Details

sample143.0ms

Algorithm

intervals

Results

41.0ms	115×	body	320	valid
38.0ms	138×	body	160	valid
26.0ms	245×	body	80	nan
0.0ms	3×	body	80	valid

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize40.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite143.0ms

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:

37.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
54.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
24.0ms	(sqrt (- (* g g) (* h h)))
25.0ms	(sqrt (- (* g g) (* h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

432.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
482.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
80.0ms	(sqrt (- (* g g) (* h h)))
90.0ms	(sqrt (- (* g g) (* h h)))

simplify1.1s

Counts

80 → 80

Iterations

Useful iterations: done (1.1s)

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

prune735.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.0b

localize54.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite92.0ms

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:

11.0ms	(- (* g g) (* h h))
53.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* g g) (* h h))
473.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
73.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify1.6s

Counts

81 → 81

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	146	1220
1	358	1084
2	1679	960
done	5001	940

prune517.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 30.3b

localize27.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
2.2b	(- (* g g) (* h h))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite74.0ms

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))
11.0ms	(- (* g g) (* h h))
31.0ms	(sqrt (- (* g g) (* h h)))
21.0ms	(sqrt (- (* g g) (* h h)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* g g) (* h h))
34.0ms	(- (* g g) (* h h))
60.0ms	(sqrt (- (* g g) (* h h)))
50.0ms	(sqrt (- (* g g) (* h h)))

simplify557.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (96.0ms)

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

prune489.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.3b

localize28.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
30.5b	(sqrt (- (* g g) (* h h)))
30.5b	(sqrt (- (* g g) (* h h)))

rewrite78.0ms

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:

9.0ms	(- (* g g) (* h h))
35.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
430.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
54.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

81 → 81

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	146	1220
1	358	1084
2	1679	960
done	5001	940

prune585.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.3b

regimes1.5s

Accuracy

67.7% (1.1b remaining)

Error of 31.7b against oracle of 30.6b and baseline of 34.0b

bsearch181.0ms

Steps

Iters	Range		Point
8	-8.655542616090105e-164	-1.300757130669729e-167	-8.483083017653632e-164

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	72
1	40	72
done	40	72

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.6s	3770×	body	320	valid
1.5s	4069×	body	160	valid
977.0ms	8040×	body	80	nan
49.0ms	161×	body	80	valid