Details

sample169.0ms

Algorithm

intervals

Results

37.0ms	77×	body	5120	valid
28.0ms	425×	body	80	nan
20.0ms	53×	body	2560	valid
16.0ms	227×	body	80	valid
12.0ms	23×	body	10240	exit
11.0ms	35×	body	1280	valid
3.0ms	11×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify112.0ms

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

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.4b

localize24.0ms

Local error

Found 4 expressions with local error:

18.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
26.2b	(+ (/ (* 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)))
13.0ms	(/ (* 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))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (* 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)))
240.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify123.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (106.0ms)

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

prune407.0ms

Filtered

168 candidates to 70 candidates (41.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.0b

localize5.0ms

Local error

Found 1 expressions with local error:

7.7b	(* (/ c0 (* 2.0 w)) 0)

rewrite7.0ms

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:

6.0ms

(* (/ 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 (281.0ms)

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

prune88.0ms

Filtered

33 candidates to 21 candidates (63.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 30.6b

localize2.0ms

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

prune27.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 30.6b

localize31.0ms

Local error

Found 4 expressions with local error:

18.2b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
26.2b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
26.2b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
26.2b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

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))))
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))))
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))))

series1.0s

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
237.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
436.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
237.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify127.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	594	2538
1	3877	2127
2	5001	2112

prune517.0ms

Filtered

120 candidates to 82 candidates (68.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 30.6b

regimes446.0ms

Accuracy

0% (2.3b remaining)

Error of 33.6b against oracle of 31.3b and baseline of 33.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	2
1	4	2

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.1s	2295×	body	5120	valid
814.0ms	12960×	body	80	nan
668.0ms	1700×	body	2560	valid
442.0ms	6808×	body	80	valid
301.0ms	569×	body	10240	exit
296.0ms	917×	body	1280	valid
112.0ms	438×	body	640	valid
40.0ms	212×	body	320	valid
15.0ms	122×	body	160	valid