Details

sample218.0ms

Algorithm

intervals

Results

67.0ms	114×	body	320	valid
64.0ms	251×	body	80	nan
56.0ms	140×	body	160	valid
0.0ms	2×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	3542
5	1922
4	928
3	370
2	119
1	47
0	19

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.5b

localize49.0ms

Local error

Found 4 expressions with local error:

7.0b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
10.3b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
29.3b	(sqrt (- (* g g) (* h h)))
29.3b	(sqrt (- (* g g) (* h h)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`cbrt-prod`
10×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `cbrt-div` `times-frac`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `pow1/3` `associate-*r/` `flip-+` `flip--`
1×	`associate-*l/` `div-inv` `distribute-lft-out--`

Counts

4 → 77

Calls

4 calls:

26.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
15.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series870.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
417.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
60.0ms	(sqrt (- (* g g) (* h h)))
64.0ms	(sqrt (- (* g g) (* h h)))

simplify1.6s

Counts

89 → 89

Iterations

Iter	Nodes
3	3622
2	1118
1	453
0	207

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.1b

localize74.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
7.0b	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
29.3b	(sqrt (- (* g g) (* h h)))
29.3b	(sqrt (- (* g g) (* h h)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`cbrt-prod` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `times-frac` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `div-inv` `distribute-lft-out--`

Counts

4 → 78

Calls

4 calls:

15.0ms	(- (* g g) (* h h))
15.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
9.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
354.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
56.0ms	(sqrt (- (* g g) (* h h)))
79.0ms	(sqrt (- (* g g) (* h h)))

simplify881.0ms

Counts

90 → 90

Iterations

Iter	Nodes
3	2821
2	802
1	336
0	167

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 29.8b

localize54.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
10.3b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
29.3b	(sqrt (- (* g g) (* h h)))
29.3b	(sqrt (- (* g g) (* h h)))

rewrite57.0ms

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))
13.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
16.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series584.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* g g) (* h h))
400.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
69.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
3	3231
2	888
1	319
0	143

prune1.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 29.8b

localize50.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
10.3b	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
29.3b	(sqrt (- (* g g) (* h h)))
29.3b	(sqrt (- (* g g) (* h h)))

rewrite64.0ms

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))
26.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* g g) (* h h))
360.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
84.0ms	(sqrt (- (* g g) (* h h)))
69.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
3	3231
2	888
1	319
0	143

prune1.4s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 29.8b

regimes821.0ms

Accuracy

75.9% (1.1b remaining)

Error of 30.8b against oracle of 29.7b and baseline of 34.3b

bsearch209.0ms

Steps

Iters	Range		Point
7	2.1251386496485567e-164	2.1335423005090859e-162	2.1044730434263153e-162

simplify7.0ms

Iterations

Iter	Nodes
2	43
1	43
0	34

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.0s	3698×	body	320	valid
2.7s	4158×	body	160	valid
1.8s	7984×	body	80	nan
30.0ms	144×	body	80	valid