Details

sample83.0ms

Algorithm

intervals

Results

21.0ms	195×	body	80	valid
14.0ms	20×	body	2560	valid
11.0ms	21×	body	1280	valid
10.0ms	256×	pre	80	true
6.0ms	12×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify40.0ms

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: 13.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))
0.0b	(+ (* x x) (* (* p p) 4))
0.7b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
15.0b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

26.0ms	(* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))
7.0ms	(+ (* x x) (* (* p p) 4))
16.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
10.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))
65.0ms	(+ (* x x) (* (* p p) 4))
91.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
58.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify2.2s

Counts

93 → 93

Iterations

Iter	Nodes
3	5212
2	1246
1	396
0	146

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.4b

localize84.0ms

Local error

Found 4 expressions with local error:

2.4b	(+ (* 0.5 0.5) (* (* (* 0.5 0.5) (/ x (+ (* p (* 4 p)) (* x x)))) (/ (* x x) (sqrt (+ (* p (* 4 p)) (* x x))))))
15.0b	(sqrt (+ (* p (* 4 p)) (* x x)))
15.0b	(sqrt (+ (* p (* 4 p)) (* x x)))
15.0b	(sqrt (+ (* p (* 4 p)) (* x x)))

rewrite106.0ms

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-+`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log`

Counts

4 → 56

Calls

4 calls:

16.0ms	(+ (* 0.5 0.5) (* (* (* 0.5 0.5) (/ x (+ (* p (* 4 p)) (* x x)))) (/ (* x x) (sqrt (+ (* p (* 4 p)) (* x x))))))
25.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
37.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
27.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (* 0.5 0.5) (* (* (* 0.5 0.5) (/ x (+ (* p (* 4 p)) (* x x)))) (/ (* x x) (sqrt (+ (* p (* 4 p)) (* x x))))))
61.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
461.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
57.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))

simplify2.0s

Counts

68 → 68

Iterations

Iter	Nodes
3	4198
2	713
1	195
0	70

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.3b

localize102.0ms

Local error

Found 4 expressions with local error:

15.0b	(sqrt (+ (* p (* 4 p)) (* x x)))
15.0b	(sqrt (+ (* p (* 4 p)) (* x x)))
15.0b	(sqrt (+ (* p (* 4 p)) (* x x)))
15.0b	(sqrt (+ (* p (* 4 p)) (* x x)))

rewrite98.0ms

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:

23.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
23.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
28.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
23.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
52.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
55.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))
71.0ms	(sqrt (+ (* p (* 4 p)) (* x x)))

simplify1.8s

Counts

72 → 72

Iterations

Iter	Nodes
5	2781
4	1329
3	582
2	237
1	93
0	41

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.2b

localize50.0ms

Local error

Found 4 expressions with local error:

15.0b	(sqrt (+ (* x x) (* (* p p) 4)))
15.0b	(sqrt (+ (* x x) (* (* p p) 4)))
15.0b	(sqrt (+ (* x x) (* (* p p) 4)))
18.4b	(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

15×	`associate-*r/`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
5×	`frac-times` `associate-*l/`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 62

Calls

4 calls:

5.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
5.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
6.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
284.0ms	(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
62.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
46.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
108.0ms	(cbrt (* (* (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4)))))))

simplify1.4s

Counts

74 → 74

Iterations

Iter	Nodes
4	3032
3	1178
2	424
1	176
0	77

prune846.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.2b

regimes233.0ms

Accuracy

0% (2.1b remaining)

Error of 14.8b against oracle of 12.7b and baseline of 14.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	6035×	body	80	valid
742.0ms	741×	body	2560	valid
338.0ms	605×	body	1280	valid
328.0ms	8000×	pre	80	true
162.0ms	308×	body	640	valid
54.0ms	67×	body	5120	valid
50.0ms	155×	body	320	valid
19.0ms	89×	body	160	valid