b	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
13×	`*-un-lft-identity`
12×	`pow1` `cbrt-prod`
9×	`flip3-+` `pow1/3` `log-pow` `flip-+`
8×	`log-div`
7×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
3×	`distribute-lft-out`
2×	`associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `log-prod` `pow-plus` `prod-exp`

Counts

4 → 69

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (exp x)))
3.0ms	(cbrt (+ 1.0 (exp x)))
3.0ms	(cbrt (+ 1.0 (exp x)))
9.0ms	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ 1.0 (exp x)))
17.0ms	(cbrt (+ 1.0 (exp x)))
18.0ms	(cbrt (+ 1.0 (exp x)))
35.0ms	(log (* (cbrt (+ 1.0 (exp x))) (cbrt (+ 1.0 (exp x)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	212	675
1	498	601
2	1640	579
3	5001	578

prune185.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	81	4	85

Merged error: 0.3b

Counts

85 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (exp (+ (log 2/3) (log (log (+ 1.0 (exp x)))))) (- (log (cbrt (+ 1.0 (exp x)))) (* x y)))
0.6b	(+ (log 2/3) (log (log (+ 1.0 (exp x)))))
0.7b	(cbrt (+ 1.0 (exp x)))
1.0b	(log 2/3)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`log-prod`
13×	`associate-+r+`
10×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
8×	`cbrt-prod` `add-log-exp`
7×	`associate--l+` `distribute-lft-out`
6×	`log-pow`
5×	`add-exp-log`
4×	`add-cbrt-cube`
3×	`associate-+l+` `flip3-+` `sum-log` `flip-+`
2×	`+-commutative` `cbrt-div`
1×	`associate-+r-` `sub-neg` `pow1/3` `diff-log` `rem-log-exp`

Counts

4 → 71

Calls

4 calls:

11.0ms	(+ (exp (+ (log 2/3) (log (log (+ 1.0 (exp x)))))) (- (log (cbrt (+ 1.0 (exp x)))) (* x y)))
4.0ms	(+ (log 2/3) (log (log (+ 1.0 (exp x)))))
3.0ms	(cbrt (+ 1.0 (exp x)))
1.0ms	(log 2/3)

series81.0ms

Counts

4 → 10

Calls

4 calls:

38.0ms	(+ (exp (+ (log 2/3) (log (log (+ 1.0 (exp x)))))) (- (log (cbrt (+ 1.0 (exp x)))) (* x y)))
26.0ms	(+ (log 2/3) (log (log (+ 1.0 (exp x)))))
17.0ms	(cbrt (+ 1.0 (exp x)))
0.0ms	(log 2/3)

simplify37.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	428	856
1	1345	774
2	5002	699

prune211.0ms

Filtered

62 candidates to 81 candidates (-30.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	79	6	85

Merged error: 0.2b

Counts

85 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (exp x) 1.0))
0.7b	(* (exp (log (log (+ (exp x) 1.0)))) 2/3)
1.1b	(log (cbrt (sqrt (+ 1.0 (exp x)))))
1.1b	(log (cbrt (sqrt (+ 1.0 (exp x)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

29×	`log-prod`
20×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
14×	`cbrt-prod` `add-cube-cbrt`
10×	`pow1`
8×	`add-exp-log` `sqrt-prod`
7×	`associate-l`
6×	`log-div` `log-pow` `add-cbrt-cube`
5×	`exp-sum`
4×	`cbrt-div` `sqrt-div` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `associate-r` `flip-+` `distribute-lft-out`
2×	`pow1/3` `unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

4.0ms	(log (+ (exp x) 1.0))
6.0ms	(* (exp (log (log (+ (exp x) 1.0)))) 2/3)
4.0ms	(log (cbrt (sqrt (+ 1.0 (exp x)))))
4.0ms	(log (cbrt (sqrt (+ 1.0 (exp x)))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(log (+ (exp x) 1.0))
12.0ms	(* (exp (log (log (+ (exp x) 1.0)))) 2/3)
27.0ms	(log (cbrt (sqrt (+ 1.0 (exp x)))))
29.0ms	(log (cbrt (sqrt (+ 1.0 (exp x)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	294	758
1	720	687
2	2240	677
3	5002	658

prune247.0ms

Filtered

67 candidates to 94 candidates (-40.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	94	6	100

Merged error: 0.2b

Counts

100 → 6

regimes118.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	20
1	22	20

end0.0ms

analyze61.0ms

Algorithm: search

sample674.0ms

Algorithm

intervals

Results

321.0ms	7256×	body	80	valid
92.0ms	299×	body	640	valid
75.0ms	134×	body	1280	valid
36.0ms	197×	body	320	valid
12.0ms	114×	body	160	valid
2.0ms	48×	body	80	invalid
0.0ms	2×	body	80	overflowed

Details

analyze66.0ms

sample31.0ms

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite13.0ms

series21.0ms

simplify50.0ms

prune87.0ms

localize13.0ms

rewrite20.0ms

series87.0ms

simplify59.0ms

prune185.0ms

localize19.0ms

rewrite22.0ms

series81.0ms

simplify37.0ms

prune211.0ms

localize20.0ms

rewrite21.0ms

series77.0ms

simplify59.0ms

prune247.0ms

regimes118.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze61.0ms

sample674.0ms

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