Details

sample166.0ms

Algorithm

intervals

Results

31.0ms	61×	body	5120	valid
29.0ms	491×	body	80	nan
20.0ms	53×	body	2560	valid
16.0ms	262×	body	80	valid
11.0ms	21×	body	10240	exit
8.0ms	28×	body	1280	valid
5.0ms	11×	body	640	valid
1.0ms	6×	body	160	valid
1.0ms	3×	body	320	valid

simplify108.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune12.0ms

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:

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))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

121×	`*-commutative`
100×	`associate-r`
96×	`times-frac`
42×	`associate-l`
30×	`associate-/r*`
26×	`sqrt-div` `frac-add`
25×	`fma-def`
20×	`associate-/l*`
13×	`flip3--` `flip--`
5×	`frac-2neg` `clear-num`
4×	`div-inv`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 165

Calls

4 calls:

9.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
9.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
89.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
94.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
94.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
239.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify105.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	547	3108
1	2903	3085
2	5001	3083

prune666.0ms

Filtered

177 candidates to 124 candidates (70.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	169	8	177
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	171	8	179

Merged error: 34.8b

Counts

179 → 8

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)

simplify54.0ms

Algorithm

egg-herbie

Counts

11 → 11

Iterations

Useful iterations: 0 (1.0ms)

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

prune52.0ms

Filtered

11 candidates to 8 candidates (72.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	10	1	11
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	11	8	19

Merged error: 32.9b

Counts

19 → 8

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune29.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Merged error: 32.9b

Counts

8 → 8

localize30.0ms

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))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 188

Calls

4 calls:

79.0ms	(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)))
9.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
86.0ms	(+ (* (/ (* c0 d) (* D D)) (/ d (* w h))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series617.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))
93.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
93.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
248.0ms	(+ (* (/ (* c0 d) (* D D)) (/ d (* w h))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify119.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1533	9515
1	5001	9464

prune847.0ms

Filtered

200 candidates to 141 candidates (70.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	194	6	200
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	198	10	208

Merged error: 31.8b

Counts

208 → 10

regimes568.0ms

Accuracy

-6.2% (3.4b remaining)

Error of 34.2b against oracle of 30.9b and baseline of 34.0b

bsearch288.0ms

Steps

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

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	29
1	47	29

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.1s	2247×	body	5120	valid
812.0ms	13058×	body	80	nan
700.0ms	1772×	body	2560	valid
435.0ms	6819×	body	80	valid
294.0ms	551×	body	10240	exit
286.0ms	885×	body	1280	valid
112.0ms	443×	body	640	valid
47.0ms	244×	body	320	valid
14.0ms	111×	body	160	valid