Details

sample195.0ms

Algorithm

intervals

Results

81.0ms	109×	body	320	valid
40.0ms	144×	body	160	valid
32.0ms	243×	body	80	nan
0.0ms	3×	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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize97.0ms

Local error

Found 4 expressions with local error:

7.1b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite92.0ms

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:

32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
38.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

410.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
453.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
78.0ms	(sqrt (- (* g g) (* h h)))
86.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1507
1	415
0	172

prune896.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 29.5b

localize50.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite73.0ms

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:

7.0ms	(- (* g g) (* h h))
42.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
14.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series702.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* g g) (* h h))
485.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
79.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1672
1	358
0	146

prune926.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.2b

localize96.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite526.0ms

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:

7.0ms	(- (* g g) (* h h))
34.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
467.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series632.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* g g) (* h h))
443.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
82.0ms	(sqrt (- (* g g) (* h h)))
54.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1672
1	358
0	146

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.2b

localize114.0ms

Local error

Found 4 expressions with local error:

28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))
28.8b	(sqrt (- (* g g) (* h h)))

rewrite72.0ms

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` `log1p-expm1-u` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

17.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))
17.0ms	(sqrt (- (* g g) (* h h)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (- (* g g) (* h h)))
77.0ms	(sqrt (- (* g g) (* h h)))
83.0ms	(sqrt (- (* g g) (* h h)))
87.0ms	(sqrt (- (* g g) (* h h)))

simplify1.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	1979
3	713
2	268
1	107
0	46

prune827.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 29.2b

regimes1.5s

Accuracy

72.1% (1.0b remaining)

Error of 31.3b against oracle of 30.4b and baseline of 33.8b

bsearch264.0ms

Steps

Iters	Range		Point
10	-1.663081557722865e-151	-2.1148202087381245e-165	-5.401023155583568e-158

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample5.2s

Algorithm

intervals

Results

1.8s	7901×	body	80	nan
1.6s	3746×	body	320	valid
1.2s	4098×	body	160	valid
16.0ms	156×	body	80	valid