Details

sample183.0ms

Algorithm

intervals

Results

68.0ms	129×	body	160	valid
46.0ms	123×	body	320	valid
32.0ms	270×	body	80	nan
1.0ms	4×	body	80	valid

simplify4.8s

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

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.9b

localize39.0ms

Local error

Found 4 expressions with local error:

9.4b	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
10.8b	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
32.1b	(sqrt (- (* g g) (* h h)))
32.1b	(sqrt (- (* g g) (* h h)))

rewrite72.0ms

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:

20.0ms	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
31.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
10.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series900.0ms

Counts

4 → 12

Calls

4 calls:

381.0ms	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
400.0ms	(cbrt (* (/ 1.0 2.0) (/ (- (- g) (sqrt (- (* g g) (* h h)))) a)))
54.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify834.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1298
1	422
0	195

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 34.2b

localize54.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (* g g) (* h h))
9.4b	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
32.1b	(sqrt (- (* g g) (* h h)))
32.1b	(sqrt (fma (- h) h (* g g)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

14.0ms	(- (* g g) (* h h))
30.0ms	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
10.0ms	(sqrt (- (* g g) (* h h)))
1.0ms	(sqrt (fma (- h) h (* g g)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* g g) (* h h))
415.0ms	(cbrt (/ (* (/ 1.0 2.0) (- (sqrt (- (* g g) (* h h))) g)) a))
86.0ms	(sqrt (- (* g g) (* h h)))
120.0ms	(sqrt (fma (- h) h (* g g)))

simplify924.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1313
1	376
0	177

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 33.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ g (sqrt (fma (- h) h (* g g))))
1.2b	(- (sqrt (fma h (- h) (* g g))) g)
32.1b	(sqrt (fma h (- h) (* g g)))
32.1b	(sqrt (fma (- h) h (* g g)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`sqrt-prod`
18×	`prod-diff`
8×	`add-log-exp`
6×	`pow1` `fma-neg`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`fma-def`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

11.0ms	(+ g (sqrt (fma (- h) h (* g g))))
32.0ms	(- (sqrt (fma h (- h) (* g g))) g)
2.0ms	(sqrt (fma h (- h) (* g g)))
3.0ms	(sqrt (fma (- h) h (* g g)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ g (sqrt (fma (- h) h (* g g))))
103.0ms	(- (sqrt (fma h (- h) (* g g))) g)
90.0ms	(sqrt (fma h (- h) (* g g)))
73.0ms	(sqrt (fma (- h) h (* g g)))

simplify2.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	4204
2	736
1	249
0	118

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 33.3b

localize92.0ms

Local error

Found 4 expressions with local error:

32.1b	(sqrt (fma (- h) h (* g g)))
32.1b	(sqrt (fma (- h) h (* g g)))
32.1b	(sqrt (fma (- h) h (* g g)))
32.1b	(sqrt (fma h (- h) (* g g)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

1.0ms	(sqrt (fma (- h) h (* g g)))
1.0ms	(sqrt (fma (- h) h (* g g)))
1.0ms	(sqrt (fma (- h) h (* g g)))
2.0ms	(sqrt (fma h (- h) (* g g)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (fma (- h) h (* g g)))
89.0ms	(sqrt (fma (- h) h (* g g)))
87.0ms	(sqrt (fma (- h) h (* g g)))
85.0ms	(sqrt (fma h (- h) (* g g)))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
8	1667
7	631
6	338
5	231
4	172
3	127
2	94
1	60
0	42

prune837.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 33.3b

regimes1.1s

Accuracy

0% (1.9b remaining)

Error of 32.6b against oracle of 30.7b and baseline of 32.6b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	44
3	44
2	43
1	38
0	28

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.6s	3804×	body	320	valid
1.1s	8006×	body	80	nan
1.1s	4042×	body	160	valid
47.0ms	154×	body	80	valid