Details

sample126.0ms

Algorithm

intervals

Results

41.0ms	118×	body	320	valid
25.0ms	295×	body	80	nan
25.0ms	134×	body	160	valid
0.0ms	4×	body	80	valid

simplify13.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	125	36
3	314	36
4	633	36
5	1023	36
6	1325	36
7	1628	36
8	2988	36
done	5001	36

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize40.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.2b	(sqrt (- (* g g) (* h h)))
32.2b	(sqrt (- (* g g) (* h h)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

53.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
70.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

437.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
440.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
86.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	172	1528
1	402	1345
2	1358	1225
done	5001	1180

prune803.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 33.9b

localize28.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.2b	(sqrt (- (* g g) (* h h)))
32.2b	(sqrt (- (* g g) (* h h)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `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:

9.0ms	(- (* g g) (* h h))
39.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
13.0ms	(sqrt (- (* g g) (* h h)))
36.0ms	(sqrt (- (* g g) (* h h)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* g g) (* h h))
452.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
67.0ms	(sqrt (- (* g g) (* h h)))
68.0ms	(sqrt (- (* g g) (* h h)))

simplify3.4s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	144	1220
1	311	1079
2	1051	975
3	4408	952
done	5000	952

prune712.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 33.6b

localize39.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
9.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.2b	(sqrt (- (* g g) (* h h)))
32.2b	(sqrt (- (* g g) (* h h)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `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:

22.0ms	(- (* g g) (* h h))
67.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
15.0ms	(sqrt (- (* g g) (* h h)))
23.0ms	(sqrt (- (* g g) (* h h)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* g g) (* h h))
428.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
92.0ms	(sqrt (- (* g g) (* h h)))
86.0ms	(sqrt (- (* g g) (* h h)))

simplify2.9s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	144	1220
1	311	1079
2	1051	975
3	4408	952
done	5000	952

prune712.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 33.6b

localize71.0ms

Local error

Found 4 expressions with local error:

32.2b	(sqrt (- (* g g) (* h h)))
32.2b	(sqrt (- (* g g) (* h h)))
32.2b	(sqrt (- (* g g) (* h h)))
32.2b	(sqrt (- (* g g) (* h h)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

16.0ms	(sqrt (- (* g g) (* h h)))
24.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- (* g g) (* h h)))
77.0ms	(sqrt (- (* g g) (* h h)))
76.0ms	(sqrt (- (* g g) (* h h)))
71.0ms	(sqrt (- (* g g) (* h h)))

simplify3.6s

Counts

84 → 84

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	46	968
1	106	828
2	251	768
3	617	744
4	1561	744
5	4888	744
done	5000	744

prune792.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 33.6b

regimes875.0ms

Accuracy

49.8% (1.9b remaining)

Error of 32.6b against oracle of 30.8b and baseline of 34.5b

bsearch177.0ms

Steps

Iters	Range		Point
8	2.1557865162740726e-166	7.485544681888464e-162	1.5711833012739066e-162

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	32	85
1	41	83
done	41	83

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.8s	3724×	body	320	valid
1.3s	4100×	body	160	valid
898.0ms	7892×	body	80	nan
49.0ms	176×	body	80	valid