Details

sample107.0ms

Algorithm

intervals

Results

32.0ms	118×	body	320	valid
23.0ms	301×	body	80	nan
21.0ms	134×	body	160	valid
0.0ms	4×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4870
7	2196
6	1617
5	1088
4	640
3	315
2	125
1	44
0	19

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize69.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
25.9b	(sqrt (- (* g g) (* h h)))
25.9b	(sqrt (- (* g g) (* h h)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `frac-times` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `log1p-expm1-u` `flip--` `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:

38.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
17.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

437.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
484.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
71.0ms	(sqrt (- (* g g) (* h h)))
62.0ms	(sqrt (- (* g g) (* h h)))

simplify2.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1507
1	415
0	172

prune972.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 26.9b

localize74.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
25.9b	(sqrt (- (* g g) (* h h)))
25.9b	(sqrt (- (* g g) (* h h)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `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))
52.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* g g) (* h h))
416.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
88.0ms	(sqrt (- (* g g) (* h h)))
77.0ms	(sqrt (- (* g g) (* h h)))

simplify1.8s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1610
1	336
0	144

prune969.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 26.2b

localize81.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
3.0b	(- (* g g) (* h h))
25.9b	(sqrt (- (* g g) (* h h)))
25.9b	(sqrt (- (* g g) (* h h)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

13.0ms	(- (* g g) (* h h))
7.0ms	(- (* g g) (* h h))
9.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* g g) (* h h))
58.0ms	(- (* g g) (* h h))
62.0ms	(sqrt (- (* g g) (* h h)))
68.0ms	(sqrt (- (* g g) (* h h)))

simplify875.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	703
1	151
0	62

prune986.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 26.2b

localize60.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.7b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
25.9b	(sqrt (- (* g g) (* h h)))
25.9b	(sqrt (- (* g g) (* h h)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `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))
28.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
16.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
425.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
54.0ms	(sqrt (- (* g g) (* h h)))
81.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1610
1	336
0	144

prune704.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 26.2b

regimes1.2s

Accuracy

0% (1.7b remaining)

Error of 32.1b against oracle of 30.3b and baseline of 32.1b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.7s	3741×	body	320	valid
1.5s	8173×	body	80	nan
1.4s	4125×	body	160	valid
15.0ms	134×	body	80	valid