Details

sample199.0ms

Algorithm

intervals

Results

44.0ms	78×	body	5120	valid
39.0ms	455×	body	80	nan
28.0ms	61×	body	2560	valid
16.0ms	205×	body	80	valid
13.0ms	22×	body	5120	exit
12.0ms	33×	body	1280	valid
3.0ms	11×	body	640	valid
2.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	60	26
1	304	25
2	3462	25
3	5003	25

prune15.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 60.4b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
27.3b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
4×	`pow1` `expm1-log1p-u` `times-frac` `log1p-expm1-u` `div-inv`
3×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 156

Calls

4 calls:

16.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
33.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
93.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
96.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
245.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify128.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	594	2246
1	3877	1589
2	5001	1584

prune324.0ms

Filtered

168 candidates to 70 candidates (41.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	165	5	170

Merged error: 35.4b

Counts

170 → 5

localize4.0ms

Local error

Found 1 expressions with local error:

6.4b	(* (/ c0 (* 2.0 w)) 0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
3×	`pow1` `times-frac` `associate-r`
2×	`cbrt-undiv` `div-exp`
1×	`expm1-log1p-u` `mul0` `pow-prod-down` `associate-l/` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 30

Calls

1 calls:

7.0ms

(* (/ c0 (* 2.0 w)) 0)

series1.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

(* (/ c0 (* 2.0 w)) 0)

simplify280.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (277.0ms)

Iter	Nodes	Cost
0	178	40
1	1861	24
2	5001	14

prune58.0ms

Filtered

33 candidates to 21 candidates (63.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	33	5	38

Merged error: 33.7b

Counts

38 → 5

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune13.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Merged error: 33.7b

Counts

5 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

16.0b	(/ (/ (* c0 (* d d)) (* w h)) (* D D))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
33.8b	(+ (/ (/ (* c0 (* d d)) (* w h)) (* D D)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

207×	`add-exp-log` `add-cbrt-cube`
103×	`prod-exp` `cbrt-unprod`
56×	`cbrt-undiv` `div-exp`
15×	`times-frac`
10×	`*-un-lft-identity`
9×	`fma-def`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`div-inv` `associate-/l*`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `associate-/r*`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`

Counts

4 → 167

Calls

4 calls:

12.0ms	(/ (/ (* c0 (* d d)) (* w h)) (* D D))
13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
33.0ms	(+ (/ (/ (* c0 (* d d)) (* w h)) (* D D)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series526.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (/ (* c0 (* d d)) (* w h)) (* D D))
95.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
94.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
242.0ms	(+ (/ (/ (* c0 (* d d)) (* w h)) (* D D)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify42.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	819	2282
1	5001	1641

prune338.0ms

Filtered

179 candidates to 78 candidates (43.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	177	7	184

Merged error: 33.5b

Counts

184 → 7

regimes393.0ms

Accuracy

-12.5% (2.9b remaining)

Error of 33.8b against oracle of 30.9b and baseline of 33.4b

bsearch264.0ms

Steps

Iters	Range		Point
7	4.0678147655887687e+40	3.243241867457378e+42	4.1213718670786918e+40
8	1.3559164959089644e+18	5.879238312391923e+20	5.828418147358303e+20

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	26
1	39	26

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.3s	2285×	body	5120	valid
1.0s	13219×	body	80	nan
828.0ms	1759×	body	2560	valid
524.0ms	6720×	body	80	valid
354.0ms	570×	body	5120	exit
346.0ms	905×	body	1280	valid
139.0ms	459×	body	640	valid
53.0ms	232×	body	320	valid
16.0ms	108×	body	160	valid