Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

sample47.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
12.0ms	113×	body	80	invalid
3.0ms	68×	body	80	nan

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4961	13
1	4961	13

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 1.9b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ k 10.0))
0.4b	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
1.8b	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`times-frac`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
31×	`associate-r`
22×	`unpow-prod-down`
20×	`add-exp-log`
12×	`add-cbrt-cube`
8×	`sqr-pow`
7×	`pow1` `associate-/l*`
6×	`div-exp` `associate-l`
5×	`prod-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`flip3-+` `associate-r/` `associate-/r` `cbrt-unprod` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `pow-prod-down` `pow-exp` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `distribute-lft-out`

Counts

3 → 120

Calls

3 calls:

6.0ms	(* k (+ k 10.0))
6.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
11.0ms	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

series51.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* k (+ k 10.0))
15.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
32.0ms	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

simplify35.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5031	1960

prune185.0ms

Filtered

94 candidates to 129 candidates (-37.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	126	5	131

Merged error: 1.9b

Counts

131 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ a (sqrt (+ 1.0 (* k (+ k 10.0)))))
0.0b	(* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
12.5b	(sqrt (+ 1.0 (* k (+ k 10.0))))
12.5b	(sqrt (+ 1.0 (* k (+ k 10.0))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-sqr-sqrt`
110×	`times-frac`
64×	`sqrt-prod`
61×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
30×	`add-exp-log`
24×	`unpow-prod-down` `associate-l`
21×	`unswap-sqr`
18×	`add-cbrt-cube`
12×	`sqr-pow`
11×	`div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 188

Calls

4 calls:

5.0ms	(/ a (sqrt (+ 1.0 (* k (+ k 10.0)))))
34.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ a (sqrt (+ 1.0 (* k (+ k 10.0)))))
32.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ k 10.0))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
4.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

simplify81.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4952	4399
1	4952	4399

prune345.0ms

Filtered

130 candidates to 200 candidates (-53.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	200	5	205

Merged error: 0b

Counts

205 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))) (sqrt (+ 1.0 (* k (+ k 10.0)))))
1.8b	(* a (/ (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))) (sqrt (+ 1.0 (* k (+ k 10.0))))))
12.5b	(sqrt (+ 1.0 (* k (+ k 10.0))))
12.5b	(sqrt (+ 1.0 (* k (+ k 10.0))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

1148×	`times-frac`
607×	`add-sqr-sqrt`
583×	`sqrt-prod`
553×	`add-cube-cbrt` `*-un-lft-identity`
294×	`associate-r`
238×	`unpow-prod-down`
82×	`sqr-pow`
48×	`associate-/l*`
34×	`sqrt-div`
30×	`add-exp-log` `associate-/r/`
18×	`add-cbrt-cube`
17×	`flip3-+` `flip-+`
15×	`div-inv` `unswap-sqr`
14×	`div-exp`
8×	`pow1`
6×	`cbrt-undiv` `associate-/r*`
5×	`prod-exp`
4×	`add-log-exp`
3×	`associate-l` `cbrt-unprod`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 721

Calls

4 calls:

24.0ms	(/ (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))) (sqrt (+ 1.0 (* k (+ k 10.0)))))
73.0ms	(* a (/ (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))) (sqrt (+ 1.0 (* k (+ k 10.0))))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
3.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))) (sqrt (+ 1.0 (* k (+ k 10.0)))))
32.0ms	(* a (/ (/ (pow k m) (sqrt (+ 1.0 (* k (+ k 10.0))))) (sqrt (+ 1.0 (* k (+ k 10.0))))))
4.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))
4.0ms	(sqrt (+ 1.0 (* k (+ k 10.0))))

simplify232.0ms

Algorithm

egg-herbie

Counts

733 → 733

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4954	19909
1	4954	19909

prune1.2s

Filtered

306 candidates to 733 candidates (-139.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	733	0	733
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	733	5	738

Merged error: 0b

Counts

738 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
0.4b	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
5.6b	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))
5.6b	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
76×	`add-sqr-sqrt`
64×	`add-cube-cbrt` `*-un-lft-identity`
54×	`sqrt-prod`
44×	`unpow-prod-down`
16×	`sqr-pow`
14×	`add-exp-log` `associate-/l*`
8×	`rem-sqrt-square` `associate-/r/` `add-cbrt-cube`
6×	`pow1` `div-exp` `associate-/r*`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `pow-exp` `clear-num`

Counts

4 → 176

Calls

4 calls:

6.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
6.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
6.0ms	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))
6.0ms	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
19.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
23.0ms	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))
23.0ms	(sqrt (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4906	3604
1	4906	3604

prune368.0ms

Filtered

152 candidates to 188 candidates (-23.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	188	5	193

Merged error: 0b

Counts

193 → 5

regimes233.0ms

Accuracy

95.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch23.0ms

Steps

Iters	Range		Point
8	8208.425914581163	2664778.6159561626	2563173.317625166

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	60
1	91	60

end0.0ms

sample1.2s

Algorithm

intervals

Results

553.0ms	8000×	body	80	valid
280.0ms	3231×	body	80	invalid
95.0ms	1992×	body	80	nan

Details

analyze1.0s

sample47.0ms

simplify82.0ms

prune11.0ms

localize10.0ms

rewrite29.0ms

series51.0ms

simplify35.0ms

prune185.0ms

localize13.0ms

rewrite54.0ms

series61.0ms

simplify81.0ms

prune345.0ms

localize13.0ms

rewrite165.0ms

series55.0ms

simplify232.0ms

prune1.2s

localize16.0ms

rewrite31.0ms

series81.0ms

simplify66.0ms

prune368.0ms

regimes233.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling