Details

sample181.0ms

Algorithm

intervals

Results

58.0ms	121×	body	320	valid
55.0ms	129×	body	160	valid
42.0ms	276×	body	80	nan
1.0ms	6×	body	80	valid

simplify889.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.4b

localize63.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
11.8b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
32.7b	(sqrt (- (* g g) (* h h)))
32.7b	(sqrt (- (* g g) (* h h)))

rewrite79.0ms

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:

23.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
21.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
15.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series854.0ms

Counts

4 → 12

Calls

4 calls:

409.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
318.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ a 1/2)))
53.0ms	(sqrt (- (* g g) (* h h)))
73.0ms	(sqrt (- (* g g) (* h h)))

simplify1.0s

Counts

162 → 162

Iterations

Iter	Nodes
done	2001
2	2001
1	890
0	409

prune1.3s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 32.8b

localize76.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.6b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
32.7b	(sqrt (- (* g g) (* h h)))
32.7b	(sqrt (- (* g g) (* h h)))

rewrite65.0ms

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:

13.0ms	(- (* g g) (* h h))
28.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* g g) (* h h))
366.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
66.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify900.0ms

Counts

85 → 85

Iterations

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

prune654.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.0b

localize57.0ms

Local error

Found 4 expressions with local error:

5.3b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ (cbrt a) 1/2)))
7.6b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
32.7b	(sqrt (- (* g g) (* h h)))
32.7b	(sqrt (- (* g g) (* h h)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
197×	`add-sqr-sqrt`
192×	`cbrt-prod`
151×	`*-un-lft-identity`
107×	`add-cube-cbrt`
46×	`difference-of-squares`
30×	`sqrt-prod`
22×	`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 → 204

Calls

4 calls:

14.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ (cbrt a) 1/2)))
14.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
15.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series888.0ms

Counts

4 → 12

Calls

4 calls:

434.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (/ (cbrt a) 1/2)))
344.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
62.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

216 → 216

Iterations

Iter	Nodes
done	2002
2	2002
1	1162
0	529

prune1.7s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 31.9b

localize146.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
7.6b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
32.7b	(sqrt (- (* g g) (* h h)))
32.7b	(sqrt (- (* g g) (* h h)))

rewrite51.0ms

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:

11.0ms	(- (* g g) (* h h))
14.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
10.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* g g) (* h h))
389.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
62.0ms	(sqrt (- (* g g) (* h h)))
64.0ms	(sqrt (- (* g g) (* h h)))

simplify1.0s

Counts

85 → 85

Iterations

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

prune828.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 31.9b

regimes1.2s

Accuracy

65.9% (1.2b remaining)

Error of 31.4b against oracle of 30.3b and baseline of 33.7b

bsearch322.0ms

Steps

Iters	Range		Point
10	3.6644910581374805e-172	7.676874108513267e-159	2.5929545688553364e-160

simplify13.0ms

Iterations

Iter	Nodes
done	43
1	43
0	35

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.5s	3790×	body	320	valid
2.2s	7981×	body	80	nan
1.9s	4074×	body	160	valid
24.0ms	136×	body	80	valid