Details

sample248.0ms

Algorithm

intervals

Results

116.0ms	143×	body	320	valid
49.0ms	227×	body	80	nan
49.0ms	109×	body	160	valid
1.0ms	4×	body	80	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3432
4	1243
3	370
2	119
1	47
0	19

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.3b

localize53.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.0b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
25.2b	(sqrt (- (* g g) (* h h)))
25.2b	(sqrt (- (* g g) (* h h)))

rewrite109.0ms

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` `insert-posit16` `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 → 72

Calls

4 calls:

28.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
47.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
15.0ms	(sqrt (- (* g g) (* h h)))

series918.0ms

Counts

4 → 12

Calls

4 calls:

400.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
402.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
48.0ms	(sqrt (- (* g g) (* h h)))
67.0ms	(sqrt (- (* g g) (* h h)))

simplify3.0s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
3	4951
2	1286
1	408
0	171

prune785.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 25.5b

localize40.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
25.2b	(sqrt (- (* g g) (* h h)))
25.2b	(sqrt (- (* g g) (* h h)))

rewrite69.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 73

Calls

4 calls:

9.0ms	(- (* g g) (* h h))
28.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* g g) (* h h))
367.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
79.0ms	(sqrt (- (* g g) (* h h)))
68.0ms	(sqrt (- (* g g) (* h h)))

simplify2.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4374
2	1042
1	322
0	145

prune868.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 24.7b

localize42.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* g g) (* h h))
2.0b	(- (* g g) (* h h))
25.2b	(sqrt (- (* g g) (* h h)))
25.2b	(sqrt (- (* g g) (* h h)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 74

Calls

4 calls:

16.0ms	(- (* g g) (* h h))
25.0ms	(- (* g g) (* h h))
17.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
34.0ms	(- (* g g) (* h h))
73.0ms	(sqrt (- (* g g) (* h h)))
81.0ms	(sqrt (- (* g g) (* h h)))

simplify2.0s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
3	1666
2	377
1	138
0	64

prune776.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 24.7b

localize50.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (* g g) (* h h))
7.9b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
25.2b	(sqrt (- (* g g) (* h h)))
25.2b	(sqrt (- (* g g) (* h h)))

rewrite109.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 73

Calls

4 calls:

10.0ms	(- (* g g) (* h h))
57.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
29.0ms	(sqrt (- (* g g) (* h h)))
12.0ms	(sqrt (- (* g g) (* h h)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* g g) (* h h))
401.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
82.0ms	(sqrt (- (* g g) (* h h)))
68.0ms	(sqrt (- (* g g) (* h h)))

simplify3.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	4374
2	1042
1	322
0	145

prune642.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 24.6b

regimes1.4s

Accuracy

58.4% (1.6b remaining)

Error of 30.4b against oracle of 28.8b and baseline of 32.7b

bsearch330.0ms

Steps

Iters	Range		Point
10	1.7822550191445485e-157	2.855344257932453e-141	4.099263178664206e-157

simplify18.0ms

Iterations

Iter	Nodes
done	46
1	46
0	33

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.6s	3746×	body	320	valid
2.5s	4110×	body	160	valid
1.8s	7860×	body	80	nan
27.0ms	144×	body	80	valid