Details

sample60.0ms

Algorithm

intervals

Results

14.0ms	30×	body	2560	valid
12.0ms	194×	body	80	valid
5.0ms	256×	pre	80	true
5.0ms	15×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	41
5	41
4	40
3	38
2	34
1	27
0	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.1b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

13.0ms	(+ (* (* 4.0 p) p) (* x x))
30.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
53.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
26.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* (* 4.0 p) p) (* x x))
78.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
105.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.1s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1422
1	305
0	127

prune530.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.4b

localize72.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (* x x) (+ (* x x) (* p (* 4.0 p))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `associate-/r*` `sqrt-pow1` `times-frac` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

14.0ms	(/ (* x x) (+ (* x x) (* p (* 4.0 p))))
12.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
7.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (* x x) (+ (* x x) (* p (* 4.0 p))))
81.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
65.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
73.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))

simplify1.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1604
1	228
0	79

prune551.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

localize77.0ms

Local error

Found 4 expressions with local error:

5.5b	(exp (log (sqrt (+ (* x x) (* p (* 4.0 p))))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
8×	`sqrt-div`
6×	`log-prod` `exp-prod` `exp-sum`
4×	`sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `log-pow`
2×	`log-div` `exp-diff`
1×	`rem-exp-log`

Counts

4 → 67

Calls

4 calls:

8.0ms	(exp (log (sqrt (+ (* x x) (* p (* 4.0 p))))))
6.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(exp (log (sqrt (+ (* x x) (* p (* 4.0 p))))))
54.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
59.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
58.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))

simplify1.7s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
4	3102
3	1031
2	338
1	146
0	81

prune593.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.4b

localize115.0ms

Local error

Found 4 expressions with local error:

16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))
16.5b	(sqrt (+ (* x x) (* p (* 4.0 p))))

rewrite26.0ms

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-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
59.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
57.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))
58.0ms	(sqrt (+ (* x x) (* p (* 4.0 p))))

simplify1.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
4	2538
3	865
2	269
1	97
0	42

prune595.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.4b

regimes389.0ms

Accuracy

0% (0.4b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	32
1	32
0	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

632.0ms	6016×	body	80	valid
317.0ms	776×	body	2560	valid
238.0ms	610×	body	1280	valid
180.0ms	8000×	pre	80	true
67.0ms	317×	body	640	valid
55.0ms	158×	body	320	valid
20.0ms	51×	body	5120	valid
7.0ms	72×	body	160	valid