Details

sample151.0ms

Algorithm

intervals

Results

41.0ms	83×	body	5120	valid
26.0ms	405×	body	80	nan
17.0ms	46×	body	2560	valid
13.0ms	211×	body	80	valid
7.0ms	22×	body	1280	valid
5.0ms	10×	body	10240	exit
5.0ms	19×	body	640	valid
1.0ms	7×	body	320	valid

simplify111.0ms

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

prune13.0ms

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: 58.8b

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)))
27.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite86.0ms

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:

13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
14.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
36.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
89.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
90.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
250.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify148.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (123.0ms)

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

prune324.0ms

Filtered

168 candidates to 70 candidates (41.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	164	6	170

Merged error: 33.6b

Counts

170 → 6

localize5.0ms

Local error

Found 1 expressions with local error:

6.9b	(* (/ c0 (* 2.0 w)) 0)

rewrite10.0ms

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:

9.0ms

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

series1.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

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

simplify285.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (280.0ms)

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

prune57.0ms

Filtered

33 candidates to 21 candidates (63.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	33	6	39

Merged error: 31.1b

Counts

39 → 6

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

prune14.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Merged error: 31.1b

Counts

6 → 6

localize24.0ms

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)))
27.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
27.5b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

14.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
14.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
34.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
38.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
94.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
258.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
252.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify132.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	594	2392
1	3877	1858
2	5001	1848

prune416.0ms

Filtered

144 candidates to 76 candidates (52.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	144	6	150

Merged error: 31.1b

Counts

150 → 6

regimes346.0ms

Accuracy

63.3% (0.8b remaining)

Error of 32.4b against oracle of 31.6b and baseline of 33.7b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	52
1	31	52

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.1s	2357×	body	5120	valid
789.0ms	13183×	body	80	nan
668.0ms	1719×	body	2560	valid
431.0ms	6766×	body	80	valid
301.0ms	584×	body	10240	exit
273.0ms	876×	body	1280	valid
107.0ms	441×	body	640	valid
45.0ms	242×	body	320	valid
12.0ms	101×	body	160	valid