Details

sample282.0ms

Algorithm

intervals

Results

240.0ms	200×	body	80	valid
5.0ms	24×	body	640	valid
3.0ms	10×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid

simplify7.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
14	3938
13	2876
12	2271
11	1825
10	1640
9	1398
8	1158
7	883
6	481
5	228
4	121
3	71
2	33
1	16
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.1b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

45.0ms	(* (- 1.0 x) y)
38.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
54.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series284.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* (- 1.0 x) y)
127.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
101.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1284
1	346
0	128

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.1b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite431.0ms

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:

24.0ms	(/ y (+ y 1.0))
392.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
9.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series352.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ y (+ y 1.0))
108.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
141.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify4.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1609
1	424
0	157

prune673.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (- y 1.0))
0.0b	(* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0)))
0.1b	(* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0))
3.3b	(- 1.0 (* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0)))

rewrite444.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
54×	`times-frac`
36×	`add-exp-log` `add-cbrt-cube`
34×	`add-cube-cbrt`
27×	`associate-l`
26×	`associate-r`
13×	`prod-exp` `cbrt-unprod`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`pow1`
10×	`frac-times`
9×	`cbrt-undiv` `div-exp`
7×	`flip3--` `associate-*l/` `flip--`
6×	`associate-*r/` `associate-/r/` `add-log-exp`
5×	`sub-neg` `associate-/r*` `distribute-lft-out`
4×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate--r+` `unswap-sqr`
3×	`div-inv` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+`

Counts

4 → 165

Calls

4 calls:

23.0ms	(/ y (- y 1.0))
156.0ms	(* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0)))
237.0ms	(* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0))
13.0ms	(- 1.0 (* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ y (- y 1.0))
260.0ms	(* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0)))
91.0ms	(* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0))
128.0ms	(- 1.0 (* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0)))

simplify13.6s

Counts

177 → 177

Iterations

Iter	Nodes
done	5005
2	3685
1	836
0	261

prune2.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

72.0ms	(+ x (- (/ 1.0 y) (* (/ x y) 1.0)))
51.0ms	(- (/ 1.0 y) (* (/ x y) 1.0))

series167.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(+ x (- (/ 1.0 y) (* (/ x y) 1.0)))
104.0ms	(- (/ 1.0 y) (* (/ x y) 1.0))

simplify8.1s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
3	2992
2	599
1	177
0	63

prune829.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes813.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.1b

bsearch418.0ms

Steps

Iters	Range		Point
9	14127485.489807976	332285973929163.2	89892178.74303682
10	-822849273294.6077	-1.963203309137196e-05	-150725849.0902553

simplify11.0ms

Iterations

Iter	Nodes
done	30
1	30
0	22

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	698×	body	640	valid
1.2s	6140×	body	80	valid
336.0ms	363×	body	1280	valid
189.0ms	503×	body	320	valid
80.0ms	296×	body	160	valid