Details

sample185.0ms

Algorithm

intervals

Results

55.0ms	280×	body	80	nan
48.0ms	122×	body	320	valid
33.0ms	130×	body	160	valid
1.0ms	4×	body	80	valid

simplify5.2s

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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.5b

localize51.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
9.5b	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
26.5b	(sqrt (- (* g g) (* h h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite104.0ms

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:

27.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
34.0ms	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
25.0ms	(sqrt (- (* g g) (* h h)))
16.0ms	(sqrt (- (* g g) (* h h)))

series905.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
430.0ms	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
52.0ms	(sqrt (- (* g g) (* h h)))
54.0ms	(sqrt (- (* g g) (* h h)))

simplify792.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1298
1	422
0	195

prune949.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.1b

localize90.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (* g g) (* h h))
7.6b	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
26.5b	(sqrt (* (- g h) (+ g h)))
26.5b	(sqrt (- (* g g) (* h h)))

rewrite76.0ms

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:

6.0ms	(- (* g g) (* h h))
36.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
18.0ms	(sqrt (* (- g h) (+ g h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* g g) (* h h))
377.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
68.0ms	(sqrt (* (- g h) (+ g h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify1.7s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	2228
1	464
0	196

prune1.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 28.4b

localize109.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
2.6b	(- (sqrt (* (- g h) (+ g h))) g)
26.5b	(sqrt (* (- g h) (+ g h)))
26.5b	(sqrt (fma (- h) h (* g g)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

1.0ms	(cbrt a)
23.0ms	(- (sqrt (* (- g h) (+ g h))) g)
10.0ms	(sqrt (* (- g h) (+ g h)))
2.0ms	(sqrt (fma (- h) h (* g g)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

354.0ms	(cbrt a)
118.0ms	(- (sqrt (* (- g h) (+ g h))) g)
102.0ms	(sqrt (* (- g h) (+ g h)))
98.0ms	(sqrt (fma (- h) h (* g g)))

simplify731.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1206
1	349
0	157

prune1.3s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 28.4b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* a 2.0))
2.6b	(- (sqrt (* (- g h) (+ g h))) g)
26.5b	(sqrt (* (- g h) (+ g h)))
26.5b	(sqrt (fma (- h) h (* g g)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

5.0ms	(cbrt (* a 2.0))
38.0ms	(- (sqrt (* (- g h) (+ g h))) g)
20.0ms	(sqrt (* (- g h) (+ g h)))
1.0ms	(sqrt (fma (- h) h (* g g)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(cbrt (* a 2.0))
108.0ms	(- (sqrt (* (- g h) (+ g h))) g)
104.0ms	(sqrt (* (- g h) (+ g h)))
83.0ms	(sqrt (fma (- h) h (* g g)))

simplify793.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1155
1	343
0	156

prune984.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 28.4b

regimes1.5s

Accuracy

0% (1.7b remaining)

Error of 32.3b against oracle of 30.6b and baseline of 32.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	42
1	42
0	32

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.0s	3683×	body	320	valid
1.6s	8083×	body	80	nan
1.1s	4170×	body	160	valid
16.0ms	147×	body	80	valid