Details

sample259.0ms

Algorithm

intervals

Results

83.0ms	236×	body	80	nan
78.0ms	113×	body	320	valid
67.0ms	139×	body	160	valid
1.0ms	4×	body	80	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	2000
4	1243
3	370
2	119
1	47
0	19

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize68.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
8.0b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
116×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
84×	`cbrt-prod`
62×	`add-cube-cbrt`
28×	`difference-of-squares`
21×	`sqrt-prod`
13×	`distribute-lft-out--`
7×	`div-inv`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `pow1/3` `associate-*r/` `flip-+` `flip--`
1×	`associate-*l/` `associate-/r/`

Counts

4 → 150

Calls

4 calls:

27.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
17.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
10.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series972.0ms

Counts

4 → 12

Calls

4 calls:

467.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
364.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
83.0ms	(sqrt (- (* g g) (* h h)))
57.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

162 → 162

Iterations

Iter	Nodes
done	2001
2	2001
1	890
0	409

prune1.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 31.0b

localize81.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
6.7b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite66.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 73

Calls

4 calls:

16.0ms	(- (* g g) (* h h))
28.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series736.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* g g) (* h h))
529.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
87.0ms	(sqrt (- (* g g) (* h h)))
80.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
3	2000
2	869
1	319
0	143

prune984.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 30.6b

localize73.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
6.7b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite58.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 73

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
15.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
15.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series623.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* g g) (* h h))
436.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
59.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
3	2000
2	869
1	319
0	143

prune832.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.6b

localize76.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))
30.0b	(sqrt (- (* g g) (* h h)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

10.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (- (* g g) (* h h)))
73.0ms	(sqrt (- (* g g) (* h h)))
55.0ms	(sqrt (- (* g g) (* h h)))
73.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	2001
5	2001
4	1362
3	565
2	236
1	108
0	47

prune887.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.6b

regimes935.0ms

Accuracy

63.8% (1.2b remaining)

Error of 31.0b against oracle of 29.8b and baseline of 33.2b

bsearch457.0ms

Steps

Iters	Range		Point
10	1.9241616092538943e-170	7.888639597900709e-156	2.4448816157766584e-161

simplify7.0ms

Iterations

Iter	Nodes
done	40
1	40
0	32

end0.0ms

sample7.5s

Algorithm

intervals

Results

2.8s	3687×	body	320	valid
2.3s	4161×	body	160	valid
1.9s	7874×	body	80	nan
28.0ms	152×	body	80	valid