Details

sample114.0ms

Algorithm

intervals

Results

41.0ms	194×	body	80	valid
24.0ms	25×	body	2560	valid
11.0ms	256×	pre	80	true
10.0ms	17×	body	1280	valid
5.0ms	8×	body	640	valid
4.0ms	8×	body	320	valid
2.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	42
4	42
3	40
2	36
1	29
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
0.5b	(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
12.7b	(sqrt (+ (* x x) (* p (* 4 p))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `sqrt-prod`
8×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-/r*` `times-frac`
5×	`add-log-exp`
4×	`pow1` `sqrt-div`
3×	`flip3-+` `flip-+` `insert-posit16`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

3 → 59

Calls

3 calls:

14.0ms	(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
35.0ms	(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series205.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p)))))
92.0ms	(+ (/ (* 0.5 x) (sqrt (+ (* x x) (* p (* 4 p))))) 0.5)
46.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify940.0ms

Counts

68 → 68

Iterations

Iter	Nodes
3	2985
2	828
1	268
0	109

prune800.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize113.0ms

Local error

Found 4 expressions with local error:

3.5b	(- 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* (* p 4) p))))))
12.7b	(sqrt (+ (* x x) (* (* p 4) p)))
12.7b	(sqrt (+ (* x x) (* (* p 4) p)))
12.7b	(sqrt (+ (* x x) (* (* p 4) p)))

rewrite57.0ms

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×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 61

Calls

4 calls:

8.0ms	(- 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* (* p 4) p))))))
12.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
12.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
24.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* (* p 4) p))))))
50.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
57.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
55.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

simplify2.1s

Counts

73 → 73

Iterations

Iter	Nodes
4	4531
3	1502
2	470
1	164
0	70

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.7b

localize112.0ms

Local error

Found 4 expressions with local error:

12.7b	(sqrt (+ (* x x) (* (* p 4) p)))
12.7b	(sqrt (+ (* x x) (* (* p 4) p)))
12.7b	(sqrt (+ (* x x) (* (* p 4) p)))
12.7b	(sqrt (+ (* x x) (* (* p 4) 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-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

7.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
65.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
45.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
50.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
5	2996
4	1481
3	650
2	253
1	97
0	42

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.7b

localize89.0ms

Local error

Found 4 expressions with local error:

12.7b	(sqrt (+ (* x x) (* (* p 4) p)))
12.7b	(sqrt (+ (* x x) (* (* p 4) p)))
12.7b	(sqrt (+ (* x x) (* (* p 4) p)))
12.7b	(sqrt (+ (* x x) (* (* p 4) p)))

rewrite24.0ms

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:

6.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
6.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
50.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
46.0ms	(sqrt (+ (* x x) (* (* p 4) p)))
50.0ms	(sqrt (+ (* x x) (* (* p 4) p)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
5	2996
4	1481
3	650
2	253
1	97
0	42

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.7b

regimes183.0ms

Accuracy

0% (0.8b remaining)

Error of 13.4b against oracle of 12.5b and baseline of 13.4b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
2	43
1	43
0	31

end0.0ms

sample2.5s

Algorithm

intervals

Results

852.0ms	754×	body	2560	valid
630.0ms	6061×	body	80	valid
349.0ms	8000×	pre	80	true
315.0ms	594×	body	1280	valid
124.0ms	284×	body	640	valid
66.0ms	67×	body	5120	valid
46.0ms	159×	body	320	valid
14.0ms	81×	body	160	valid