Details

sample302.0ms

Algorithm

intervals

Results

164.0ms	1258×	body	80	nan
69.0ms	418×	body	80	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 29.0b

Counts

2 → 1

localize36.0ms

Local error

Found 4 expressions with local error:

9.7b	(* (* (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))))
12.7b	(pow (/ d l) (/ 1.0 2.0))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
15.6b	(pow (/ d h) (/ 1.0 2.0))

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:

15.0ms	(* (* (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))
14.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms	(pow (/ d h) (/ 1.0 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

672.0ms	(* (* (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))
784.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
71.0ms	(pow (/ d h) (/ 1.0 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5001	2125

prune809.0ms

Filtered

202 candidates to 119 candidates (58.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	182	20	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	20	203

Merged error: 14.5b

Counts

203 → 20

localize47.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
9.7b	(* (* (* (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))))
12.7b	(pow (/ d l) (/ 1.0 2.0))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite86.0ms

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))
37.0ms	(* (* (* (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))
14.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (* M D) (* 2.0 d))
678.0ms	(* (* (* (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))))
73.0ms	(pow (/ d l) (/ 1.0 2.0))
799.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify78.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1710	6060
1	5001	5717

prune873.0ms

Filtered

286 candidates to 104 candidates (36.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	279	7	286
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	282	24	306

Merged error: 14.0b

Counts

306 → 24

localize63.0ms

Local error

Found 4 expressions with local error:

2.7b	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
4.6b	(/ (* M D) (* 2.0 d))
9.7b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

5947×	`add-exp-log`
4317×	`prod-exp`
1997×	`pow-exp`
1387×	`div-exp`
643×	`pow-to-exp`
55×	`add-cbrt-cube`
27×	`cbrt-unprod`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `unpow-prod-down` `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 → 997

Calls

4 calls:

13.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
6.0ms	(/ (* M D) (* 2.0 d))
80.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.6s

Counts

4 → 12

Calls

4 calls:

126.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
29.0ms	(/ (* M D) (* 2.0 d))
675.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
783.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify346.0ms

Algorithm

egg-herbie

Counts

1009 → 1009

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	4169	38921
1	5001	37861

prune972.0ms

Filtered

1009 candidates to 99 candidates (9.8%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	1007	2	1009
Fresh	1	22	23
Picked	1	0	1
Done	0	0	0
Total	1009	24	1033

Merged error: 12.3b

Counts

1033 → 24

localize58.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
6.0b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
7.2b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
9.7b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

5908×	`add-exp-log`
4305×	`prod-exp`
1987×	`pow-exp`
1368×	`div-exp`
641×	`pow-to-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 → 988

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
8.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
81.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

series2.5s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
988.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
793.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
676.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))

simplify354.0ms

Algorithm

egg-herbie

Counts

1000 → 1000

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	4125	41200
1	5001	39750

prune731.0ms

Filtered

1000 candidates to 84 candidates (8.4%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	998	2	1000
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	999	25	1024

Merged error: 12.0b

Counts

1024 → 25

regimes1.5s

Accuracy

28.2% (3.7b remaining)

Error of 14.3b against oracle of 10.6b and baseline of 15.7b

bsearch475.0ms

Steps

Iters	Range		Point
7	3.432581516423483e-49	2.646456886040572e-47	1.5422825791862263e-47
6	-1.5343906860921258e-63	-3.076153805814668e-64	-6.164335148124461e-64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	82
1	66	82

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.8s	38276×	body	80	nan
2.1s	12871×	body	80	valid