Details

sample138.0ms

Algorithm

intervals

Results

41.0ms	126×	body	320	valid
29.0ms	127×	body	160	valid
26.0ms	251×	body	80	nan
0.0ms	3×	body	80	valid

simplify12.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	2537
7	1639
6	1310
5	984
4	595
3	287
2	124
1	44
0	19

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize150.0ms

Local error

Found 4 expressions with local error:

8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite186.0ms

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` `insert-posit16` `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 → 72

Calls

4 calls:

66.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
73.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
15.0ms	(sqrt (- (* g g) (* h h)))
25.0ms	(sqrt (- (* g g) (* h h)))

series1.8s

Counts

4 → 12

Calls

4 calls:

788.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
833.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
106.0ms	(sqrt (- (* g g) (* h h)))
104.0ms	(sqrt (- (* g g) (* h h)))

simplify7.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
3	4816
2	1291
1	408
0	175

prune1.9s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 27.8b

localize172.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite136.0ms

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`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `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 → 73

Calls

4 calls:

16.0ms	(- (* g g) (* h h))
82.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
14.0ms	(sqrt (- (* g g) (* h h)))
20.0ms	(sqrt (- (* g g) (* h h)))

series1.2s

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* g g) (* h h))
900.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
86.0ms	(sqrt (- (* g g) (* h h)))
90.0ms	(sqrt (- (* g g) (* h h)))

simplify6.6s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4419
2	1062
1	342
0	149

prune1.9s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 27.4b

localize154.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
8.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite119.0ms

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`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `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 → 73

Calls

4 calls:

19.0ms	(- (* g g) (* h h))
60.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(sqrt (- (* g g) (* h h)))
14.0ms	(sqrt (- (* g g) (* h h)))

series1.5s

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* g g) (* h h))
1.2s	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
81.0ms	(sqrt (- (* g g) (* h h)))
108.0ms	(sqrt (- (* g g) (* h h)))

simplify6.6s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4419
2	1062
1	342
0	149

prune1.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.4b

localize286.0ms

Local error

Found 4 expressions with local error:

26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

29.0ms	(sqrt (- (* g g) (* h h)))
30.0ms	(sqrt (- (* g g) (* h h)))
29.0ms	(sqrt (- (* g g) (* h h)))
29.0ms	(sqrt (- (* g g) (* h h)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (- (* g g) (* h h)))
80.0ms	(sqrt (- (* g g) (* h h)))
66.0ms	(sqrt (- (* g g) (* h h)))
86.0ms	(sqrt (- (* g g) (* h h)))

simplify6.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
5	4007
4	1320
3	551
2	235
1	108
0	47

prune1.5s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 27.4b

regimes3.2s

Accuracy

70% (1.1b remaining)

Error of 32.2b against oracle of 31.1b and baseline of 34.7b

bsearch319.0ms

Steps

Iters	Range		Point
10	-1.0379169882309884e-191	-1.149502580977988e-207	-1.0197648282366805e-191

simplify13.0ms

Iterations

Iter	Nodes
done	39
1	39
0	31

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.1s	3724×	body	320	valid
1.4s	8035×	body	80	nan
1.0s	4130×	body	160	valid
49.0ms	146×	body	80	valid