Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	125×	pre	10240	exit
12.0ms	256×	body	80	valid
3.0ms	131×	pre	80	true

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	10
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.8b	(/ x0 (- 1.0 x1))
7.5b	(- (/ x0 (- 1.0 x1)) x0)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`times-frac`
12×	`add-cube-cbrt`
6×	`difference-of-squares`
5×	`associate-/r*` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 52

Calls

2 calls:

12.0ms	(/ x0 (- 1.0 x1))
45.0ms	(- (/ x0 (- 1.0 x1)) x0)

series98.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ x0 (- 1.0 x1))
52.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify1.5s

Counts

58 → 58

Iterations

Iter	Nodes
done	5002
3	3811
2	873
1	264
0	117

prune210.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (sqrt x0) (/ (- 1.0 x1) (sqrt x0)))
7.5b	(- (/ (sqrt x0) (/ (- 1.0 x1) (sqrt x0))) x0)

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

424×	`times-frac`
301×	`add-sqr-sqrt`
277×	`*-un-lft-identity`
215×	`sqrt-prod`
191×	`add-cube-cbrt`
49×	`difference-of-squares`
44×	`distribute-lft-out--`
34×	`associate-/r*`
9×	`div-inv`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow1` `associate-/r/`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `diff-log` `flip--`

Counts

2 → 281

Calls

2 calls:

27.0ms	(/ (sqrt x0) (/ (- 1.0 x1) (sqrt x0)))
209.0ms	(- (/ (sqrt x0) (/ (- 1.0 x1) (sqrt x0))) x0)

series122.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (sqrt x0) (/ (- 1.0 x1) (sqrt x0)))
80.0ms	(- (/ (sqrt x0) (/ (- 1.0 x1) (sqrt x0))) x0)

simplify610.0ms

Counts

287 → 287

Iterations

Iter	Nodes
done	5001
1	995
0	372

prune751.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sqrt x0) (- (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))
7.1b	(- (/ (sqrt x0) (- 1.0 x1)) (sqrt x0))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
14×	`sqrt-prod`
12×	`difference-of-squares`
10×	`associate-r`
9×	`*-un-lft-identity`
8×	`times-frac`
6×	`associate-l`
5×	`add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 54

Calls

2 calls:

179.0ms	(* (sqrt x0) (- (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))
92.0ms	(- (/ (sqrt x0) (- 1.0 x1)) (sqrt x0))

series248.0ms

Counts

2 → 6

Calls

2 calls:

154.0ms	(* (sqrt x0) (- (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))
94.0ms	(- (/ (sqrt x0) (- 1.0 x1)) (sqrt x0))

simplify530.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
2	1156
1	260
0	97

prune173.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (+ (* x0 (- x0)) (* (sqrt x0) (pow (/ (sqrt x0) (- 1.0 x1)) 3))) (+ (* (/ (sqrt x0) (- 1.0 x1)) (/ (sqrt x0) (- 1.0 x1))) (+ (* (sqrt x0) (sqrt x0)) (* (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))))
0.7b	(+ (* (sqrt x0) (sqrt x0)) (* (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))
1.0b	(* (/ (sqrt x0) (- 1.0 x1)) (/ (sqrt x0) (- 1.0 x1)))
5.8b	(+ (* x0 (- x0)) (* (sqrt x0) (pow (/ (sqrt x0) (- 1.0 x1)) 3)))

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

206×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
193×	`times-frac`
92×	`add-cube-cbrt` `sqrt-prod`
62×	`swap-sqr`
44×	`distribute-lft-out--`
36×	`associate-r` `associate-l`
28×	`difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r/`
11×	`pow1`
9×	`unswap-sqr`
8×	`add-log-exp`
7×	`flip3-+` `flip-+`
6×	`frac-add`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`flip3--` `prod-exp` `cbrt-unprod` `flip--`
3×	`frac-times` `associate-/r` `associate-l/` `associate-r/` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/l/`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `distribute-rgt-out` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 227

Calls

4 calls:

94.0ms	(/ (+ (* x0 (- x0)) (* (sqrt x0) (pow (/ (sqrt x0) (- 1.0 x1)) 3))) (+ (* (/ (sqrt x0) (- 1.0 x1)) (/ (sqrt x0) (- 1.0 x1))) (+ (* (sqrt x0) (sqrt x0)) (* (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))))
306.0ms	(+ (* (sqrt x0) (sqrt x0)) (* (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))
68.0ms	(* (/ (sqrt x0) (- 1.0 x1)) (/ (sqrt x0) (- 1.0 x1)))
8.0ms	(+ (* x0 (- x0)) (* (sqrt x0) (pow (/ (sqrt x0) (- 1.0 x1)) 3)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (+ (* x0 (- x0)) (* (sqrt x0) (pow (/ (sqrt x0) (- 1.0 x1)) 3))) (+ (* (/ (sqrt x0) (- 1.0 x1)) (/ (sqrt x0) (- 1.0 x1))) (+ (* (sqrt x0) (sqrt x0)) (* (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))))
47.0ms	(+ (* (sqrt x0) (sqrt x0)) (* (/ (sqrt x0) (- 1.0 x1)) (sqrt x0)))
56.0ms	(* (/ (sqrt x0) (- 1.0 x1)) (/ (sqrt x0) (- 1.0 x1)))
82.0ms	(+ (* x0 (- x0)) (* (sqrt x0) (pow (/ (sqrt x0) (- 1.0 x1)) 3)))

simplify440.0ms

Counts

239 → 239

Iterations

Iter	Nodes
done	5000
1	1289
0	389

prune695.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.3b

regimes97.0ms

Accuracy

0% (1.0b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 6.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	29
2	29
1	28
0	23

end0.0ms

sample976.0ms

Algorithm

intervals

Results

465.0ms	3928×	pre	10240	exit
184.0ms	8000×	body	80	valid
122.0ms	4072×	pre	80	true