Details

analyze541.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

sample43.0ms

Algorithm

intervals

Results

11.0ms	182×	body	80	valid
5.0ms	23×	body	1280	valid
5.0ms	28×	body	640	valid
4.0ms	21×	body	1280	nan
3.0ms	23×	body	640	nan
2.0ms	17×	body	320	valid
1.0ms	13×	body	320	nan
1.0ms	17×	body	80	nan
0.0ms	6×	body	160	valid
0.0ms	7×	body	160	nan

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5039	12

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.4b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.3b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
27×	`times-frac`
16×	`add-cube-cbrt` `difference-of-squares`
14×	`distribute-lft-out--`
6×	`add-exp-log` `log-prod`
5×	`associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`log-div` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `log-pow` `div-inv` `associate--r-`

Counts

3 → 84

Calls

3 calls:

8.0ms	(/ (- x y) (- 1.0 y))
14.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
14.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series29.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (- x y) (- 1.0 y))
11.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
12.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5817	1253

prune163.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 0.1b

Counts

94 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
3.3b	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
12.3b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
37×	`cbrt-prod`
34×	`*-un-lft-identity`
15×	`difference-of-squares`
14×	`add-cube-cbrt` `cbrt-div`
12×	`pow1` `times-frac`
10×	`swap-sqr`
9×	`log-prod` `flip3--` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `pow1/3`
6×	`add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`log-div` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `associate--r-`

Counts

4 → 109

Calls

4 calls:

3.0ms	(cbrt (- 1.0 y))
11.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
42.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
45.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (- 1.0 y))
7.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
13.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
10.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4953	1734
1	4953	1734

prune258.0ms

Filtered

93 candidates to 121 candidates (-30.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Merged error: 0.1b

Counts

125 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3))
0.3b	(pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)
2.6b	(+ 1.0 (/ (- y x) (- 1.0 y)))
3.3b	(log (+ 1.0 (/ (- y x) (- 1.0 y))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`pow1`
8×	`unpow-prod-down` `cube-prod`
6×	`add-exp-log` `add-log-exp`
5×	`log-pow` `add-cbrt-cube`
4×	`log-prod`
3×	`pow-unpow`
2×	`cube-mult` `log-div` `flip3-+` `unpow3` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `pow-pow` `pow1/3` `div-sub` `rem-log-exp` `pow-exp` `sum-log` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 76

Calls

4 calls:

2.0ms	(cbrt (pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3))
2.0ms	(pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)
13.0ms	(+ 1.0 (/ (- y x) (- 1.0 y)))
13.0ms	(log (+ 1.0 (/ (- y x) (- 1.0 y))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt (pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3))
43.0ms	(pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)
7.0ms	(+ 1.0 (/ (- y x) (- 1.0 y)))
11.0ms	(log (+ 1.0 (/ (- y x) (- 1.0 y))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5126	1672

prune143.0ms

Filtered

55 candidates to 88 candidates (-60.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	88	4	92

Merged error: 0.1b

Counts

92 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)
0.3b	(pow (cbrt (pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)) 3)
2.6b	(+ 1.0 (/ (- y x) (- 1.0 y)))
3.3b	(log (+ 1.0 (/ (- y x) (- 1.0 y))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down` `cube-prod`
28×	`cbrt-prod`
21×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow1`
7×	`add-exp-log` `log-pow`
6×	`pow-unpow` `add-log-exp`
5×	`add-cbrt-cube`
4×	`cube-mult` `log-prod` `unpow3` `sqr-pow`
3×	`pow-pow`
2×	`pow-to-exp` `log-div` `flip3-+` `pow-exp` `flip-+` `distribute-lft-out` `rem-cube-cbrt`
1×	`+-commutative` `associate-+r-` `pow1/3` `div-sub` `rem-log-exp` `sum-log`

Counts

4 → 105

Calls

4 calls:

3.0ms	(pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)
5.0ms	(pow (cbrt (pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)) 3)
13.0ms	(+ 1.0 (/ (- y x) (- 1.0 y)))
14.0ms	(log (+ 1.0 (/ (- y x) (- 1.0 y))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)
42.0ms	(pow (cbrt (pow (log (+ 1.0 (/ (- y x) (- 1.0 y)))) 3)) 3)
7.0ms	(+ 1.0 (/ (- y x) (- 1.0 y)))
13.0ms	(log (+ 1.0 (/ (- y x) (- 1.0 y))))

simplify76.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5009	2607

prune190.0ms

Filtered

61 candidates to 117 candidates (-91.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	117	4	121

Merged error: 0.1b

Counts

121 → 4

regimes99.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 16.5b

bsearch120.0ms

Steps

Iters	Range		Point
12	0.009567756222966819	3.917209238092376e+36	70732103.26940797
9	-1959097767914.7449	-78495.28115778102	-53177574.82438583

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	140	48
1	140	48

end0.0ms

sample1.2s

Algorithm

intervals

Results

269.0ms	5729×	body	80	valid
196.0ms	812×	body	1280	valid
139.0ms	798×	body	640	valid
129.0ms	690×	body	1280	nan
99.0ms	712×	body	640	nan
54.0ms	433×	body	320	valid
46.0ms	447×	body	320	nan
21.0ms	228×	body	160	valid
14.0ms	211×	body	160	nan
12.0ms	342×	body	80	nan

Details

analyze541.0ms

sample43.0ms

simplify111.0ms

prune6.0ms

localize8.0ms

rewrite39.0ms

series29.0ms

simplify51.0ms

prune163.0ms

localize12.0ms

rewrite108.0ms

series35.0ms

simplify48.0ms

prune258.0ms

localize11.0ms

rewrite33.0ms

series71.0ms

simplify45.0ms

prune143.0ms

localize15.0ms

rewrite38.0ms

series110.0ms

simplify76.0ms

prune190.0ms

regimes99.0ms

bsearch120.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling