Details

sample743.0ms

Algorithm

intervals

Results

475.0ms	1407×	body	80	nan
124.0ms	411×	body	80	valid

simplify6.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5041
4	4005
3	655
2	170
1	54
0	22

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize100.0ms

Local error

Found 4 expressions with local error:

6.4b	(* (* (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))))
12.7b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
12.8b	(pow (/ d h) (/ 1.0 2.0))
13.3b	(pow (/ d l) (/ 1.0 2.0))

rewrite304.0ms

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:

127.0ms	(* (* (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))))
108.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
32.0ms	(pow (/ d h) (/ 1.0 2.0))
16.0ms	(pow (/ d l) (/ 1.0 2.0))

series2.9s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* (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))))
1.4s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
120.0ms	(pow (/ d h) (/ 1.0 2.0))
95.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify5.4s

Counts

202 → 202

Iterations

Iter	Nodes
done	5001
2	4662
1	1405
0	463

prune2.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.2b

localize236.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) (* 2.0 d))
6.4b	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.3b	(pow (/ d l) (/ 1.0 2.0))

rewrite747.0ms

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:

28.0ms	(/ (* M D) (* 2.0 d))
547.0ms	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
111.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
10.0ms	(pow (/ d l) (/ 1.0 2.0))

series2.9s

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* M D) (* 2.0 d))
1.4s	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
1.4s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
115.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify3.6s

Counts

286 → 286

Iterations

Iter	Nodes
done	5001
1	1635
0	570

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 10.4b

localize283.0ms

Local error

Found 4 expressions with local error:

2.6b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
3.8b	(/ (* M D) (* 2.0 d))
6.4b	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
12.7b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite2.2s

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:

27.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
23.0ms	(/ (* M D) (* 2.0 d))
961.0ms	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
93.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series4.0s

Counts

4 → 12

Calls

4 calls:

383.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
54.0ms	(/ (* M D) (* 2.0 d))
2.0s	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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))))
1.6s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify7.3s

Counts

1255 → 1255

Iterations

Iter	Nodes
done	5000
1	3407
0	1516

prune3.3s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.5b

localize277.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* M D) (* 2.0 d))
4.8b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.4b	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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)))
7.7b	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

6964×	`add-exp-log`
5245×	`prod-exp`
2612×	`pow-exp`
1626×	`div-exp`
788×	`pow-to-exp`
232×	`rec-exp` `1-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 → 1242

Calls

4 calls:

23.0ms	(/ (* M D) (* 2.0 d))
96.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.0s	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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)))
87.0ms	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

series5.1s

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* M D) (* 2.0 d))
1.5s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
2.0s	(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (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)))
1.5s	(/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l)

simplify8.8s

Counts

1254 → 1254

Iterations

Iter	Nodes
done	5000
1	3253
0	1490

prune3.9s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 8.0b

regimes6.1s

Accuracy

-5.1% (6.8b remaining)

Error of 15.7b against oracle of 8.9b and baseline of 15.3b

bsearch2.1s

Steps

Iters	Range	Point
4	2.137943356240003e+146	3.2866166890404634e+146	3.250720647390449e+146
7	2.266942447605223e-76	5.979089740469276e-75	2.5975516398894835e-76
5	-3.3364175928162192e-192	-9.119619150392353e-193	-2.0606592951816603e-192

Iters

Range

Point

2.137943356240003e+146

3.2866166890404634e+146

3.250720647390449e+146

2.266942447605223e-76

5.979089740469276e-75

2.5975516398894835e-76

-3.3364175928162192e-192

-9.119619150392353e-193

-2.0606592951816603e-192

simplify75.0ms

Iterations

Iter	Nodes
done	76
1	76
0	59

end0.0ms

sample33.6s

Algorithm

intervals

Results

19.3s	39051×	body	80	nan
10.0s	12887×	body	80	valid