Details

sample154.0ms

Algorithm

intervals

Results

63.0ms	301×	body	80	nan
35.0ms	118×	body	320	valid
27.0ms	134×	body	160	valid
0.0ms	4×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	19	645
1	44	645
2	125	645
3	315	645
4	640	645
5	1088	645
6	1617	645
7	2196	645
8	4870	645
done	5000	645

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize61.0ms

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)))

rewrite101.0ms

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:

40.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
39.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(sqrt (- (* g g) (* h h)))

series923.0ms

Counts

4 → 12

Calls

4 calls:

360.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
433.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
61.0ms	(sqrt (- (* g g) (* h h)))
69.0ms	(sqrt (- (* g g) (* h h)))

simplify1.6s

Counts

80 → 80

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	172	33766
1	415	30654
2	1507	29284
done	5001	28454

prune700.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 26.9b

localize51.0ms

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)))

rewrite68.0ms

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))
34.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* g g) (* h h))
415.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
65.0ms	(sqrt (- (* g g) (* h h)))
64.0ms	(sqrt (- (* g g) (* h h)))

simplify1.6s

Counts

81 → 81

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	144	26930
1	336	23107
2	1610	22817
done	5001	22422

prune822.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 26.2b

localize77.0ms

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)))

rewrite43.0ms

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:

8.0ms	(- (* g g) (* h h))
6.0ms	(- (* g g) (* h h))
12.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* g g) (* h h))
47.0ms	(- (* g g) (* h h))
73.0ms	(sqrt (- (* g g) (* h h)))
74.0ms	(sqrt (- (* g g) (* h h)))

simplify772.0ms

Counts

82 → 82

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	62	20094
1	151	15960
2	703	15960
done	5000	15960

prune690.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 26.2b

localize70.0ms

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)))

rewrite35.0ms

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:

7.0ms	(- (* g g) (* h h))
8.0ms	(- (* g g) (* h h))
10.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* g g) (* h h))
52.0ms	(- (* g g) (* h h))
56.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify814.0ms

Counts

82 → 82

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	62	20094
1	151	15960
2	703	15960
done	5000	15960

prune650.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 26.2b

regimes1.3s

Accuracy

0% (1.7b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	725
1	25	725
done	25	725

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.0s	3741×	body	320	valid
1.5s	8173×	body	80	nan
1.3s	4125×	body	160	valid
14.0ms	134×	body	80	valid