Details

sample359.0ms

Algorithm

intervals

Results

210.0ms	1219×	body	80	nan
87.0ms	398×	body	80	valid

simplify30.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize29.0ms

Local error

Found 4 expressions with local error:

7.3b	(* (* (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))))
10.2b	(pow (/ d h) (/ 1.0 2.0))
11.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.7b	(pow (/ d l) (/ 1.0 2.0))

rewrite76.0ms

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:

33.0ms	(* (* (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))))
4.0ms	(pow (/ d h) (/ 1.0 2.0))
25.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

614.0ms	(* (* (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))))
65.0ms	(pow (/ d h) (/ 1.0 2.0))
705.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
65.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5001	2125

prune735.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.6b

localize42.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* M D) (* 2.0 d))
7.3b	(* (* (* (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))))
11.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.7b	(pow (/ d l) (/ 1.0 2.0))

rewrite248.0ms

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:

4.0ms	(/ (* M D) (* 2.0 d))
194.0ms	(* (* (* (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))))
25.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
4.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
626.0ms	(* (* (* (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))))
732.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
68.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify82.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1710	6060
1	5001	5717

prune807.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.9b

localize55.0ms

Local error

Found 4 expressions with local error:

2.0b	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
3.2b	(/ (* M D) (* 2.0 d))
7.3b	(* (* (* (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))))
11.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite549.0ms

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:

9.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
4.0ms	(/ (* M D) (* 2.0 d))
343.0ms	(* (* (* (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))))
22.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

119.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
33.0ms	(/ (* M D) (* 2.0 d))
628.0ms	(* (* (* (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))))
738.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify329.0ms

Algorithm

egg-herbie

Counts

1009 → 1009

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	4166	38921
1	5001	37861

prune910.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.9b

localize59.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* M D) (* 2.0 d))
4.8b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
5.4b	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
7.3b	(* (* (* (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)))

rewrite569.0ms

Algorithm

rewrite-expression-head

Rules

5936×	`add-exp-log`
4313×	`prod-exp`
1992×	`pow-exp`
1384×	`div-exp`
642×	`pow-to-exp`
57×	`add-cbrt-cube`
42×	`prod-diff`
36×	`add-sqr-sqrt` `*-un-lft-identity`
34×	`add-cube-cbrt`
27×	`cbrt-unprod`
23×	`distribute-rgt-in` `distribute-lft-in`
22×	`times-frac`
11×	`pow1`
10×	`cbrt-undiv`
8×	`associate-r` `div-inv`
4×	`expm1-log1p-u` `pow-prod-down` `associate-l/` `associate-/r` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l*`
1×	`flip3--` `flip--` `associate-/l/` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 1010

Calls

4 calls:

4.0ms	(/ (* M D) (* 2.0 d))
19.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
22.0ms	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
352.0ms	(* (* (* (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)))

series2.3s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
739.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
929.0ms	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)
620.0ms	(* (* (* (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)))

simplify369.0ms

Algorithm

egg-herbie

Counts

1022 → 1022

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	4244	42597
1	5001	41143

prune753.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.8b

regimes863.0ms

Accuracy

-0.7% (4.5b remaining)

Error of 15.6b against oracle of 11.1b and baseline of 15.6b

bsearch605.0ms

Steps

Iters	Range		Point
9	1.2731826265573756e+246	2.725542050564335e+252	1.2656987513771255e+248
9	5.918584834930847e-55	2.364314595882201e-46	2.3155022248962846e-46

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	125
1	83	125

end0.0ms

sample10.9s

Algorithm

intervals

Results

6.5s	37707×	body	80	nan
2.8s	12686×	body	80	valid