Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	182×	body	80	valid
5.0ms	26×	body	640	valid
4.0ms	27×	body	320	valid
3.0ms	12×	body	1280	valid
1.0ms	9×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	74	11
4	153	11
5	413	11
6	1662	11
done	5001	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize19.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.8b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `times-frac` `associate-/r*` `add-log-exp`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `associate-*l/` `associate-/r/` `flip--` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

32.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
41.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series199.0ms

Counts

2 → 6

Calls

2 calls:

120.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
78.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.3s

Counts

47 → 47

Iterations

Useful iterations: 2 (358.0ms)

Iter	Nodes	Cost
0	104	694
1	296	648
2	1680	584
done	5000	584

prune298.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.2b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `flip--` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

23.0ms	(/ y (+ y 1.0))
93.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
12.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series295.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ y (+ y 1.0))
83.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
145.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify2.2s

Counts

97 → 97

Iterations

Useful iterations: 2 (541.0ms)

Iter	Nodes	Cost
0	157	1229
1	424	1152
2	2493	1056
done	5000	1056

prune482.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (+ x (/ 1.0 y)) (* 1.0 (/ x y)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
2×	`diff-log` `associate-*r/` `frac-sub`
1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `flip3--` `*-un-lft-identity` `flip3-+` `associate--l+` `sum-log` `add-cbrt-cube` `flip--` `flip-+`

Counts

1 → 16

Calls

1 calls:

154.0ms

(- (+ x (/ 1.0 y)) (* 1.0 (/ x y)))

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

(- (+ x (/ 1.0 y)) (* 1.0 (/ x y)))

simplify826.0ms

Counts

19 → 19

Iterations

Useful iterations: done (825.0ms)

Iter	Nodes	Cost
0	59	373
1	171	356
2	879	322
done	5000	301

prune108.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
0.1b	(* (sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
2.2b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
2.2b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
14×	`sqrt-div`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3--` `sqrt-pow1` `pow1/2` `flip--`
8×	`swap-sqr` `add-log-exp`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 96

Calls

4 calls:

9.0ms	(sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
61.0ms	(* (sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
10.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
10.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
108.0ms	(* (sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (sqrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
121.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
113.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	120	2888
1	277	2108
2	1213	1906
done	5000	1847

prune488.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes352.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.4b

bsearch182.0ms

Steps

Iters	Range		Point
10	0.013914501587729765	1368294241.5238848	150372736.82230544
10	-1.5312203001569835e+19	-3934.6710789005906	-131050117.71074806

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	19	41
1	26	31
done	26	31

end0.0ms

sample1.3s

Algorithm

intervals

Results

494.0ms	6084×	body	80	valid
162.0ms	738×	body	640	valid
155.0ms	353×	body	1280	valid
138.0ms	526×	body	320	valid
35.0ms	299×	body	160	valid