Details

sample139.0ms

Algorithm

intervals

Results

43.0ms	128×	body	320	valid
41.0ms	236×	body	80	nan
25.0ms	123×	body	160	valid
1.0ms	5×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4583
7	1834
6	1286
5	947
4	584
3	298
2	122
1	43
0	19

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize55.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

37.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
33.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

440.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
442.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
68.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1399
1	395
0	166

prune851.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 28.4b

localize69.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite76.0ms

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`
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 → 59

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
42.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
13.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* g g) (* h h))
456.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
58.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1596
1	343
0	137

prune841.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.3b

localize55.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite98.0ms

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`
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 → 59

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
48.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
13.0ms	(sqrt (- (* g g) (* h h)))
22.0ms	(sqrt (- (* g g) (* h h)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* g g) (* h h))
492.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
60.0ms	(sqrt (- (* g g) (* h h)))
84.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1596
1	343
0	137

prune862.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 28.3b

localize60.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite58.0ms

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` `flip3--` `flip--`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
33.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* g g) (* h h))
467.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
72.0ms	(sqrt (- (* g g) (* h h)))
76.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1538
1	321
0	135

prune771.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 28.1b

regimes1.7s

Accuracy

64.3% (1.3b remaining)

Error of 31.1b against oracle of 29.8b and baseline of 33.5b

bsearch592.0ms

Steps

Iters	Range		Point
13	-7.829763555410595e-304	1.2597964146603314e-220	1.2431276235478423e-220

simplify19.0ms

Iterations

Iter	Nodes
done	45
1	45
0	34

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.9s	3756×	body	320	valid
1.6s	8091×	body	80	nan
1.2s	4076×	body	160	valid
19.0ms	168×	body	80	valid