Details

sample161.0ms

Algorithm

intervals

Results

51.0ms	230×	body	80	nan
39.0ms	147×	body	160	valid
36.0ms	102×	body	320	valid
1.0ms	7×	body	80	valid

simplify7.8s

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize41.0ms

Local error

Found 4 expressions with local error:

7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.6b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite79.0ms

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:

26.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
14.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

443.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
469.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
75.0ms	(sqrt (- (* g g) (* h h)))
52.0ms	(sqrt (- (* g g) (* h h)))

simplify3.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	4959
2	1302
1	406
0	172

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 29.9b

localize97.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(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`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `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:

8.0ms	(- (* g g) (* h h))
31.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
10.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* g g) (* h h))
469.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
58.0ms	(sqrt (- (* g g) (* h h)))

simplify3.1s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4412
2	1081
1	342
0	146

prune1.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.5b

localize75.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
2.6b	(- (* g g) (* h h))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite46.0ms

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))
8.0ms	(- (* g g) (* h h))
13.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* g g) (* h h))
56.0ms	(- (* g g) (* h h))
66.0ms	(sqrt (- (* g g) (* h h)))
59.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

82 → 82

Iterations

Iter	Nodes
done	5022
3	1658
2	371
1	136
0	62

prune963.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 29.5b

localize93.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.3b	(sqrt (- (* g g) (* h h)))
28.3b	(sqrt (- (* g g) (* h h)))

rewrite104.0ms

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` `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:

13.0ms	(- (* g g) (* h h))
54.0ms	(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)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* g g) (* h h))
413.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
70.0ms	(sqrt (- (* g g) (* h h)))
80.0ms	(sqrt (- (* g g) (* h h)))

simplify3.1s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
3	4412
2	1081
1	342
0	146

prune720.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 29.5b

regimes1.9s

Accuracy

71.5% (1.0b remaining)

Error of 32.0b against oracle of 31.0b and baseline of 34.6b

bsearch387.0ms

Steps

Iters	Range		Point
12	-1.8813990987943826e-134	-1.0883707337798972e-185	-8.764066339061835e-157

simplify10.0ms

Iterations

Iter	Nodes
done	44
1	44
0	35

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.1s	3702×	body	320	valid
1.4s	4151×	body	160	valid
899.0ms	7759×	body	80	nan
39.0ms	147×	body	80	valid