Details

sample102.0ms

Algorithm

intervals

Results

37.0ms	304×	body	80	valid
12.0ms	92×	body	80	nan

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	177	18
4	441	18
5	2573	18
done	5001	18

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
8.0b	(/ (* M D) (* 2.0 d))
10.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

43.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
11.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms	(/ (* M D) (* 2.0 d))
78.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

631.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
577.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
48.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.6s

Counts

125 → 125

Iterations

Useful iterations: 2 (484.0ms)

Iter	Nodes	Cost
0	236	2311
1	620	2115
2	3082	1929
done	5001	1929

prune513.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize25.0ms

Local error

Found 4 expressions with local error:

4.2b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.5b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.4b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
8.0b	(/ (* M D) (* 2.0 d))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
26×	`prod-exp`
23×	`add-cbrt-cube`
20×	`div-exp`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `pow-exp`
9×	`associate-l`
6×	`cbrt-undiv` `unpow-prod-down` `cbrt-unprod`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`associate-/r*` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

16.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
21.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
30.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
19.0ms	(/ (* M D) (* 2.0 d))

series2.6s

Counts

4 → 12

Calls

4 calls:

621.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
981.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
998.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
48.0ms	(/ (* M D) (* 2.0 d))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	224	1799
1	562	1670
2	3055	1502
done	5001	1496

prune523.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.5b

localize27.0ms

Local error

Found 4 expressions with local error:

4.2b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.5b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
8.0b	(/ (* M D) (* 2.0 d))
8.0b	(/ (* M D) (* 2.0 d))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

352×	`add-exp-log`
173×	`prod-exp`
125×	`div-exp`
75×	`pow-exp`
37×	`add-cbrt-cube`
15×	`pow-to-exp`
11×	`cbrt-undiv` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-/r*` `sqrt-prod`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 136

Calls

4 calls:

17.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
53.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
25.0ms	(/ (* M D) (* 2.0 d))
14.0ms	(/ (* M D) (* 2.0 d))

series1.6s

Counts

4 → 12

Calls

4 calls:

597.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
910.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
42.0ms	(/ (* M D) (* 2.0 d))
38.0ms	(/ (* M D) (* 2.0 d))

simplify1.5s

Counts

148 → 148

Iterations

Useful iterations: 2 (494.0ms)

Iter	Nodes	Cost
0	265	4074
1	787	3743
2	3344	2359
done	5000	2359

prune521.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize26.0ms

Local error

Found 4 expressions with local error:

4.2b	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.5b	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
8.0b	(/ (* M D) (* 2.0 d))
8.1b	(/ (* 2.0 d) (* M D))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

938×	`add-exp-log`
446×	`prod-exp`
401×	`div-exp`
218×	`pow-exp`
40×	`rec-exp` `1-exp`
37×	`add-cbrt-cube`
26×	`pow-to-exp`
11×	`cbrt-undiv` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-/r*` `sqrt-prod`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 224

Calls

4 calls:

22.0ms	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
68.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
20.0ms	(/ (* M D) (* 2.0 d))
30.0ms	(/ (* 2.0 d) (* M D))

series1.6s

Counts

4 → 12

Calls

4 calls:

527.0ms	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
985.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
34.0ms	(/ (* M D) (* 2.0 d))
47.0ms	(/ (* 2.0 d) (* M D))

simplify679.0ms

Counts

236 → 236

Iterations

Useful iterations: done (668.0ms)

Iter	Nodes	Cost
0	479	7403
1	1558	6669
done	5000	5853

prune446.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

regimes990.0ms

Accuracy

0% (2.3b remaining)

Error of 9.2b against oracle of 6.9b and baseline of 9.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	34
1	31	34
done	31	34

end0.0ms

sample2.5s

Algorithm

intervals

Results

948.0ms	9371×	body	80	valid
676.0ms	2971×	body	80	nan