Details

sample148.0ms

Algorithm

intervals

Results

46.0ms	147×	body	160	valid
37.0ms	102×	body	320	valid
28.0ms	230×	body	80	nan
1.0ms	7×	body	80	valid

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
8	2064
7	1304
6	1067
5	847
4	542
3	270
2	121
1	43
0	19

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize55.0ms

Local error

Found 4 expressions with local error:

7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite119.0ms

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:

51.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

506.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
431.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
80.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify2.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5003
3	4580
2	1256
1	386
0	166

prune919.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 29.9b

localize67.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
46.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
436.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
71.0ms	(sqrt (- (* g g) (* h h)))
83.0ms	(sqrt (- (* g g) (* h h)))

simplify2.5s

Counts

71 → 71

Iterations

Iter	Nodes
done	5004
3	4070
2	1041
1	326
0	137

prune953.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.5b

localize75.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
2.6b	(- (* g g) (* h h))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
6.0ms	(- (* g g) (* h h))
7.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* g g) (* h h))
43.0ms	(- (* g g) (* h h))
64.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	1431
2	331
1	126
0	55

prune794.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 29.5b

localize59.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
34.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
14.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series611.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
453.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
59.0ms	(sqrt (- (* g g) (* h h)))
64.0ms	(sqrt (- (* g g) (* h h)))

simplify2.6s

Counts

71 → 71

Iterations

Iter	Nodes
done	5004
3	4070
2	1041
1	326
0	137

prune634.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 29.5b

regimes1.6s

Accuracy

71.5% (1.0b remaining)

Error of 32.0b against oracle of 31.0b and baseline of 34.6b

bsearch368.0ms

Steps

Iters	Range		Point
12	-1.8813990987943826e-134	-1.0883707337798972e-185	-8.764066339061835e-157

simplify9.0ms

Iterations

Iter	Nodes
done	44
1	44
0	35

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.4s	3702×	body	320	valid
1.3s	7759×	body	80	nan
1.2s	4151×	body	160	valid
362.0ms	147×	body	80	valid