Details

sample131.0ms

Algorithm

intervals

Results

49.0ms	136×	body	160	valid
27.0ms	117×	body	320	valid
22.0ms	294×	body	80	nan
0.0ms	3×	body	80	valid

simplify13.2s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize32.0ms

Local error

Found 4 expressions with local error:

5.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
5.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite202.0ms

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:

69.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
71.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
25.0ms	(sqrt (- (* g g) (* h h)))
36.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

482.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
497.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
63.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify1.3s

Counts

80 → 80

Iterations

Useful iterations: done (1.3s)

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

prune680.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 32.8b

localize60.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
5.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite112.0ms

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))
73.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
16.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* g g) (* h h))
399.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
54.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify2.7s

Counts

81 → 81

Iterations

Useful iterations: done (2.7s)

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

prune675.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 31.6b

localize53.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
5.8b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite132.0ms

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:

17.0ms	(- (* g g) (* h h))
86.0ms	(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)))

series673.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
486.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
84.0ms	(sqrt (- (* g g) (* h h)))
61.0ms	(sqrt (- (* g g) (* h h)))

simplify2.8s

Counts

81 → 81

Iterations

Useful iterations: done (2.8s)

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

prune771.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 31.6b

localize36.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
5.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite82.0ms

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))
44.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
11.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* g g) (* h h))
452.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
61.0ms	(sqrt (- (* g g) (* h h)))
63.0ms	(sqrt (- (* g g) (* h h)))

simplify2.6s

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

prune490.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 31.6b

regimes1.1s

Accuracy

81.5% (1.1b remaining)

Error of 31.9b against oracle of 30.8b and baseline of 36.5b

bsearch218.0ms

Steps

Iters	Range		Point
10	-2.2642462469951956e-148	-5.565598515937264e-162	-2.4223450526411114e-160

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	92
1	41	92
done	41	92

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.8s	3693×	body	320	valid
1.2s	7970×	body	80	nan
1.1s	4152×	body	160	valid
15.0ms	155×	body	80	valid