Details

sample37.0ms

Algorithm

intervals

Results

8.0ms	193×	body	80	valid
3.0ms	20×	body	640	valid
2.0ms	20×	body	320	valid
2.0ms	11×	body	1280	valid
1.0ms	12×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
14	4122
13	3069
12	2474
11	2032
10	1843
9	1602
8	1334
7	972
6	535
5	248
4	118
3	71
2	33
1	16
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.9b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

16.0ms	(* (- 1.0 x) y)
27.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
27.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series205.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (- 1.0 x) y)
96.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
62.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1286
1	346
0	128

prune313.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
0.0b	(/ y (+ y 1.0))
3.9b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite79.0ms

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

Counts

3 → 88

Calls

3 calls:

51.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
17.0ms	(/ y (+ y 1.0))
6.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series210.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
53.0ms	(/ y (+ y 1.0))
87.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.6s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1637
1	425
0	157

prune464.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-log-exp`
3×	`times-frac` `difference-of-squares`
2×	`pow1` `sum-log` `flip3-+` `add-cbrt-cube` `diff-log` `add-exp-log` `frac-sub` `add-cube-cbrt` `flip-+` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

2 → 33

Calls

2 calls:

167.0ms	(- (+ (/ 1.0 y) x) (/ x (/ y 1.0)))
17.0ms	(+ (/ 1.0 y) x)

series74.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (+ (/ 1.0 y) x) (/ x (/ y 1.0)))
29.0ms	(+ (/ 1.0 y) x)

simplify3.0s

Counts

39 → 39

Iterations

Iter	Nodes
done	5017
3	4547
2	801
1	202
0	79

prune179.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1.0 y) x)) (cbrt (+ (/ 1.0 y) x)))
0.6b	(cbrt (+ (/ 1.0 y) x))
0.6b	(cbrt (+ (/ 1.0 y) x))
0.6b	(cbrt (+ (/ 1.0 y) x))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

77.0ms	(* (cbrt (+ (/ 1.0 y) x)) (cbrt (+ (/ 1.0 y) x)))
17.0ms	(cbrt (+ (/ 1.0 y) x))
14.0ms	(cbrt (+ (/ 1.0 y) x))
8.0ms	(cbrt (+ (/ 1.0 y) x))

series626.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (cbrt (+ (/ 1.0 y) x)) (cbrt (+ (/ 1.0 y) x)))
156.0ms	(cbrt (+ (/ 1.0 y) x))
143.0ms	(cbrt (+ (/ 1.0 y) x))
157.0ms	(cbrt (+ (/ 1.0 y) x))

simplify2.5s

Counts

107 → 107

Iterations

Iter	Nodes
done	5005
3	3438
2	1124
1	420
0	164

prune689.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes419.0ms

Accuracy

98.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 14.3b

bsearch70.0ms

Steps

Iters	Range		Point
10	4.9803363081918155	422514113030.77625	361767606.44001645
5	-2.085807323628561e+25	-8.665460962243007e+24	-8.76265571073903e+24

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end1.0ms

sample1.0s

Algorithm

intervals

Results

414.0ms	6102×	body	80	valid
131.0ms	744×	body	640	valid
113.0ms	538×	body	320	valid
74.0ms	336×	body	1280	valid
71.0ms	280×	body	160	valid