Details

sample44.0ms

Algorithm

intervals

Results

17.0ms	299×	body	80	valid
6.0ms	112×	body	80	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	80	18
3	172	18
4	405	18
5	1246	18
6	4859	18
done	5000	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.4b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b	(/ (* M D) (* 2.0 d))
7.1b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite34.0ms

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:

8.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.0ms	(/ (* M D) (* 2.0 d))
15.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.8s

Counts

4 → 12

Calls

4 calls:

424.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
390.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
28.0ms	(/ (* M D) (* 2.0 d))
915.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify807.0ms

Counts

125 → 125

Iterations

Useful iterations: 2 (258.0ms)

Iter	Nodes	Cost
0	236	2311
1	610	2083
2	2308	1927
done	5000	1927

prune399.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.2b

localize14.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.4b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.5b	(/ (* M D) (* 2.0 d))

rewrite32.0ms

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:

9.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
9.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
4.0ms	(/ (* M D) (* 2.0 d))

series1.9s

Counts

4 → 12

Calls

4 calls:

718.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
757.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
382.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
30.0ms	(/ (* M D) (* 2.0 d))

simplify777.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (214.0ms)

Iter	Nodes	Cost
0	224	1799
1	560	1636
2	2312	1480
done	5000	1480

prune364.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

5.4b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))
5.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
4.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.2s

Counts

4 → 12

Calls

4 calls:

389.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))
28.0ms	(/ (* M D) (* 2.0 d))
35.0ms	(/ (* M D) (* 2.0 d))
755.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify729.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (159.0ms)

Iter	Nodes	Cost
0	175	1958
1	446	1574
2	1757	1384
done	5000	1384

prune364.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize26.0ms

Local error

Found 4 expressions with local error:

5.4b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) l)))
5.5b	(/ (* 2.0 d) (* M D))
5.5b	(/ (* M D) (* 2.0 d))
5.9b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log`
38×	`prod-exp`
30×	`div-exp` `add-cbrt-cube`
29×	`add-sqr-sqrt`
24×	`associate-l`
23×	`unpow-prod-down`
22×	`times-frac`
19×	`*-un-lft-identity`
16×	`add-cube-cbrt` `pow-exp`
9×	`cbrt-unprod`
8×	`cbrt-undiv`
6×	`div-inv`
5×	`pow1` `rec-exp` `1-exp` `sqrt-prod` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-r`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) l)))
4.0ms	(/ (* 2.0 d) (* M D))
4.0ms	(/ (* M D) (* 2.0 d))
24.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

series1.2s

Counts

4 → 12

Calls

4 calls:

383.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)) l)))
35.0ms	(/ (* 2.0 d) (* M D))
28.0ms	(/ (* M D) (* 2.0 d))
730.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)

simplify980.0ms

Counts

130 → 130

Iterations

Useful iterations: 2 (264.0ms)

Iter	Nodes	Cost
0	283	2582
1	743	2367
2	2728	1813
done	5001	1813

prune462.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

regimes844.0ms

Accuracy

0% (1.8b remaining)

Error of 9.4b against oracle of 7.6b and baseline of 9.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

475.0ms	9351×	body	80	valid
171.0ms	3125×	body	80	nan