Details

sample265.0ms

Algorithm

intervals

Results

115.0ms	122×	body	320	valid
62.0ms	128×	body	160	valid
54.0ms	244×	body	80	nan
2.0ms	6×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	3795
4	1313
3	379
2	120
1	47
0	19

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize59.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
9.3b	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ g h))))))
32.4b	(sqrt (* (- g h) (+ g h)))
32.4b	(sqrt (* (- g h) (+ g h)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
12×	`frac-times`
10×	`pow1` `cbrt-div`
8×	`flip3-+` `flip3--` `associate-*r/` `flip-+` `flip--`
6×	`associate-*l/`
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 → 78

Calls

4 calls:

36.0ms	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
8.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ g h))))))
15.0ms	(sqrt (* (- g h) (+ g h)))
16.0ms	(sqrt (* (- g h) (+ g h)))

series1.2s

Counts

4 → 12

Calls

4 calls:

507.0ms	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
468.0ms	(cbrt (* (/ -1/2 a) (+ g (sqrt (* (- g h) (+ g h))))))
102.0ms	(sqrt (* (- g h) (+ g h)))
85.0ms	(sqrt (* (- g h) (+ g h)))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1670
1	454
0	195

prune999.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.7b

localize59.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (* (- g h) (+ g h))) g)
7.9b	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
32.4b	(sqrt (* (- g h) (+ g h)))
32.4b	(sqrt (* (- g h) (+ g h)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

29.0ms	(- (sqrt (* (- g h) (+ g h))) g)
53.0ms	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
22.0ms	(sqrt (* (- g h) (+ g h)))
25.0ms	(sqrt (* (- g h) (+ g h)))

series862.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(- (sqrt (* (- g h) (+ g h))) g)
549.0ms	(cbrt (* (/ 1/2 a) (- (sqrt (* (- g h) (+ g h))) g)))
98.0ms	(sqrt (* (- g h) (+ g h)))
81.0ms	(sqrt (* (- g h) (+ g h)))

simplify1.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1347
1	414
0	186

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ g (sqrt (* (- g h) (+ g h))))
1.1b	(- (sqrt (* (- g h) (+ g h))) g)
32.4b	(sqrt (* (- g h) (+ g h)))
32.4b	(sqrt (* (- g h) (+ g h)))

rewrite74.0ms

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:

9.0ms	(+ g (sqrt (* (- g h) (+ g h))))
25.0ms	(- (sqrt (* (- g h) (+ g h))) g)
19.0ms	(sqrt (* (- g h) (+ g h)))
20.0ms	(sqrt (* (- g h) (+ g h)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ g (sqrt (* (- g h) (+ g h))))
131.0ms	(- (sqrt (* (- g h) (+ g h))) g)
92.0ms	(sqrt (* (- g h) (+ g h)))
77.0ms	(sqrt (* (- g h) (+ g h)))

simplify2.9s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
3	4702
2	1127
1	338
0	137

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.2b

localize112.0ms

Local error

Found 4 expressions with local error:

32.4b	(sqrt (* (- g h) (+ g h)))
32.4b	(sqrt (* (- g h) (+ g h)))
32.4b	(sqrt (* (- g h) (+ g h)))
32.4b	(sqrt (* (- g h) (+ g h)))

rewrite54.0ms

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

series313.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (* (- g h) (+ g h)))
69.0ms	(sqrt (* (- g h) (+ g h)))
74.0ms	(sqrt (* (- g h) (+ g h)))
92.0ms	(sqrt (* (- g h) (+ g h)))

simplify2.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	3171
2	762
1	165
0	64

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.2b

regimes650.0ms

Accuracy

40.8% (1.5b remaining)

Error of 31.2b against oracle of 29.6b and baseline of 32.2b

bsearch205.0ms

Steps

Iters	Range		Point
6	-1.893145012823655e-157	-2.997343141526986e-158	-3.035091110489776e-158

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	30

end0.0ms

sample8.2s

Algorithm

intervals

Results

3.4s	3745×	body	320	valid
2.4s	4109×	body	160	valid
1.9s	8042×	body	80	nan
27.0ms	146×	body	80	valid