Details

sample143.0ms

Algorithm

intervals

Results

41.0ms	118×	body	160	valid
38.0ms	133×	body	320	valid
27.0ms	297×	body	80	nan
0.0ms	5×	body	80	valid

simplify13.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (30.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize32.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
9.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `frac-times` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-*l/` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

85.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
50.0ms	(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)))

series1.2s

Counts

4 → 12

Calls

4 calls:

480.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
531.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
84.0ms	(sqrt (- (* g g) (* h h)))
79.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

80 → 80

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	183	1500
1	403	1315
2	1361	1211
done	5000	1166

prune723.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 27.9b

localize48.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite128.0ms

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:

13.0ms	(- (* g g) (* h h))
86.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
13.0ms	(sqrt (- (* g g) (* h h)))
13.0ms	(sqrt (- (* g g) (* h h)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* g g) (* h h))
511.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
67.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))

simplify2.6s

Counts

81 → 81

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	144	1192
1	303	1048
2	913	954
3	3379	944
done	5000	934

prune846.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 26.9b

localize33.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite111.0ms

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:

10.0ms	(- (* g g) (* h h))
62.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
20.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* g g) (* h h))
408.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
55.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify2.2s

Counts

81 → 81

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	144	1192
1	303	1048
2	913	954
3	3379	944
done	5000	934

prune732.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 26.9b

localize25.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (* g g) (* h h))
9.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite107.0ms

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:

18.0ms	(- (* g g) (* h h))
46.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* g g) (* h h))
484.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
76.0ms	(sqrt (- (* g g) (* h h)))
86.0ms	(sqrt (- (* g g) (* h h)))

simplify2.7s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.3s)

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

prune614.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 26.9b

regimes1.0s

Accuracy

65.8% (1.2b remaining)

Error of 30.6b against oracle of 29.4b and baseline of 33.0b

bsearch308.0ms

Steps

Iters	Range		Point
10	-2.6442941124154403e-179	-3.996486807713146e-190	-1.213814236807821e-179

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	71
1	36	71
done	36	71

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.9s	3714×	body	320	valid
1.3s	4134×	body	160	valid
918.0ms	8019×	body	80	nan
51.0ms	152×	body	80	valid