Details

sample184.0ms

Algorithm

intervals

Results

74.0ms	131×	body	320	valid
34.0ms	306×	body	80	nan
34.0ms	122×	body	160	valid
1.0ms	3×	body	80	valid

simplify13.3s

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: 37.7b

localize22.0ms

Local error

Found 4 expressions with local error:

6.1b	(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))))))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite122.0ms

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:

39.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
44.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
25.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

492.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
478.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
64.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

80 → 80

Iterations

Useful iterations: done (1.7s)

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

prune773.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 34.6b

localize38.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
6.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite113.0ms

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`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+`
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))
67.0ms	(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)))

series663.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* g g) (* h h))
456.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
89.0ms	(sqrt (- (* g g) (* h h)))
64.0ms	(sqrt (- (* g g) (* h h)))

simplify3.3s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	146	1220
1	334	1078
2	1124	960
3	4776	938
done	5000	938

prune822.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 34.0b

localize62.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

17.0ms	(- (* g g) (* h h))
9.0ms	(- (* g g) (* h h))
11.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* g g) (* h h))
60.0ms	(- (* g g) (* h h))
66.0ms	(sqrt (- (* g g) (* h h)))
68.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

82 → 82

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	62	912
1	132	824
2	347	722
3	1112	722
done	5001	712

prune679.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 34.0b

localize24.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (* g g) (* h h))
4.4b	(- (* g g) (* h h))
32.6b	(sqrt (- (* g g) (* h h)))
32.6b	(sqrt (- (* g g) (* h h)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

9.0ms	(- (* g g) (* h h))
9.0ms	(- (* g g) (* h h))
18.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
33.0ms	(- (* g g) (* h h))
48.0ms	(sqrt (- (* g g) (* h h)))
51.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	62	912
1	132	824
2	347	722
3	1112	722
done	5001	712

prune522.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 34.0b

regimes975.0ms

Accuracy

67.3% (1.2b remaining)

Error of 31.9b against oracle of 30.8b and baseline of 34.3b

bsearch392.0ms

Steps

Iters	Range		Point
12	-8.46579077171639e-185	-2.054593841555946e-229	-8.359356862874829e-185

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	84
1	42	84
done	42	84

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.4s	3717×	body	320	valid
1.1s	8068×	body	80	nan
1.0s	4133×	body	160	valid
16.0ms	150×	body	80	valid