Details

analyze1.9s

Algorithm: search

sample137.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
37.0ms	244×	body	80	nan
25.0ms	136×	body	80	invalid

simplify202.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	17
1	174	17
2	710	17
3	4940	17
4	5002	17

prune9.0ms

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: 28.3b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

7.6b	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
9.6b	(pow (/ d h) (/ 1.0 2.0))
12.9b	(pow (/ d l) (/ 1.0 2.0))
13.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
30×	`add-cbrt-cube`
26×	`unpow-prod-down` `pow-unpow`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`distribute-rgt-in` `sub-neg` `pow-pow` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 176

Calls

4 calls:

14.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
5.0ms	(pow (/ d h) (/ 1.0 2.0))
5.0ms	(pow (/ d l) (/ 1.0 2.0))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series546.0ms

Counts

4 → 12

Calls

4 calls:

278.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(pow (/ d l) (/ 1.0 2.0))
241.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify49.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1519	2226
1	5002	2033

prune585.0ms

Filtered

109 candidates to 188 candidates (-72.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	169	19	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	19	189

Merged error: 14.8b

Counts

189 → 19

localize41.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (* M D) (* 2.0 d))
7.6b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.9b	(pow (/ d l) (/ 1.0 2.0))
13.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

818×	`add-exp-log`
567×	`prod-exp`
280×	`pow-exp`
187×	`div-exp`
94×	`pow-to-exp`
46×	`add-cbrt-cube`
32×	`rec-exp` `1-exp`
28×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1` `cbrt-undiv`
4×	`div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 292

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
6.0ms	(pow (/ d l) (/ 1.0 2.0))
14.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series583.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
324.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms	(pow (/ d l) (/ 1.0 2.0))
240.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify83.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	2070	5969
1	5002	5549

prune793.0ms

Filtered

95 candidates to 304 candidates (-220.0%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	294	10	304
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	299	24	323

Merged error: 14.5b

Counts

323 → 24

localize57.0ms

Local error

Found 4 expressions with local error:

3.0b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.3b	(/ (* M D) (* 2.0 d))
7.6b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite405.0ms

Algorithm

rewrite-expression-head

Rules

8121×	`add-exp-log`
6369×	`prod-exp`
3426×	`pow-exp`
1900×	`div-exp`
967×	`pow-to-exp`
592×	`rec-exp` `1-exp`
55×	`add-cbrt-cube`
37×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`cbrt-unprod`
22×	`unpow-prod-down`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-undiv` `cbrt-prod`
4×	`pow-prod-down` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1525

Calls

4 calls:

7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
97.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series602.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
319.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
240.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify445.0ms

Algorithm

egg-herbie

Counts

1537 → 1537

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5001	51143

prune959.0ms

Filtered

131 candidates to 1537 candidates (-1073.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	1531	6	1537
Fresh	5	18	23
Picked	1	0	1
Done	0	0	0
Total	1537	24	1561

Merged error: 13.3b

Counts

1561 → 24

localize60.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (* M D) (* 2.0 d))
7.1b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
7.4b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
7.6b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

8092×	`add-exp-log`
6361×	`prod-exp`
3419×	`pow-exp`
1884×	`div-exp`
965×	`pow-to-exp`
592×	`rec-exp` `1-exp`
60×	`add-cbrt-cube`
29×	`cbrt-unprod`
11×	`pow1`
10×	`cbrt-undiv`
8×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*`
6×	`add-cube-cbrt`
4×	`pow-prod-down` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `times-frac` `associate-r/` `associate-l` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 1478

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
7.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
91.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

series775.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
232.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
217.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
319.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

simplify433.0ms

Algorithm

egg-herbie

Counts

1490 → 1490

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5001	50816

prune638.0ms

Filtered

96 candidates to 1490 candidates (-1452.1%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	1485	5	1490
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	1486	28	1514

Merged error: 12.4b

Counts

1514 → 28

regimes2.0s

Accuracy

13.1% (5.0b remaining)

Error of 15.4b against oracle of 10.4b and baseline of 16.1b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	107
1	82	107

end0.0ms

analyze1.9s

Algorithm: search

sample4.3s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8348×	body	80	nan
875.0ms	4705×	body	80	invalid

Details

analyze1.9s

sample137.0ms

simplify202.0ms

prune9.0ms

localize31.0ms

rewrite47.0ms

series546.0ms

simplify49.0ms

prune585.0ms

localize41.0ms

rewrite79.0ms

series583.0ms

simplify83.0ms

prune793.0ms

localize57.0ms

rewrite405.0ms

series602.0ms

simplify445.0ms

prune959.0ms

localize60.0ms

rewrite397.0ms

series775.0ms

simplify433.0ms

prune638.0ms

regimes2.0s

bsearch4.0ms

simplify2.0ms

end0.0ms

analyze1.9s

sample4.3s

Profiling