Details

sample100.0ms

Algorithm

intervals

Results

29.0ms	18×	body	2560	valid
18.0ms	191×	body	80	valid
10.0ms	21×	body	1280	valid
8.0ms	256×	pre	80	true
5.0ms	13×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
1.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite292.0ms

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×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

57.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
37.0ms	(+ (* (* 4.0 p) p) (* x x))
122.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
71.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms	(+ (* (* 4.0 p) p) (* x x))
158.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
108.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify6.5s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
3	4397
2	1069
1	307
0	128

prune880.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.5b	(/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x))
1.3b	(+ 1.0 (/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)))
11.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite799.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
83×	`*-un-lft-identity`
81×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
39×	`sqrt-prod`
22×	`associate-/r*`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1` `div-inv`
3×	`cbrt-undiv` `flip3-+` `flip-+` `associate-/l*`
2×	`+-commutative` `rec-exp` `sqrt-div` `1-exp` `sum-log` `distribute-lft-out`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 151

Calls

4 calls:

37.0ms	(+ (* (* 4.0 p) p) (* x x))
558.0ms	(/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x))
135.0ms	(+ 1.0 (/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)))
51.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (* (* 4.0 p) p) (* x x))
142.0ms	(/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x))
171.0ms	(+ 1.0 (/ 1 (/ (sqrt (+ (* (* 4.0 p) p) (* x x))) x)))
118.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify2.9s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	1920
1	626
0	237

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

localize121.0ms

Local error

Found 4 expressions with local error:

2.7b	(/ (* x x) (+ (* (* p 4.0) p) (* x x)))
11.4b	(sqrt (+ (* (* p 4.0) p) (* x x)))
11.4b	(sqrt (+ (* (* p 4.0) p) (* x x)))
11.4b	(sqrt (+ (* (* p 4.0) p) (* x x)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

72.0ms	(/ (* x x) (+ (* (* p 4.0) p) (* x x)))
52.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))
55.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))
56.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (* x x) (+ (* (* p 4.0) p) (* x x)))
117.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))
105.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))
120.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))

simplify2.6s

Counts

80 → 80

Iterations

Iter	Nodes
done	5002
2	1033
1	232
0	79

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.8b

localize194.0ms

Local error

Found 4 expressions with local error:

5.5b	(exp (log (sqrt (+ (* (* p 4.0) p) (* x x)))))
11.4b	(sqrt (+ (* (* p 4.0) p) (* x x)))
11.4b	(sqrt (+ (* (* p 4.0) p) (* x x)))
11.4b	(sqrt (+ (* (* p 4.0) p) (* x x)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`sqrt-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`sqrt-div`
6×	`log-prod` `exp-prod` `exp-sum`
4×	`add-exp-log` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `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:

47.0ms	(exp (log (sqrt (+ (* (* p 4.0) p) (* x x)))))
55.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))
51.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))
47.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(exp (log (sqrt (+ (* (* p 4.0) p) (* x x)))))
109.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))
109.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))
115.0ms	(sqrt (+ (* (* p 4.0) p) (* x x)))

simplify6.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
5	3293
4	1449
3	694
2	311
1	149
0	81

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.8b

regimes838.0ms

Accuracy

0% (0.5b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 13.1b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	36
1	36
0	24

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	8000×	pre	80	true
674.0ms	6090×	body	80	valid
566.0ms	707×	body	2560	valid
278.0ms	594×	body	1280	valid
214.0ms	304×	body	640	valid
50.0ms	62×	body	5120	valid
44.0ms	170×	body	320	valid
13.0ms	73×	body	160	valid