Details

sample270.0ms

Algorithm

intervals

Results

141.0ms	1288×	body	80	nan
63.0ms	438×	body	80	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	17
1	174	17
2	720	17
3	5001	17

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: 25.0b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* (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))))
10.6b	(pow (/ d l) (/ 1.0 2.0))
10.7b	(pow (/ d h) (/ 1.0 2.0))
13.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
40×	`pow-exp`
30×	`add-cbrt-cube`
26×	`unpow-prod-down` `pow-unpow`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 190

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))))
6.0ms	(pow (/ d l) (/ 1.0 2.0))
6.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

612.0ms	(* (* (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))))
64.0ms	(pow (/ d l) (/ 1.0 2.0))
65.0ms	(pow (/ d h) (/ 1.0 2.0))
710.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify56.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5002	2125

prune740.0ms

Filtered

202 candidates to 119 candidates (58.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	181	21	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	21	203

Merged error: 11.5b

Counts

203 → 21

localize42.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
6.5b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
10.6b	(pow (/ d l) (/ 1.0 2.0))
13.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

738×	`add-exp-log`
487×	`prod-exp`
216×	`pow-exp`
171×	`div-exp`
78×	`pow-to-exp`
46×	`add-cbrt-cube`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1` `cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `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 → 274

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
35.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.4s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
619.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
64.0ms	(pow (/ d l) (/ 1.0 2.0))
717.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify80.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1710	6060
1	5001	5717

prune827.0ms

Filtered

286 candidates to 104 candidates (36.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	277	9	286
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	283	24	307

Merged error: 11.0b

Counts

307 → 24

localize59.0ms

Local error

Found 4 expressions with local error:

2.3b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
4.6b	(/ (* M D) (* 2.0 d))
6.5b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
13.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

6965×	`add-exp-log`
5245×	`prod-exp`
2614×	`pow-exp`
1626×	`div-exp`
789×	`pow-to-exp`
232×	`rec-exp` `1-exp`
55×	`add-cbrt-cube`
37×	`times-frac`
34×	`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`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1243

Calls

4 calls:

7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
83.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))

series1.9s

Counts

4 → 12

Calls

4 calls:

177.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
27.0ms	(/ (* M D) (* 2.0 d))
975.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
732.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify394.0ms

Algorithm

egg-herbie

Counts

1255 → 1255

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5001	45180

prune1.3s

Filtered

1255 candidates to 144 candidates (11.5%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	1248	7	1255
Fresh	1	22	23
Picked	1	0	1
Done	0	0	0
Total	1250	29	1279

Merged error: 8.7b

Counts

1279 → 29

localize56.0ms

Local error

Found 4 expressions with local error:

4.4b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
4.6b	(/ (* M D) (* 2.0 d))
6.3b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
6.5b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

6936×	`add-exp-log`
5237×	`prod-exp`
2607×	`pow-exp`
1610×	`div-exp`
787×	`pow-to-exp`
232×	`rec-exp` `1-exp`
60×	`add-cbrt-cube`
30×	`prod-diff`
29×	`cbrt-unprod`
24×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
10×	`cbrt-undiv`
8×	`times-frac` `associate-r` `div-inv`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `associate-r/` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 1220

Calls

4 calls:

8.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.0ms	(/ (* M D) (* 2.0 d))
17.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
84.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))

series2.6s

Counts

4 → 12

Calls

4 calls:

721.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
26.0ms	(/ (* M D) (* 2.0 d))
927.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
971.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))

simplify379.0ms

Algorithm

egg-herbie

Counts

1232 → 1232

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5001	46241

prune748.0ms

Filtered

1232 candidates to 93 candidates (7.5%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	1225	7	1232
Fresh	2	26	28
Picked	1	0	1
Done	0	0	0
Total	1228	33	1261

Merged error: 8.6b

Counts

1261 → 33

regimes1.4s

Accuracy

3.3% (5.6b remaining)

Error of 15.4b against oracle of 9.7b and baseline of 15.6b

bsearch392.0ms

Steps

Iters	Range		Point
10	-2.3398489408278778e-151	-1.006683451920089e-167	-2.299316884642459e-151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	75
1	64	75

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.2s	38667×	body	80	nan
1.8s	12847×	body	80	valid