Details

sample635.0ms

Algorithm

intervals

Results

398.0ms	1099×	body	80	nan
164.0ms	400×	body	80	valid

simplify376.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

376.0ms

(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.3b

localize84.0ms

Local error

Found 4 expressions with local error:

13.7b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.7b	(pow (/ d l) (/ 1 2))
11.0b	(pow (/ d h) (/ 1 2))
6.4b	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

331×	`add-exp-log`
179×	`prod-exp`
99×	`div-exp`
60×	`pow-exp`
45×	`times-frac`
40×	`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`
5×	`cbrt-undiv` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`distribute-rgt-in` `sub-neg` `pow-pow` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 208

Calls

4 calls:

Slowest

74.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
51.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.0ms	(pow (/ d h) (/ 1 2))
4.0ms	(pow (/ d l) (/ 1 2))

series634.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

357.0ms	(* (* (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))
85.0ms	(pow (/ d l) (/ 1 2))
76.0ms	(pow (/ d h) (/ 1 2))

simplify39.5s

Counts

182 → 220

Calls

182 calls:

Slowest

887.0ms	(+ (+ (- (log 1) (log 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (log (/ h l)))
870.0ms	(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
841.0ms	(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
836.0ms	(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
685.0ms	(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))

prune4.5s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 11.7b

localize85.0ms

Local error

Found 4 expressions with local error:

13.7b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.7b	(pow (/ d l) (/ 1 2))
6.4b	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.9b	(/ (* M D) (* 2 d))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

368×	`add-exp-log`
207×	`prod-exp`
103×	`div-exp`
60×	`pow-exp`
46×	`add-cbrt-cube`
28×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
20×	`cbrt-unprod`
18×	`pow-to-exp`
16×	`associate-r`
14×	`rec-exp` `1-exp`
13×	`pow-unpow` `unpow-prod-down`
9×	`pow1` `cbrt-undiv`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `associate-/r` `pow-pow` `frac-2neg` `flip3--` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 196

Calls

4 calls:

Slowest

171.0ms	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
60.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
21.0ms	(/ (* M D) (* 2 d))
5.0ms	(pow (/ d l) (/ 1 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

Slowest

1.2s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
116.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
96.0ms	(pow (/ d l) (/ 1 2))
34.0ms	(/ (* M D) (* 2 d))

simplify44.9s

Counts

168 → 208

Calls

168 calls:

Slowest

1.2s	(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
1.2s	(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (pow (/ (cbrt d) (cbrt h)) (/ 1 2)) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
1.1s	(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
1.1s	(* (* (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2)))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
805.0ms	(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))

prune5.0s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.0b

localize120.0ms

Local error

Found 4 expressions with local error:

13.7b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.4b	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
5.9b	(/ (* M D) (* 2 d))
0.6b	(cbrt l)

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

404×	`add-exp-log`
241×	`prod-exp`
103×	`div-exp`
60×	`pow-exp`
55×	`add-cbrt-cube`
27×	`cbrt-unprod`
18×	`pow-to-exp`
16×	`associate-r`
14×	`rec-exp` `1-exp`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`times-frac`
9×	`cbrt-undiv`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `associate-l/` `associate-r/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative` `div-inv`
1×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `flip3--` `pow1/3` `flip--` `associate-/l`

Counts

4 → 177

Calls

4 calls:

Slowest

246.0ms	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
48.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.0ms	(/ (* M D) (* 2 d))
1.0ms	(cbrt l)

series2.1s

Counts

4 → 12

Calls

4 calls:

Slowest

1.6s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
312.0ms	(cbrt l)
106.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
49.0ms	(/ (* M D) (* 2 d))

simplify46.7s

Counts

150 → 189

Calls

150 calls:

Slowest

923.0ms	(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
891.0ms	(+ (* 1 1) (+ (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (* 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
825.0ms	(+ (+ (log (/ 1 2)) (* (- (+ (log M) (log D)) (+ (log 2) (log d))) 2)) (- (log h) (log l)))
748.0ms	(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
733.0ms	(* (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))))

prune5.3s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 7.7b

localize116.0ms

Local error

Found 4 expressions with local error:

7.0b	(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
6.7b	(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
6.4b	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
5.9b	(/ (* D M) (* 2 d))

rewrite537.0ms

Algorithm

rewrite-expression-head

Rules

687×	`add-exp-log`
588×	`add-cbrt-cube`
395×	`prod-exp`
317×	`cbrt-unprod`
188×	`div-exp`
178×	`cbrt-undiv`
20×	`pow-exp`
14×	`pow1`
10×	`add-sqr-sqrt` `pow-to-exp`
9×	`-un-lft-identity` `associate-r*`
8×	`associate-*l/`
6×	`pow-prod-down` `add-cube-cbrt`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`distribute-rgt-in` `frac-times` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `distribute-lft-in` `times-frac` `associate-l` `-commutative` `div-inv` `associate-/l*` `difference-of-squares`
1×	`flip3--` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 273

Calls

4 calls:

Slowest

232.0ms	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
155.0ms	(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
119.0ms	(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
21.0ms	(/ (* D M) (* 2 d))

series1.9s

Counts

4 → 12

Calls

4 calls:

Slowest

1.6s	(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))))
125.0ms	(/ (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* 2 l))
110.0ms	(* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)
38.0ms	(/ (* D M) (* 2 d))

simplify1.4m

Counts

244 → 285

Calls

244 calls:

Slowest

2.6s	(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))
2.5s	(/ (* (* (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
2.2s	(/ (* (* (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) h)) (* (* (* 2 2) 2) (* (* l l) l)))
2.2s	(/ (* (* (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) (/ (* D M) (* 2 d))) (* (* (/ (* D M) (* 2 d)) (/ (* D M) (* 2 d))) (/ (* D M) (* 2 d)))) (* (* h h) h)) (* (* (* 2 2) 2) (* (* l l) l)))
2.1s	(* (* (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* D D) D) (* (* M M) M)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* h h) h))

prune8.0s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 5.9b

regimes2.6s

Accuracy

25% (4.0b remaining)

Error of 10.2b against oracle of 6.1b and baseline of 11.5b

bsearch33.0ms

end0.0ms

sample25.8s

Algorithm

intervals

Results

16.8s	38110×	body	80	nan
6.3s	12891×	body	80	valid