Details

sample210.0ms

Algorithm

intervals

Results

70.0ms	130×	body	160	valid
53.0ms	118×	body	320	valid
35.0ms	257×	body	80	nan
1.0ms	8×	body	80	valid

simplify7.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize83.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.6b	(sqrt (- (* g g) (* h h)))
31.6b	(sqrt (- (* g g) (* h h)))

rewrite193.0ms

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:

65.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
70.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
24.0ms	(sqrt (- (* g g) (* h h)))
31.0ms	(sqrt (- (* g g) (* h h)))

series1.4s

Counts

4 → 12

Calls

4 calls:

590.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
604.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
93.0ms	(sqrt (- (* g g) (* h h)))
95.0ms	(sqrt (- (* g g) (* h h)))

simplify1.6s

Counts

80 → 80

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	172	1528
1	415	1349
2	1520	1225
done	5002	1184

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 33.6b

localize87.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.6b	(sqrt (- (* g g) (* h h)))
31.6b	(sqrt (- (* g g) (* h h)))

rewrite152.0ms

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:

20.0ms	(- (* g g) (* h h))
78.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
24.0ms	(sqrt (- (* g g) (* h h)))
26.0ms	(sqrt (- (* g g) (* h h)))

series874.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* g g) (* h h))
629.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
94.0ms	(sqrt (- (* g g) (* h h)))
87.0ms	(sqrt (- (* g g) (* h h)))

simplify2.4s

Counts

81 → 81

Iterations

Useful iterations: done (2.4s)

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

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.7b

localize74.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
31.6b	(sqrt (- (* g g) (* h h)))
31.6b	(sqrt (- (* g g) (* h h)))

rewrite98.0ms

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))
17.0ms	(- (* g g) (* h h))
38.0ms	(sqrt (- (* g g) (* h h)))
23.0ms	(sqrt (- (* g g) (* h h)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* g g) (* h h))
61.0ms	(- (* g g) (* h h))
94.0ms	(sqrt (- (* g g) (* h h)))
84.0ms	(sqrt (- (* g g) (* h h)))

simplify860.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (171.0ms)

Iter	Nodes	Cost
0	62	912
1	151	832
2	699	722
done	5001	722

prune1.2s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 32.6b

localize72.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
7.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.6b	(sqrt (- (* g g) (* h h)))
31.6b	(sqrt (- (* g g) (* h h)))

rewrite155.0ms

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:

22.0ms	(- (* g g) (* h h))
69.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
37.0ms	(sqrt (- (* g g) (* h h)))
23.0ms	(sqrt (- (* g g) (* h h)))

series835.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* g g) (* h h))
599.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
81.0ms	(sqrt (- (* g g) (* h h)))
93.0ms	(sqrt (- (* g g) (* h h)))

simplify2.9s

Counts

81 → 81

Iterations

Useful iterations: done (2.9s)

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

prune1.1s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 32.6b

regimes2.1s

Accuracy

0% (1.8b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	38
1	24	38
done	24	38

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.4s	3702×	body	320	valid
1.8s	4139×	body	160	valid
1.3s	8023×	body	80	nan
64.0ms	159×	body	80	valid