Details

sample114.0ms

Algorithm

intervals

Results

32.0ms	128×	body	320	valid
29.0ms	123×	body	160	valid
18.0ms	236×	body	80	nan
0.0ms	5×	body	80	valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
8	2064
7	1304
6	1067
5	847
4	542
3	270
2	121
1	43
0	19

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize69.0ms

Local error

Found 4 expressions with local error:

7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`frac-times` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `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 → 60

Calls

4 calls:

54.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
14.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

478.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
399.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
63.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))

simplify2.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	4575
2	1256
1	386
0	166

prune672.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 28.4b

localize87.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite72.0ms

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×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

11.0ms	(- (* g g) (* h h))
42.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* g g) (* h h))
442.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
85.0ms	(sqrt (- (* g g) (* h h)))
61.0ms	(sqrt (- (* g g) (* h h)))

simplify2.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5004
3	4070
2	1041
1	326
0	137

prune785.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 28.3b

localize67.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite66.0ms

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×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
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` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
33.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
14.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* g g) (* h h))
383.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
79.0ms	(sqrt (- (* g g) (* h h)))
54.0ms	(sqrt (- (* g g) (* h h)))

simplify2.7s

Counts

71 → 71

Iterations

Iter	Nodes
done	5004
3	4070
2	1041
1	326
0	137

prune743.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.3b

localize54.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* g g) (* h h))
7.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
27.0b	(sqrt (- (* g g) (* h h)))
27.0b	(sqrt (- (* g g) (* h h)))

rewrite53.0ms

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` `flip3--` `flip--`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
32.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* g g) (* h h))
331.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
54.0ms	(sqrt (- (* g g) (* h h)))
57.0ms	(sqrt (- (* g g) (* h h)))

simplify2.7s

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
3	3964
2	991
1	304
0	135

prune641.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.3b

regimes1.7s

Accuracy

71.4% (1.0b remaining)

Error of 30.9b against oracle of 29.9b and baseline of 33.5b

bsearch241.0ms

Steps

Iters	Range		Point
7	-7.643812144979563e-155	-3.2336746362726576e-157	-3.3237508248189883e-157

simplify7.0ms

Iterations

Iter	Nodes
done	43
1	43
0	33

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.1s	3756×	body	320	valid
1.9s	8091×	body	80	nan
1.2s	4076×	body	160	valid
18.0ms	168×	body	80	valid