Details

sample119.0ms

Algorithm

intervals

Results

33.0ms	119×	body	320	valid
25.0ms	133×	body	160	valid
24.0ms	276×	body	80	nan
0.0ms	4×	body	80	valid

simplify5.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	125	36
3	315	36
4	640	36
5	1087	36
6	1581	36
7	2180	36
8	4936	36
done	5000	36

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize23.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
8.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
26.8b	(sqrt (- (* g g) (* h h)))
26.8b	(sqrt (- (* g g) (* h h)))

rewrite177.0ms

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:

82.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
58.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

457.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
477.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
66.0ms	(sqrt (- (* g g) (* h h)))
79.0ms	(sqrt (- (* g g) (* h h)))

simplify1.4s

Counts

80 → 80

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	183	1500
1	418	1325
2	1557	1219
done	5002	1192

prune785.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 28.4b

localize50.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
8.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
26.8b	(sqrt (- (* g g) (* h h)))
26.8b	(sqrt (- (* g g) (* h h)))

rewrite106.0ms

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))
36.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
34.0ms	(sqrt (- (* g g) (* h h)))
24.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* g g) (* h h))
487.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
81.0ms	(sqrt (- (* g g) (* h h)))
485.0ms	(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	1601	975
done	5001	956

prune653.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 27.0b

localize55.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
8.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
26.8b	(sqrt (- (* g g) (* h h)))
26.8b	(sqrt (- (* g g) (* h h)))

rewrite104.0ms

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))
51.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
21.0ms	(sqrt (- (* g g) (* h h)))
22.0ms	(sqrt (- (* g g) (* h h)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
337.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
55.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts

81 → 81

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	144	1220
1	336	1085
2	1601	975
done	5001	956

prune724.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.0b

localize27.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
26.8b	(sqrt (- (* g g) (* h h)))
26.8b	(sqrt (- (* g g) (* h h)))

rewrite142.0ms

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:

15.0ms	(- (* g g) (* h h))
71.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
22.0ms	(sqrt (- (* g g) (* h h)))
31.0ms	(sqrt (- (* g g) (* h h)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* g g) (* h h))
413.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
83.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify896.0ms

Counts

81 → 81

Iterations

Useful iterations: done (892.0ms)

Iter	Nodes	Cost
0	144	1192
1	325	1060
2	1391	956
done	5000	946

prune547.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.0b

regimes1.1s

Accuracy

77.8% (0.8b remaining)

Error of 30.9b against oracle of 30.2b and baseline of 33.6b

bsearch252.0ms

Steps

Iters	Range		Point
11	-4.1358965839418397e-138	-7.460458216569464e-159	-8.762222041795177e-159

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	112
1	42	112
done	42	112

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.6s	3795×	body	320	valid
1.4s	8155×	body	80	nan
1.2s	4054×	body	160	valid
14.0ms	151×	body	80	valid