Details

sample215.0ms

Algorithm

intervals

Results

90.0ms	117×	body	320	valid
53.0ms	137×	body	160	valid
44.0ms	238×	body	80	nan
0.0ms	2×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
6	3167
5	1812
4	841
3	353
2	116
1	46
0	19

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.7b

localize65.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (* (/ (+ g (sqrt (* (+ g h) (- g h)))) a) -1/2))
8.2b	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (* 2 a)))
30.0b	(sqrt (* (+ g h) (- g h)))
30.0b	(sqrt (* (+ g h) (- g h)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

13.0ms	(cbrt (* (/ (+ g (sqrt (* (+ g h) (- g h)))) a) -1/2))
22.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (* 2 a)))
16.0ms	(sqrt (* (+ g h) (- g h)))
16.0ms	(sqrt (* (+ g h) (- g h)))

series906.0ms

Counts

4 → 12

Calls

4 calls:

353.0ms	(cbrt (* (/ (+ g (sqrt (* (+ g h) (- g h)))) a) -1/2))
395.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (* 2 a)))
89.0ms	(sqrt (* (+ g h) (- g h)))
69.0ms	(sqrt (* (+ g h) (- g h)))

simplify1.7s

Counts

82 → 82

Iterations

Iter	Nodes
3	4497
2	1206
1	416
0	202

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 30.3b

localize50.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ g (sqrt (* (+ g h) (- g h))))
8.2b	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (* 2 a)))
30.0b	(sqrt (* (+ g h) (- g h)))
30.0b	(sqrt (* (+ g h) (- g h)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`pow1` `*-un-lft-identity`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `frac-times`
7×	`flip3-+` `flip-+`
6×	`flip3--` `add-cube-cbrt` `flip--` `add-log-exp`
5×	`times-frac`
4×	`sqrt-pow1` `add-cbrt-cube` `associate-l/` `associate-r/` `add-exp-log` `insert-posit16`
2×	`pow1/2` `pow-prod-down` `sqrt-prod`
1×	`+-commutative` `cbrt-div` `sum-log` `pow1/3` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

9.0ms	(+ g (sqrt (* (+ g h) (- g h))))
23.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (* 2 a)))
27.0ms	(sqrt (* (+ g h) (- g h)))
15.0ms	(sqrt (* (+ g h) (- g h)))

series670.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ g (sqrt (* (+ g h) (- g h))))
385.0ms	(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (* 2 a)))
80.0ms	(sqrt (* (+ g h) (- g h)))
106.0ms	(sqrt (* (+ g h) (- g h)))

simplify1.4s

Counts

84 → 84

Iterations

Iter	Nodes
3	4670
2	1166
1	387
0	185

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 29.9b

localize65.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt (* (+ g h) (- g h)))
30.0b	(sqrt (* (+ g h) (- g h)))
30.0b	(sqrt (* (+ g h) (- g h)))
30.0b	(sqrt (* (+ g h) (- g h)))

rewrite77.0ms

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` `*-un-lft-identity` `add-cbrt-cube` `pow1/2` `pow-prod-down` `add-exp-log` `add-cube-cbrt` `sqrt-prod` `insert-posit16` `add-log-exp`

Counts

4 → 80

Calls

4 calls:

16.0ms	(sqrt (* (+ g h) (- g h)))
17.0ms	(sqrt (* (+ g h) (- g h)))
17.0ms	(sqrt (* (+ g h) (- g h)))
24.0ms	(sqrt (* (+ g h) (- g h)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt (* (+ g h) (- g h)))
109.0ms	(sqrt (* (+ g h) (- g h)))
78.0ms	(sqrt (* (+ g h) (- g h)))
90.0ms	(sqrt (* (+ g h) (- g h)))

simplify722.0ms

Counts

92 → 92

Iterations

Iter	Nodes
3	2310
2	515
1	136
0	62

prune2.0s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 29.9b

localize36.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ g (sqrt (* (+ g h) (- g h))))
6.7b	(cbrt (* (/ (+ g (sqrt (* (+ g h) (- g h)))) a) -1/2))
30.0b	(sqrt (* (+ g h) (- g h)))
30.0b	(sqrt (* (+ g h) (- g h)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`pow1`
8×	`frac-times`
7×	`flip3-+` `flip-+`
6×	`*-un-lft-identity` `flip3--` `flip--` `add-log-exp`
5×	`associate-*l/`
4×	`add-sqr-sqrt` `sqrt-pow1` `add-cbrt-cube` `associate-*r/` `add-exp-log` `add-cube-cbrt` `insert-posit16`
2×	`pow1/2` `pow-prod-down` `sqrt-prod`
1×	`cbrt-prod` `+-commutative` `cbrt-div` `sum-log` `pow1/3` `distribute-lft-out`

Counts

4 → 64

Calls

4 calls:

5.0ms	(+ g (sqrt (* (+ g h) (- g h))))
7.0ms	(cbrt (* (/ (+ g (sqrt (* (+ g h) (- g h)))) a) -1/2))
9.0ms	(sqrt (* (+ g h) (- g h)))
16.0ms	(sqrt (* (+ g h) (- g h)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ g (sqrt (* (+ g h) (- g h))))
339.0ms	(cbrt (* (/ (+ g (sqrt (* (+ g h) (- g h)))) a) -1/2))
79.0ms	(sqrt (* (+ g h) (- g h)))
83.0ms	(sqrt (* (+ g h) (- g h)))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
3	5049
2	1148
1	346
0	160

prune1.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 29.9b

regimes1.2s

Accuracy

59.2% (1.6b remaining)

Error of 30.6b against oracle of 29.0b and baseline of 32.8b

bsearch267.0ms

Steps

Iters	Range		Point
9	1.1552024854319542e-163	3.6408140752197565e-156	1.5914749870004055e-162

simplify400.0ms

Iterations

Iter	Nodes
2	45
1	45
0	36

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.6s	3859×	body	320	valid
2.3s	4004×	body	160	valid
2.1s	8060×	body	80	nan
26.0ms	137×	body	80	valid