Details

sample211.0ms

Algorithm

intervals

Results

92.0ms	121×	body	320	valid
50.0ms	266×	body	80	nan
45.0ms	135×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
5	2018
4	871
3	351
2	114
1	44
0	19

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.4b

localize57.0ms

Local error

Found 4 expressions with local error:

9.1b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.8b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
35.4b	(sqrt (- (* g g) (* h h)))
35.4b	(sqrt (- (* g g) (* h h)))

rewrite139.0ms

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` `insert-posit16` `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 → 64

Calls

4 calls:

53.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
55.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
15.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series951.0ms

Counts

4 → 12

Calls

4 calls:

414.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
423.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
51.0ms	(sqrt (- (* g g) (* h h)))
63.0ms	(sqrt (- (* g g) (* h h)))

simplify4.7s

Counts

76 → 76

Iterations

Iter	Nodes
3	4174
2	1164
1	389
0	165

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 35.3b

localize59.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
9.8b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
35.4b	(sqrt (- (* g g) (* h h)))
35.4b	(sqrt (- (* g g) (* h h)))

rewrite105.0ms

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` `insert-posit16`
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 → 63

Calls

4 calls:

14.0ms	(- (* g g) (* h h))
60.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
14.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (* g g) (* h h))
448.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
64.0ms	(sqrt (- (* g g) (* h h)))
62.0ms	(sqrt (- (* g g) (* h h)))

simplify2.2s

Counts

75 → 75

Iterations

Iter	Nodes
3	3654
2	986
1	307
0	136

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 34.6b

localize97.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
9.8b	(cbrt (/ (- (+ (sqrt (- (* g g) (* h h))) g)) (/ a 1/2)))
35.4b	(sqrt (- (* g g) (* h h)))
35.4b	(sqrt (- (* g g) (* h h)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

264×	`times-frac`
182×	`*-un-lft-identity`
161×	`cbrt-prod`
132×	`add-sqr-sqrt`
130×	`add-cube-cbrt`
52×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
26×	`distribute-lft-out`
13×	`neg-mul-1` `div-inv`
8×	`sqrt-prod`
6×	`pow1` `add-log-exp`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `sub-neg` `pow1/3` `diff-log` `associate-/r/`

Counts

4 → 219

Calls

4 calls:

14.0ms	(- (* g g) (* h h))
50.0ms	(cbrt (/ (- (+ (sqrt (- (* g g) (* h h))) g)) (/ a 1/2)))
15.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* g g) (* h h))
251.0ms	(cbrt (/ (- (+ (sqrt (- (* g g) (* h h))) g)) (/ a 1/2)))
60.0ms	(sqrt (- (* g g) (* h h)))
60.0ms	(sqrt (- (* g g) (* h h)))

simplify3.4s

Counts

231 → 231

Iterations

Iter	Nodes
2	3002
1	1196
0	583

prune2.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 34.5b

localize88.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (* g g) (* h h))
4.1b	(cbrt (/ (- (+ (sqrt (- (* g g) (* h h))) g)) (/ (cbrt a) 1/2)))
35.4b	(sqrt (- (* g g) (* h h)))
35.4b	(sqrt (- (* g g) (* h h)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
377×	`cbrt-prod`
317×	`*-un-lft-identity`
231×	`add-sqr-sqrt`
229×	`add-cube-cbrt`
88×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
44×	`distribute-lft-out`
22×	`neg-mul-1`
13×	`div-inv`
8×	`sqrt-prod`
6×	`pow1` `add-log-exp`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3--` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `sub-neg` `pow1/3` `diff-log` `associate-/r/`

Counts

4 → 327

Calls

4 calls:

10.0ms	(- (* g g) (* h h))
25.0ms	(cbrt (/ (- (+ (sqrt (- (* g g) (* h h))) g)) (/ (cbrt a) 1/2)))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

series791.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* g g) (* h h))
585.0ms	(cbrt (/ (- (+ (sqrt (- (* g g) (* h h))) g)) (/ (cbrt a) 1/2)))
72.0ms	(sqrt (- (* g g) (* h h)))
70.0ms	(sqrt (- (* g g) (* h h)))

simplify3.3s

Counts

339 → 339

Iterations

Iter	Nodes
2	3991
1	1735
0	807

prune5.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 34.5b

regimes1.7s

Accuracy

15.6% (1.8b remaining)

Error of 31.4b against oracle of 29.6b and baseline of 31.8b

bsearch210.0ms

Steps

Iters	Range		Point
6	7.866015919465401e-146	1.2582464300175928e-144	7.991130677509223e-146

simplify31.0ms

Iterations

Iter	Nodes
5	67
4	67
3	66
2	58
1	54
0	40

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.7s	3651×	body	320	valid
2.4s	4188×	body	160	valid
2.2s	8074×	body	80	nan
31.0ms	161×	body	80	valid