Details

sample112.0ms

Algorithm

intervals

Results

45.0ms	117×	body	320	valid
21.0ms	137×	body	160	valid
18.0ms	244×	body	80	nan
0.0ms	2×	body	80	valid

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	125	36
3	315	36
4	640	36
5	1088	36
6	1617	36
7	2196	36
8	4870	36
done	5000	36

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize49.0ms

Local error

Found 4 expressions with local error:

7.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
10.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.9b	(sqrt (- (* g g) (* h h)))
28.9b	(sqrt (- (* g g) (* h h)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `frac-times` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `log1p-expm1-u` `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 → 68

Calls

4 calls:

47.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
36.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

480.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
417.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
71.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify1.0s

Counts

80 → 80

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	172	1528
1	415	1349
2	1507	1225
done	5001	1182

prune850.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 30.8b

localize37.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
7.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.9b	(sqrt (- (* g g) (* h h)))
28.9b	(sqrt (- (* g g) (* h h)))

rewrite81.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

12.0ms	(- (* g g) (* h h))
49.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (* g g) (* h h))
427.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
72.0ms	(sqrt (- (* g g) (* h h)))
79.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

81 → 81

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	144	1220
1	336	1085
2	1610	975
done	5001	956

prune864.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 29.9b

localize46.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
2.6b	(- (* g g) (* h h))
28.9b	(sqrt (- (* g g) (* h h)))
28.9b	(sqrt (- (* g g) (* h h)))

rewrite50.0ms

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:

6.0ms	(- (* g g) (* h h))
6.0ms	(- (* g g) (* h h))
25.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* g g) (* h h))
44.0ms	(- (* g g) (* h h))
67.0ms	(sqrt (- (* g g) (* h h)))
55.0ms	(sqrt (- (* g g) (* h h)))

simplify536.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	62	912
1	151	832
2	703	722
done	5000	722

prune987.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.8b

localize64.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
2.6b	(- (* g g) (* h h))
28.9b	(sqrt (- (* g g) (* h h)))
28.9b	(sqrt (- (* g g) (* h h)))

rewrite47.0ms

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:

12.0ms	(- (* g g) (* h h))
7.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* g g) (* h h))
44.0ms	(- (* g g) (* h h))
59.0ms	(sqrt (- (* g g) (* h h)))
92.0ms	(sqrt (- (* g g) (* h h)))

simplify611.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	62	912
1	151	832
2	703	722
done	5000	722

prune667.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 29.8b

regimes1.5s

Accuracy

0% (1.6b remaining)

Error of 32.3b against oracle of 30.7b and baseline of 32.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	38
1	24	38
done	24	38

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.6s	4127×	body	160	valid
1.6s	7969×	body	80	nan
1.5s	3716×	body	320	valid
18.0ms	157×	body	80	valid