Details

sample142.0ms

Algorithm

intervals

Results

38.0ms	34×	body	2560	valid
32.0ms	186×	body	80	valid
22.0ms	18×	body	1280	valid
15.0ms	256×	pre	80	true
9.0ms	12×	body	640	valid
3.0ms	6×	body	320	valid

simplify48.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	40
4	40
3	38
2	34
1	27
0	14

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* p p) 4))
0.0b	(* (* p p) 4)
0.5b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
17.0b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16`
3×	`flip3-+` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`+-commutative` `sum-log` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

16.0ms	(+ (* x x) (* (* p p) 4))
33.0ms	(* (* p p) 4)
24.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
12.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (* x x) (* (* p p) 4))
53.0ms	(* (* p p) 4)
113.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
52.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
3	2963
2	877
1	282
0	109

prune804.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
17.0b	(sqrt (+ (* x x) (* (* p p) 4)))
17.0b	(sqrt (+ (* x x) (* (* p p) 4)))
17.0b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 60

Calls

4 calls:

20.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
6.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
6.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
7.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
59.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
46.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
50.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify2.7s

Counts

72 → 72

Iterations

Iter	Nodes
4	4703
3	1661
2	511
1	173
0	69

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.4b

localize99.0ms

Local error

Found 4 expressions with local error:

17.0b	(sqrt (+ (* (* p p) 4) (* x x)))
17.0b	(sqrt (+ (* (* p p) 4) (* x x)))
17.0b	(sqrt (+ (* (* p p) 4) (* x x)))
17.0b	(sqrt (+ (* (* p p) 4) (* x x)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

34.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
25.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
24.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
20.0ms	(sqrt (+ (* (* p p) 4) (* x x)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
89.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
80.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
90.0ms	(sqrt (+ (* (* p p) 4) (* x x)))

simplify2.1s

Counts

76 → 76

Iterations

Iter	Nodes
5	2622
4	1415
3	655
2	237
1	97
0	42

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.4b

localize107.0ms

Local error

Found 4 expressions with local error:

17.0b	(sqrt (+ (* (* p p) 4) (* x x)))
17.8b	(cbrt (+ (* (* p p) 4) (* x x)))
17.8b	(cbrt (+ (* (* p p) 4) (* x x)))
17.8b	(cbrt (+ (* (* p p) 4) (* x x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

28.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
10.0ms	(cbrt (+ (* (* p p) 4) (* x x)))
10.0ms	(cbrt (+ (* (* p p) 4) (* x x)))
17.0ms	(cbrt (+ (* (* p p) 4) (* x x)))

series713.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
217.0ms	(cbrt (+ (* (* p p) 4) (* x x)))
233.0ms	(cbrt (+ (* (* p p) 4) (* x x)))
192.0ms	(cbrt (+ (* (* p p) 4) (* x x)))

simplify2.8s

Counts

70 → 70

Iterations

Iter	Nodes
4	4810
3	1320
2	423
1	172
0	79

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

regimes201.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.5b and baseline of 12.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.0s	6091×	body	80	valid
577.0ms	735×	body	2560	valid
367.0ms	603×	body	1280	valid
313.0ms	8000×	pre	80	true
145.0ms	316×	body	640	valid
40.0ms	141×	body	320	valid
32.0ms	46×	body	5120	valid
13.0ms	68×	body	160	valid