Details

sample520.0ms

Algorithm

intervals

Results

290.0ms	1244×	body	80	nan
96.0ms	406×	body	80	valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	35
1	54	35
2	174	35
3	717	35
4	4580	35
done	5000	35

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize56.0ms

Local error

Found 4 expressions with local error:

8.4b	(* (* (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))))
11.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.6b	(pow (/ d l) (/ 1.0 2.0))
12.4b	(pow (/ d h) (/ 1.0 2.0))

rewrite222.0ms

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:

84.0ms	(* (* (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))))
102.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms	(pow (/ d l) (/ 1.0 2.0))
13.0ms	(pow (/ d h) (/ 1.0 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

848.0ms	(* (* (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))))
944.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
89.0ms	(pow (/ d l) (/ 1.0 2.0))
100.0ms	(pow (/ d h) (/ 1.0 2.0))

simplify2.2s

Counts

202 → 202

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	463	5058
1	1140	4644
2	3982	4180
done	5000	4172

prune941.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.9b

localize80.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (* M D) (* 2.0 d))
8.4b	(* (* (* (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))))
11.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.6b	(pow (/ d l) (/ 1.0 2.0))

rewrite546.0ms

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:

21.0ms	(/ (* M D) (* 2.0 d))
411.0ms	(* (* (* (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))))
74.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (* (* (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))))
979.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
93.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify684.0ms

Counts

286 → 286

Iterations

Useful iterations: done (671.0ms)

Iter	Nodes	Cost
0	574	11962
1	1333	10811
done	5000	9346

prune1.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.9b

localize97.0ms

Local error

Found 4 expressions with local error:

1.9b	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
2.4b	(/ (* M D) (* 2.0 d))
8.4b	(* (* (* (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))))
11.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.1s

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:

18.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
14.0ms	(/ (* M D) (* 2.0 d))
745.0ms	(* (* (* (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))))
64.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.1s

Counts

4 → 12

Calls

4 calls:

167.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0))
40.0ms	(/ (* M D) (* 2.0 d))
833.0ms	(* (* (* (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))))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.5s

Counts

1009 → 1009

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	1205	72885
1	2081	61704
done	5000	52345

prune1.4s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.2b

localize99.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (* M D) (* 2.0 d))
5.2b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
5.3b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
8.4b	(* (* (* (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))))

rewrite1.2s

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:

13.0ms	(/ (* M D) (* 2.0 d))
34.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
65.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
846.0ms	(* (* (* (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))))

series3.6s

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* M D) (* 2.0 d))
1.2s	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.2s	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))
1.1s	(* (* (* (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))))

simplify1.4s

Counts

1000 → 1000

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	1194	77301
1	2070	65138
done	5000	55360

prune1.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.7b

regimes2.0s

Accuracy

28.8% (3.7b remaining)

Error of 13.8b against oracle of 10.0b and baseline of 15.3b

bsearch937.0ms

Steps

Iters	Range		Point
9	8036768482737.778	9.320433134551654e+17	9729194181935.69
8	-8.746545328485692e-18	-3.0251795372243202e-22	-1.803741056830327e-21

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	51	368
1	67	298
done	67	298

end0.0ms

sample17.5s

Algorithm

intervals

Results

10.2s	38387×	body	80	nan
3.8s	12747×	body	80	valid