Details

sample729.0ms

Algorithm

intervals

Results

472.0ms	1159×	body	80	nan
175.0ms	408×	body	80	valid

simplify5.3s

Counts: 1 → 1

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.9b

localize65.0ms

Local error

Found 4 expressions with local error:

12.0b	(pow (/ d l) (/ 1 2))
11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.2b	(pow (/ d h) (/ 1 2))
7.9b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

331×	`add-exp-log`
179×	`prod-exp`
99×	`div-exp`
60×	`pow-exp`
45×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
30×	`add-cbrt-cube`
26×	`pow-unpow` `unpow-prod-down`
18×	`pow-to-exp`
16×	`associate-r`
14×	`rec-exp` `1-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 222

Calls

4 calls:

Slowest

85.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
53.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.0ms	(pow (/ d h) (/ 1 2))
9.0ms	(pow (/ d l) (/ 1 2))

series730.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

439.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
115.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
98.0ms	(pow (/ d h) (/ 1 2))
78.0ms	(pow (/ d l) (/ 1 2))

simplify2.8s

Counts: 234 → 234

prune4.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.1b

localize79.0ms

Local error

Found 4 expressions with local error:

12.0b	(pow (/ d l) (/ 1 2))
11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.9b	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
4.4b	(/ (* M D) (* 2 d))

rewrite438.0ms

Algorithm

rewrite-expression-head

Rules

320×	`add-exp-log`
171×	`prod-exp`
96×	`div-exp`
46×	`add-cbrt-cube` `pow-exp`
28×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`cbrt-unprod`
16×	`associate-r`
14×	`rec-exp` `1-exp`
13×	`pow-unpow` `unpow-prod-down`
11×	`pow-to-exp`
9×	`pow1` `cbrt-undiv`
7×	`associate-*l/`
6×	`prod-diff` `associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-times` `sqrt-div`
2×	`sub-neg` `flip3--` `associate-l` `pow-prod-down` `*-commutative` `flip--`
1×	`clear-num` `associate-/r` `pow-pow` `frac-2neg` `associate-/l` `sqr-pow`

Counts

4 → 201

Calls

4 calls:

Slowest

339.0ms	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
62.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
23.0ms	(/ (* M D) (* 2 d))
5.0ms	(pow (/ d l) (/ 1 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

1.3s	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
140.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
77.0ms	(pow (/ d l) (/ 1 2))
49.0ms	(/ (* M D) (* 2 d))

simplify1.0s

Counts: 213 → 213

prune4.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 12.3b

localize141.0ms

Local error

Found 4 expressions with local error:

11.0b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.9b	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
4.4b	(/ (* M D) (* 2 d))
3.6b	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2)

rewrite674.0ms

Algorithm

rewrite-expression-head

Rules

617×	`add-exp-log`
388×	`prod-exp`
143×	`div-exp`
113×	`pow-exp`
55×	`add-cbrt-cube`
31×	`pow-to-exp`
27×	`cbrt-unprod`
23×	`pow1`
16×	`associate-r`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
14×	`rec-exp` `1-exp`
10×	`times-frac`
9×	`cbrt-undiv`
8×	`pow-prod-down`
7×	`associate-*l/`
6×	`pow-pow` `prod-diff` `associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `pow-unpow` `sqrt-div`
2×	`sub-neg` `flip3--` `associate-l` `*-commutative` `div-inv` `flip--`
1×	`pow2` `clear-num` `associate-/r` `unpow-prod-down` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `associate-/l` `unpow1/2` `sqr-pow`

Counts

4 → 242

Calls

4 calls:

Slowest

556.0ms	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
57.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
23.0ms	(/ (* M D) (* 2 d))
20.0ms	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2)

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

1.3s	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
147.0ms	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2)
130.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
57.0ms	(/ (* M D) (* 2 d))

simplify1.2s

Counts: 254 → 254

prune6.9s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 8.4b

localize163.0ms

Local error

Found 4 expressions with local error:

7.9b	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (/ (* h (/ (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))) 2)) l)))
6.2b	(/ (* h (/ (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))) 2)) l)
6.0b	(* (/ M 2) (/ D d))
6.0b	(* (/ M 2) (/ D d))

rewrite689.0ms

Algorithm

rewrite-expression-head

Rules

559×	`add-exp-log`
334×	`prod-exp`
260×	`add-cbrt-cube`
148×	`div-exp`
113×	`cbrt-unprod`
102×	`cbrt-undiv`
88×	`add-sqr-sqrt`
68×	`pow-exp`
65×	`times-frac`
64×	`*-un-lft-identity`
61×	`add-cube-cbrt`
42×	`prod-diff`
32×	`associate-r`
27×	`associate-l`
23×	`distribute-rgt-in` `distribute-lft-in`
22×	`pow-to-exp`
17×	`pow1`
11×	`div-inv`
8×	`pow-prod-down` `associate-*r/` `unswap-sqr`
6×	`associate-*l/`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `sqrt-div` `-commutative`
2×	`sub-neg` `flip3--` `flip--` `difference-of-squares`
1×	`clear-num` `frac-2neg` `associate-/l*` `distribute-lft-out--` `associate-/l/`

Counts

4 → 319

Calls

4 calls:

Slowest

486.0ms	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (/ (* h (/ (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))) 2)) l)))
165.0ms	(/ (* h (/ (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))) 2)) l)
13.0ms	(* (/ M 2) (/ D d))
13.0ms	(* (/ M 2) (/ D d))

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

1.4s	(* (* (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) h))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (/ (* h (/ (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))) 2)) l)))
136.0ms	(/ (* h (/ (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))) 2)) l)
54.0ms	(* (/ M 2) (/ D d))
46.0ms	(* (/ M 2) (/ D d))

simplify2.3s

Counts: 331 → 331

prune9.0s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 8.3b

regimes2.7s

Accuracy

5.5% (6.5b remaining)

Error of 15.6b against oracle of 9.1b and baseline of 16.0b

bsearch657.0ms

end0.0ms

sample25.9s

Algorithm

intervals

Results

16.9s	39256×	body	80	nan
6.0s	12940×	body	80	valid