Details

sample161.0ms

Algorithm

intervals

Results

34.0ms	61×	body	5120	valid
29.0ms	491×	body	80	nan
21.0ms	53×	body	2560	valid
16.0ms	262×	body	80	valid
11.0ms	21×	body	10240	exit
9.0ms	28×	body	1280	valid
3.0ms	11×	body	640	valid
1.0ms	6×	body	160	valid
1.0ms	3×	body	320	valid

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	26
1	298	26
2	3398	26
3	5002	26

prune4.0ms

Filtered

1 candidates to 0 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: 58.9b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
24.9b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-commutative`
80×	`associate-r`
72×	`times-frac`
34×	`associate-l`
30×	`associate-/r*`
26×	`sqrt-div` `frac-add`
20×	`associate-/l*`
13×	`flip3--` `flip--`
5×	`frac-2neg` `clear-num`
3×	`div-inv`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 140

Calls

4 calls:

8.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
8.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
8.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
85.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
93.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
95.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
257.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify106.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	516	3349
1	2796	3346
2	5002	3346

prune618.0ms

Filtered

152 candidates to 108 candidates (71.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	143	9	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	9	153

Merged error: 34.6b

Counts

153 → 9

localize5.0ms

Local error

Found 1 expressions with local error:

4.2b	(* (/ c0 (* 2.0 w)) 0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`associate-*l/`
2×	`associate-/r` `-commutative`
1×	`frac-2neg` `mul0` `associate-l` `clear-num` `div-inv`

Counts

1 → 8

Calls

1 calls:

4.0ms

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

series1.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

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

simplify58.0ms

Algorithm

egg-herbie

Counts

11 → 11

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	0
1	286	0
2	5001	0

prune56.0ms

Filtered

11 candidates to 8 candidates (72.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	10	1	11
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	11	9	20

Merged error: 32.7b

Counts

20 → 9

localize3.0ms

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

prune31.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Merged error: 32.7b

Counts

9 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

15.3b	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.0b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
31.0b	(+ (* (/ (* c0 d) (* D D)) (/ d (* w h))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-commutative`
98×	`sqrt-div`
96×	`frac-add`
70×	`frac-times`
68×	`associate-/r*`
49×	`flip3--` `flip--`
48×	`times-frac` `associate-r`
32×	`clear-num` `associate-/l*`
30×	`frac-2neg`
20×	`associate-l`
14×	`associate-*l/`
10×	`associate-*r/`
4×	`sqrt-prod` `difference-of-squares`
2×	`un-div-inv` `div-inv`
1×	`+-commutative` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 180

Calls

4 calls:

66.0ms	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
8.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
8.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
85.0ms	(+ (* (/ (* c0 d) (* D D)) (/ d (* w h))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
94.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
94.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
253.0ms	(+ (* (/ (* c0 d) (* D D)) (/ d (* w h))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify128.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1439	10465
1	5001	10452

prune973.0ms

Filtered

192 candidates to 135 candidates (70.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	187	5	192
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	190	11	201

Merged error: 31.6b

Counts

201 → 11

regimes602.0ms

Accuracy

-5.1% (4.1b remaining)

Error of 34.2b against oracle of 30.1b and baseline of 34.0b

bsearch300.0ms

Steps

Iters	Range		Point
9	1.6197691259082564e+33	3.977340724400501e+41	1.655128485054022e+33
9	2697524.489058797	25585202444336.44	25187178024456.76

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	29
1	47	29

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.1s	2247×	body	5120	valid
800.0ms	13058×	body	80	nan
684.0ms	1772×	body	2560	valid
417.0ms	6819×	body	80	valid
290.0ms	551×	body	10240	exit
278.0ms	885×	body	1280	valid
110.0ms	443×	body	640	valid
44.0ms	244×	body	320	valid
13.0ms	111×	body	160	valid