Details

sample248.0ms

Algorithm

intervals

Results

93.0ms	106×	body	320	valid
63.0ms	141×	body	160	valid
56.0ms	257×	body	80	nan
2.0ms	9×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
6	2529
5	1599
4	844
3	368
2	117
1	45
0	19

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.5b

localize81.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
8.7b	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `pow1/3` `associate-l/` `associate-r/` `flip-+` `flip--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

27.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
15.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
8.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series932.0ms

Counts

4 → 12

Calls

4 calls:

412.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
388.0ms	(cbrt (* (/ (- (sqrt (- (* g g) (* h h))) g) a) 1/2))
62.0ms	(sqrt (- (* g g) (* h h)))
69.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
3	3643
2	1080
1	410
0	178

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.8b

localize65.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))

rewrite68.0ms

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` `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 → 69

Calls

4 calls:

13.0ms	(- (* g g) (* h h))
37.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
8.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* g g) (* h h))
405.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
59.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

81 → 81

Iterations

Iter	Nodes
3	3387
2	867
1	312
0	140

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.2b

localize49.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
3.4b	(- (* g g) (* h h))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

13.0ms	(- (* g g) (* h h))
13.0ms	(- (* g g) (* h h))
16.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
42.0ms	(- (* g g) (* h h))
59.0ms	(sqrt (- (* g g) (* h h)))
82.0ms	(sqrt (- (* g g) (* h h)))

simplify4.7s

Counts

82 → 82

Iterations

Iter	Nodes
4	9194
3	1797
2	402
1	134
0	62

prune1.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.2b

localize93.0ms

Local error

Found 4 expressions with local error:

30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))
30.7b	(sqrt (- (* g g) (* h h)))

rewrite59.0ms

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` `log1p-expm1-u` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

9.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (- (* g g) (* h h)))
71.0ms	(sqrt (- (* g g) (* h h)))
61.0ms	(sqrt (- (* g g) (* h h)))
71.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

84 → 84

Iterations

Iter	Nodes
5	4073
4	1336
3	567
2	233
1	105
0	46

prune1.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.2b

regimes777.0ms

Accuracy

67.2% (1.2b remaining)

Error of 30.5b against oracle of 29.3b and baseline of 32.9b

bsearch335.0ms

Steps

Iters	Range		Point
9	4.357350291335334e-183	4.09161270623166e-175	4.0263109172966606e-175

simplify7.0ms

Iterations

Iter	Nodes
2	38
1	38
0	31

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.8s	4150×	body	160	valid
2.5s	3697×	body	320	valid
2.1s	7982×	body	80	nan
29.0ms	153×	body	80	valid