Details

sample175.0ms

Algorithm

intervals

Results

55.0ms	244×	body	80	nan
45.0ms	117×	body	320	valid
35.0ms	137×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4583
7	1834
6	1286
5	947
4	584
3	298
2	122
1	43
0	19

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize39.0ms

Local error

Found 4 expressions with local error:

7.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.9b	(sqrt (- (* g g) (* h h)))
28.9b	(sqrt (- (* g g) (* h h)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`frac-times` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series996.0ms

Counts

4 → 12

Calls

4 calls:

405.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
441.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
67.0ms	(sqrt (- (* g g) (* h h)))
83.0ms	(sqrt (- (* g g) (* h h)))

simplify683.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1399
1	395
0	166

prune962.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 30.7b

localize71.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
7.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.9b	(sqrt (- (* g g) (* h h)))
28.9b	(sqrt (* (- g h) (+ g h)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqrt-div`
8×	`pow1`
7×	`flip3--` `flip--`
6×	`add-sqr-sqrt` `frac-times` `add-log-exp`
5×	`cbrt-div` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `associate-*r/` `add-exp-log`
3×	`sqrt-pow1` `flip3-+` `associate-*l/` `flip-+`
2×	`pow1/2` `difference-of-squares`
1×	`cbrt-prod` `rem-sqrt-square` `sub-neg` `pow1/3` `diff-log` `pow-prod-down`

Counts

4 → 62

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
51.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
14.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (* (- g h) (+ g h)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* g g) (* h h))
432.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
81.0ms	(sqrt (- (* g g) (* h h)))
88.0ms	(sqrt (* (- g h) (+ g h)))

simplify1.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	2525
1	446
0	178

prune905.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.9b

localize60.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- g) (sqrt (* (+ g h) (- g h))))
1.4b	(- (sqrt (* (- g h) (+ g h))) g)
28.9b	(sqrt (* (- g h) (+ g h)))
28.9b	(sqrt (* (+ g h) (- g h)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`pow1` `*-un-lft-identity` `add-log-exp`
8×	`add-sqr-sqrt` `frac-times` `flip3--` `flip--`
6×	`flip3-+` `flip-+`
4×	`sqrt-pow1` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log` `add-cube-cbrt`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `pow1/2` `pow-prod-down` `sqrt-prod` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 69

Calls

4 calls:

22.0ms	(- (- g) (sqrt (* (+ g h) (- g h))))
35.0ms	(- (sqrt (* (- g h) (+ g h))) g)
30.0ms	(sqrt (* (- g h) (+ g h)))
17.0ms	(sqrt (* (+ g h) (- g h)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (- g) (sqrt (* (+ g h) (- g h))))
110.0ms	(- (sqrt (* (- g h) (+ g h))) g)
86.0ms	(sqrt (* (- g h) (+ g h)))
108.0ms	(sqrt (* (+ g h) (- g h)))

simplify709.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	1477
1	316
0	141

prune1.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 29.8b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- g) (sqrt (* (+ g h) (- g h))))
1.4b	(- (sqrt (* (- g h) (+ g h))) g)
28.9b	(sqrt (* (- g h) (+ g h)))
28.9b	(sqrt (* (+ g h) (- g h)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`pow1` `*-un-lft-identity` `add-log-exp`
8×	`add-sqr-sqrt` `frac-times` `flip3--` `flip--`
6×	`flip3-+` `flip-+`
4×	`sqrt-pow1` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log` `add-cube-cbrt`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `pow1/2` `pow-prod-down` `sqrt-prod` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 69

Calls

4 calls:

21.0ms	(- (- g) (sqrt (* (+ g h) (- g h))))
38.0ms	(- (sqrt (* (- g h) (+ g h))) g)
9.0ms	(sqrt (* (- g h) (+ g h)))
9.0ms	(sqrt (* (+ g h) (- g h)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (- g) (sqrt (* (+ g h) (- g h))))
96.0ms	(- (sqrt (* (- g h) (+ g h))) g)
94.0ms	(sqrt (* (- g h) (+ g h)))
91.0ms	(sqrt (* (+ g h) (- g h)))

simplify715.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	1477
1	316
0	141

prune778.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 29.8b

regimes2.3s

Accuracy

34.5% (1.1b remaining)

Error of 31.8b against oracle of 30.7b and baseline of 32.3b

bsearch387.0ms

Steps

Iters	Range		Point
11	9.716392544916912e-185	3.996805054832145e-156	2.776832660171497e-160

simplify15.0ms

Iterations

Iter	Nodes
done	59
2	59
1	54
0	40

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.9s	7969×	body	80	nan
1.5s	3716×	body	320	valid
919.0ms	4127×	body	160	valid
16.0ms	157×	body	80	valid