Details

sample189.0ms

Algorithm

intervals

Results

70.0ms	105×	body	320	valid
49.0ms	144×	body	160	valid
45.0ms	275×	body	80	nan
1.0ms	7×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.7b

localize79.0ms

Local error

Found 4 expressions with local error:

8.6b	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ h g))))))
9.6b	(cbrt (* (/ (- (sqrt (* (- g h) (+ h g))) g) a) 1/2))
27.8b	(sqrt (* (- g h) (+ h g)))
27.8b	(sqrt (* (- g h) (+ h g)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`frac-times` `pow1`
8×	`flip3-+` `flip-+`
6×	`cbrt-div` `flip3--` `associate-l/` `associate-r/` `flip--`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `pow1/2` `pow1/3` `pow-prod-down` `sqrt-prod`

Counts

4 → 74

Calls

4 calls:

7.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ h g))))))
17.0ms	(cbrt (* (/ (- (sqrt (* (- g h) (+ h g))) g) a) 1/2))
20.0ms	(sqrt (* (- g h) (+ h g)))
21.0ms	(sqrt (* (- g h) (+ h g)))

series972.0ms

Counts

4 → 12

Calls

4 calls:

428.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ h g))))))
360.0ms	(cbrt (* (/ (- (sqrt (* (- g h) (+ h g))) g) a) 1/2))
103.0ms	(sqrt (* (- g h) (+ h g)))
81.0ms	(sqrt (* (- g h) (+ h g)))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5010
2	1627
1	481
0	204

prune834.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 28.6b

localize55.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (* (- g h) (+ h g))) g)
9.6b	(cbrt (* (/ (- (sqrt (* (- g h) (+ h g))) g) a) 1/2))
27.8b	(sqrt (* (- g h) (+ h g)))
27.8b	(sqrt (* (- g h) (+ h g)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`prod-diff` `add-cube-cbrt`
10×	`pow1`
8×	`frac-times`
7×	`flip3--` `flip--`
6×	`flip3-+` `sqrt-prod` `flip-+` `add-log-exp`
5×	`associate-*l/`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `fma-neg` `associate-*r/` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`pow1/2` `pow-prod-down`
1×	`cbrt-prod` `cbrt-div` `sub-neg` `pow1/3` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

23.0ms	(- (sqrt (* (- g h) (+ h g))) g)
14.0ms	(cbrt (* (/ (- (sqrt (* (- g h) (+ h g))) g) a) 1/2))
19.0ms	(sqrt (* (- g h) (+ h g)))
20.0ms	(sqrt (* (- g h) (+ h g)))

series644.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (sqrt (* (- g h) (+ h g))) g)
359.0ms	(cbrt (* (/ (- (sqrt (* (- g h) (+ h g))) g) a) 1/2))
84.0ms	(sqrt (* (- g h) (+ h g)))
78.0ms	(sqrt (* (- g h) (+ h g)))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1333
1	470
0	202

prune1.1s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 27.8b

localize79.0ms

Local error

Found 4 expressions with local error:

2.1b	(+ g (sqrt (* (- g h) (+ h g))))
2.2b	(- (sqrt (* (- g h) (+ h g))) g)
27.8b	(sqrt (* (- g h) (+ h g)))
27.8b	(sqrt (* (- g h) (+ h g)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`sqrt-div`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`prod-diff`
10×	`pow1`
8×	`frac-times` `add-log-exp`
7×	`flip3-+` `flip3--` `flip-+` `flip--`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `fma-neg` `associate-l/` `associate-r/` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`pow1/2` `pow-prod-down`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

5.0ms	(+ g (sqrt (* (- g h) (+ h g))))
25.0ms	(- (sqrt (* (- g h) (+ h g))) g)
15.0ms	(sqrt (* (- g h) (+ h g)))
10.0ms	(sqrt (* (- g h) (+ h g)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ g (sqrt (* (- g h) (+ h g))))
115.0ms	(- (sqrt (* (- g h) (+ h g))) g)
111.0ms	(sqrt (* (- g h) (+ h g)))
77.0ms	(sqrt (* (- g h) (+ h g)))

simplify3.1s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
3	4912
2	1157
1	354
0	143

prune1.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 27.7b

localize73.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (* (- g h) (+ h g)))
27.8b	(sqrt (* (- g h) (+ h g)))
27.8b	(sqrt (* (- g h) (+ h g)))
27.8b	(sqrt (* (- g h) (+ h g)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-div`
16×	`frac-times` `pow1`
12×	`flip3-+` `flip3--` `flip-+` `flip--`
8×	`sqrt-pow1` `associate-l/` `associate-r/`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `pow1/2` `pow-prod-down` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 88

Calls

4 calls:

19.0ms	(sqrt (* (- g h) (+ h g)))
12.0ms	(sqrt (* (- g h) (+ h g)))
10.0ms	(sqrt (* (- g h) (+ h g)))
11.0ms	(sqrt (* (- g h) (+ h g)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (* (- g h) (+ h g)))
82.0ms	(sqrt (* (- g h) (+ h g)))
92.0ms	(sqrt (* (- g h) (+ h g)))
87.0ms	(sqrt (* (- g h) (+ h g)))

simplify2.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	3513
2	787
1	175
0	70

prune1.1s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 27.7b

regimes903.0ms

Accuracy

42.1% (1.2b remaining)

Error of 30.8b against oracle of 29.5b and baseline of 31.7b

bsearch375.0ms

Steps

Iters	Range		Point
10	-1.7568584363366094e-151	-1.5754220496330615e-165	-6.3921017940024375e-161

simplify8.0ms

Iterations

Iter	Nodes
done	41
1	41
0	33

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.3s	3731×	body	320	valid
2.3s	4114×	body	160	valid
1.7s	8090×	body	80	nan
60.0ms	155×	body	80	valid