Details

sample233.0ms

Algorithm

intervals

Results

87.0ms	139×	body	160	valid
71.0ms	113×	body	320	valid
45.0ms	236×	body	80	nan
1.0ms	4×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2005
5	2005
4	1170
3	353
2	116
1	46
0	19

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

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×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `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 → 69

Calls

4 calls:

37.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
20.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* 2 a)))
9.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

389.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
306.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* 2 a)))
67.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	2000
3	2000
2	1070
1	431
0	199

prune939.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.0b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

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` `insert-posit16`
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 → 63

Calls

4 calls:

8.0ms	(- (* g g) (* h h))
34.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
14.0ms	(sqrt (- (* g g) (* h h)))
23.0ms	(sqrt (- (* g g) (* h h)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
449.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
78.0ms	(sqrt (- (* g g) (* h h)))
77.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	2002
3	2002
2	832
1	303
0	134

prune745.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.6b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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` `insert-posit16`
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 → 63

Calls

4 calls:

13.0ms	(- (* g g) (* h h))
42.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
14.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* g g) (* h h))
428.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
70.0ms	(sqrt (- (* g g) (* h h)))
74.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

75 → 75

Iterations

Iter	Nodes
done	2002
3	2002
2	832
1	303
0	134

prune835.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.6b

localize118.0ms

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)))

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×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

14.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (- (* g g) (* h h)))
85.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))
77.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	2001
5	2001
4	1120
3	471
2	205
1	99
0	45

prune800.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.6b

regimes891.0ms

Accuracy

64% (1.2b remaining)

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

bsearch416.0ms

Steps

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

simplify37.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.0s	3687×	body	320	valid
2.3s	7874×	body	80	nan
2.0s	4161×	body	160	valid
29.0ms	152×	body	80	valid