Details

sample184.0ms

Algorithm

intervals

Results

58.0ms	121×	body	320	valid
58.0ms	276×	body	80	nan
43.0ms	129×	body	160	valid
1.0ms	6×	body	80	valid

simplify1.0s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.4b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

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:

33.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
19.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* 2 a)))
14.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series949.0ms

Counts

4 → 12

Calls

4 calls:

435.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
378.0ms	(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* 2 a)))
66.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

81 → 81

Iterations

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

prune736.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 32.9b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

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:

7.0ms	(- (* g g) (* h h))
38.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
13.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* g g) (* h h))
416.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
65.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

75 → 75

Iterations

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

prune763.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.0b

localize41.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
2.8b	(- (* g g) (* h h))
32.7b	(sqrt (- (* g g) (* h h)))
32.7b	(sqrt (- (* g g) (* h h)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 62

Calls

4 calls:

15.0ms	(- (* g g) (* h h))
14.0ms	(- (* g g) (* h h))
23.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* g g) (* h h))
58.0ms	(- (* g g) (* h h))
88.0ms	(sqrt (- (* g g) (* h h)))
83.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	2002
4	2002
3	1567
2	347
1	129
0	57

prune621.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

15.0ms	(- (* g g) (* h h))
22.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
10.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

series624.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
428.0ms	(cbrt (* (/ -1/2 a) (+ (sqrt (- (* g g) (* h h))) g)))
72.0ms	(sqrt (- (* g g) (* h h)))
81.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

75 → 75

Iterations

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

prune547.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 32.0b

regimes976.0ms

Accuracy

66.1% (1.2b remaining)

Error of 31.4b against oracle of 30.2b and baseline of 33.8b

bsearch649.0ms

Steps

Iters	Range		Point
10	3.6644910581374805e-172	7.676874108513267e-159	1.079954365560622e-159

simplify37.0ms

Iterations

Iter	Nodes
done	43
1	43
0	35

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.6s	3790×	body	320	valid
1.8s	7981×	body	80	nan
1.7s	4074×	body	160	valid
22.0ms	136×	body	80	valid