Details

sample71.0ms

Algorithm

intervals

Results

20.0ms	118×	body	320	valid
15.0ms	136×	body	160	valid
14.0ms	229×	body	80	nan
0.0ms	2×	body	80	valid

simplify8.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize18.0ms

Local error

Found 4 expressions with local error:

8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
28.2b	(sqrt (- (* g g) (* h h)))
28.2b	(sqrt (- (* g g) (* h h)))

rewrite107.0ms

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:

32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
11.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
311.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
45.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify805.0ms

Counts

80 → 80

Iterations

Useful iterations: done (802.0ms)

Iter	Nodes	Cost
0	183	1500
1	403	1315
2	1363	1211
done	5000	1166

prune437.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 30.2b

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
8.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
28.2b	(sqrt (- (* g g) (* h h)))
28.2b	(sqrt (- (* g g) (* h h)))

rewrite80.0ms

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:

8.0ms	(- (* g g) (* h h))
46.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
11.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* g g) (* h h))
308.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
49.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify1.8s

Counts

81 → 81

Iterations

Useful iterations: done (1.8s)

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

prune461.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.5b

localize23.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.2b	(sqrt (- (* g g) (* h h)))
28.2b	(sqrt (- (* g g) (* h h)))

rewrite67.0ms

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:

8.0ms	(- (* g g) (* h h))
35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
307.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

81 → 81

Iterations

Useful iterations: 3 (993.0ms)

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

prune478.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.5b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (* g g) (* h h))
8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.2b	(sqrt (- (* g g) (* h h)))
28.2b	(sqrt (- (* g g) (* h h)))

rewrite66.0ms

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:

8.0ms	(- (* g g) (* h h))
32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
13.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
309.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
45.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

81 → 81

Iterations

Useful iterations: 3 (969.0ms)

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

prune396.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 29.5b

regimes755.0ms

Accuracy

82.6% (1.0b remaining)

Error of 31.7b against oracle of 30.7b and baseline of 36.4b

bsearch184.0ms

Steps

Iters	Range		Point
8	4.247425426467879e-244	1.8445018050753954e-240	1.6514801812138535e-243

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	73
1	44	73
done	44	73

end0.0ms

sample2.0s

Algorithm

intervals

Results

621.0ms	3687×	body	320	valid
460.0ms	4170×	body	160	valid
407.0ms	7970×	body	80	nan
8.0ms	143×	body	80	valid