Details

sample158.0ms

Algorithm

intervals

Results

57.0ms	117×	body	320	valid
33.0ms	137×	body	160	valid
28.0ms	244×	body	80	nan
0.0ms	2×	body	80	valid

simplify4.6s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.8b

localize71.0ms

Local error

Found 4 expressions with local error:

7.5b	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
10.2b	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
28.9b	(sqrt (- (* g g) (* h h)))
28.9b	(sqrt (- (* g g) (* h h)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`cbrt-prod` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`times-frac`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `pow1/3` `flip--` `difference-of-squares`
1×	`frac-times` `associate-l/` `associate-r/` `div-inv`

Counts

4 → 68

Calls

4 calls:

39.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
35.0ms	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
16.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series849.0ms

Counts

4 → 12

Calls

4 calls:

400.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
335.0ms	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
59.0ms	(sqrt (- (* g g) (* h h)))
55.0ms	(sqrt (- (* g g) (* h h)))

simplify783.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1298
1	422
0	195

prune1.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.0b

localize67.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (* g g) (* h h))
7.5b	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
28.9b	(sqrt (* (- g h) (+ g h)))
28.9b	(sqrt (- (* g g) (* h h)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqrt-div`
8×	`pow1`
6×	`add-sqr-sqrt` `add-log-exp`
5×	`frac-times` `*-un-lft-identity` `flip3--` `add-cube-cbrt` `sqrt-prod` `flip--`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cbrt-div` `sqrt-pow1` `flip3-+` `associate-l/` `associate-r/` `flip-+`
2×	`pow1/2` `difference-of-squares`
1×	`cbrt-prod` `rem-sqrt-square` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `pow-prod-down`

Counts

4 → 70

Calls

4 calls:

13.0ms	(- (* g g) (* h h))
44.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
21.0ms	(sqrt (* (- g h) (+ g h)))
19.0ms	(sqrt (- (* g g) (* h h)))

series611.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* g g) (* h h))
373.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
95.0ms	(sqrt (* (- g h) (+ g h)))
80.0ms	(sqrt (- (* g g) (* h h)))

simplify1.8s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	2228
1	464
0	196

prune1.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.2b

localize71.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- g) (sqrt (fma (- h) h (* g g))))
1.4b	(- (sqrt (* (- g h) (+ g h))) g)
28.9b	(sqrt (* (- g h) (+ g h)))
28.9b	(sqrt (fma (- h) h (* g g)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
61×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
54×	`add-cube-cbrt`
39×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`fma-neg`
10×	`add-log-exp`
8×	`pow1` `sqrt-div`
7×	`neg-mul-1`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sqrt-pow1` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `pow1/2` `associate-l/` `associate-r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-prod-down` `neg-log`

Counts

4 → 158

Calls

4 calls:

33.0ms	(- (- g) (sqrt (fma (- h) h (* g g))))
48.0ms	(- (sqrt (* (- g h) (+ g h))) g)
13.0ms	(sqrt (* (- g h) (+ g h)))
2.0ms	(sqrt (fma (- h) h (* g g)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- g) (sqrt (fma (- h) h (* g g))))
118.0ms	(- (sqrt (* (- g h) (+ g h))) g)
84.0ms	(sqrt (* (- g h) (+ g h)))
100.0ms	(sqrt (fma (- h) h (* g g)))

simplify1.7s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	2537
1	534
0	230

prune1.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 30.1b

localize76.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (* (+ g h) (- g h))) g)
2.9b	(exp (log (- (sqrt (* (+ g h) (- g h))) g)))
28.9b	(sqrt (fma (- h) h (* g g)))
28.9b	(sqrt (* (+ g h) (- g h)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
12×	`prod-diff`
9×	`pow1`
8×	`sqrt-div` `sqrt-prod`
6×	`add-log-exp`
5×	`log-prod` `flip3--` `exp-sum` `flip--`
4×	`expm1-log1p-u` `frac-times` `exp-prod` `add-cbrt-cube` `fma-neg` `add-exp-log` `log1p-expm1-u`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`log-div` `pow1/2` `exp-diff` `associate-l/` `associate-r/` `distribute-lft-out--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `diff-log` `pow-prod-down` `log-pow` `rem-exp-log`

Counts

4 → 89

Calls

4 calls:

36.0ms	(- (sqrt (* (+ g h) (- g h))) g)
41.0ms	(exp (log (- (sqrt (* (+ g h) (- g h))) g)))
1.0ms	(sqrt (fma (- h) h (* g g)))
26.0ms	(sqrt (* (+ g h) (- g h)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (sqrt (* (+ g h) (- g h))) g)
120.0ms	(exp (log (- (sqrt (* (+ g h) (- g h))) g)))
73.0ms	(sqrt (fma (- h) h (* g g)))
76.0ms	(sqrt (* (+ g h) (- g h)))

simplify671.0ms

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1023
1	331
0	169

prune1.6s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 30.1b

regimes1.5s

Accuracy

73.8% (0.7b remaining)

Error of 31.7b against oracle of 31.1b and baseline of 33.6b

bsearch327.0ms

Steps

Iters	Range		Point
11	9.716392544916912e-185	3.996805054832145e-156	2.776832660171497e-160

simplify6.0ms

Iterations

Iter	Nodes
done	53
1	53
0	42

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	3716×	body	320	valid
1.2s	4127×	body	160	valid
1.1s	7969×	body	80	nan
18.0ms	157×	body	80	valid