Details

sample61.0ms

Algorithm

intervals

Results

13.0ms	194×	body	80	valid
12.0ms	25×	body	2560	valid
7.0ms	20×	body	1280	valid
6.0ms	256×	pre	80	true
3.0ms	11×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify72.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize22.0ms

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))
0.7b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.2b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite135.0ms

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:

26.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(+ (* (* 4.0 p) p) (* x x))
75.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
19.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
41.0ms	(+ (* (* 4.0 p) p) (* x x))
105.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
84.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify665.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1423
1	305
0	127

prune396.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) (* p (* p 4.0)))))
0.0b	(+ (* x x) (* p (* p 4.0)))
0.7b	(+ 1.0 (/ x (sqrt (+ (* x x) (* p (* p 4.0))))))
14.2b	(sqrt (+ (* x x) (* p (* p 4.0))))

rewrite50.0ms

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:

10.0ms	(/ x (sqrt (+ (* x x) (* p (* p 4.0)))))
7.0ms	(+ (* x x) (* p (* p 4.0)))
25.0ms	(+ 1.0 (/ x (sqrt (+ (* x x) (* p (* p 4.0))))))
6.0ms	(sqrt (+ (* x x) (* p (* p 4.0))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ x (sqrt (+ (* x x) (* p (* p 4.0)))))
42.0ms	(+ (* x x) (* p (* p 4.0)))
83.0ms	(+ 1.0 (/ x (sqrt (+ (* x x) (* p (* p 4.0))))))
59.0ms	(sqrt (+ (* x x) (* p (* p 4.0))))

simplify520.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1395
1	303
0	127

prune405.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* p (* p 4.0)) (* x x))
0.2b	(* x (/ 1 (sqrt (+ (* p (* p 4.0)) (* x x)))))
3.2b	(+ 1.0 (* x (/ 1 (sqrt (+ (* p (* p 4.0)) (* x x))))))
14.2b	(sqrt (+ (* p (* p 4.0)) (* x x)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
22×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`unswap-sqr`
4×	`flip3-+` `sqrt-div` `prod-exp` `flip-+`
3×	`associate-l`
2×	`+-commutative` `sum-log` `div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

12.0ms	(+ (* p (* p 4.0)) (* x x))
58.0ms	(* x (/ 1 (sqrt (+ (* p (* p 4.0)) (* x x)))))
4.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* p (* p 4.0)) (* x x))))))
17.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* p (* p 4.0)) (* x x))
63.0ms	(* x (/ 1 (sqrt (+ (* p (* p 4.0)) (* x x)))))
84.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* p (* p 4.0)) (* x x))))))
65.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))

simplify662.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1905
1	429
0	151

prune383.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))))
7.3b	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))))))
14.2b	(sqrt (+ (* p (* p 4.0)) (* x x)))
14.2b	(sqrt (+ (* p (* p 4.0)) (* x x)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
20×	`*-un-lft-identity`
18×	`pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

85.0ms	(* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))))
50.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))))))
15.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))
20.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))))
80.0ms	(+ 1.0 (/ x (* (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))) (sqrt (sqrt (+ (* p (* p 4.0)) (* x x)))))))
62.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))
62.0ms	(sqrt (+ (* p (* p 4.0)) (* x x)))

simplify834.0ms

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	1351
1	322
0	141

prune416.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.1b

regimes141.0ms

Accuracy

0% (0.5b remaining)

Error of 13.5b against oracle of 13.1b and baseline of 13.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

435.0ms	8000×	pre	80	true
381.0ms	6045×	body	80	valid
316.0ms	728×	body	2560	valid
140.0ms	624×	body	1280	valid
64.0ms	331×	body	640	valid
21.0ms	62×	body	5120	valid
18.0ms	138×	body	320	valid
7.0ms	72×	body	160	valid