Details

sample66.0ms

Algorithm

intervals

Results

31.0ms	286×	body	80	valid
9.0ms	100×	body	80	nan

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	81	18
3	176	18
4	422	18
5	1174	18
6	4570	18
done	5000	18

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize30.0ms

Local error

Found 4 expressions with local error:

2.0b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.6b	(/ (* M D) (* 2.0 d))
5.4b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
9.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite95.0ms

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:

22.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
14.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
49.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.9s

Counts

4 → 12

Calls

4 calls:

588.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
37.0ms	(/ (* M D) (* 2.0 d))
461.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
856.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.1s

Counts

125 → 125

Iterations

Useful iterations: 2 (320.0ms)

Iter	Nodes	Cost
0	236	2311
1	577	2083
2	2254	1927
done	5001	1927

prune540.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.1b

localize20.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.6b	(/ (* M D) (* 2.0 d))
5.4b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite109.0ms

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:

24.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
19.0ms	(/ (* M D) (* 2.0 d))
14.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
46.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.2s

Counts

4 → 12

Calls

4 calls:

827.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
33.0ms	(/ (* M D) (* 2.0 d))
423.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
924.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: 2 (397.0ms)

Iter	Nodes	Cost
0	224	1799
1	534	1636
2	2226	1480
done	5000	1480

prune436.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize32.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
4.6b	(/ (* M D) (* 2.0 d))
5.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
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)))

rewrite104.0ms

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:

24.0ms	(/ (* M D) (* 2.0 d))
19.0ms	(/ (* M D) (* 2.0 d))
38.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
18.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

series1.6s

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (* M D) (* 2.0 d))
42.0ms	(/ (* M D) (* 2.0 d))
965.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
505.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)))

simplify896.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (264.0ms)

Iter	Nodes	Cost
0	175	1958
1	422	1574
2	1724	1384
done	5000	1384

prune458.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize42.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
4.7b	(* (* M D) (/ 1 (* 2.0 d)))
5.1b	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)
5.4b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) l)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

20.0ms	(/ (* M D) (* 2.0 d))
55.0ms	(* (* M D) (/ 1 (* 2.0 d)))
51.0ms	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)
20.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) l)))

series1.6s

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (* M D) (* 2.0 d))
44.0ms	(* (* M D) (/ 1 (* 2.0 d)))
912.0ms	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)
610.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) l)))

simplify1.7s

Counts

126 → 126

Iterations

Useful iterations: 2 (644.0ms)

Iter	Nodes	Cost
0	247	2467
1	585	1816
2	2414	1576
done	5001	1576

prune581.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.5b

regimes1.5s

Accuracy

31.9% (1.3b remaining)

Error of 8.8b against oracle of 7.5b and baseline of 9.4b

bsearch3.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	44	112
1	57	112
done	57	112

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.9s	9391×	body	80	valid
387.0ms	3020×	body	80	nan