Details

sample51.0ms

Algorithm

intervals

Results

10.0ms	186×	body	80	valid
9.0ms	33×	body	1280	valid
4.0ms	22×	body	640	valid
4.0ms	96×	body	80	nan
2.0ms	14×	body	640	nan
2.0ms	11×	body	320	valid
1.0ms	8×	body	1280	nan
0.0ms	4×	body	320	nan
0.0ms	4×	body	160	valid
0.0ms	3×	body	160	nan

simplify137.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	29	12
3	41	12
4	54	12
5	62	12
6	70	12
7	85	12
8	103	12
9	116	12
done	116	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
1.7b	(- 1.0 (/ (- x y) (- 1.0 y)))
6.0b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

54.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
28.0ms	(/ (- x y) (- 1.0 y))
46.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
50.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
53.0ms	(/ (- x y) (- 1.0 y))
67.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
124.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.9s

Counts

120 → 120

Iterations

Useful iterations: 3 (873.0ms)

Iter	Nodes	Cost
0	205	1894
1	489	1792
2	1226	1680
3	3267	1671
done	5000	1671

prune428.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
6.0b	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
12.6b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
37×	`cbrt-prod`
34×	`*-un-lft-identity`
15×	`difference-of-squares`
14×	`add-cube-cbrt` `cbrt-div`
12×	`pow1` `times-frac`
10×	`swap-sqr`
9×	`log-prod` `flip3--` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `pow1/3`
6×	`add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`log-div` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `associate--r-`

Counts

4 → 110

Calls

4 calls:

7.0ms	(cbrt (- 1.0 y))
41.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
100.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
88.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (- 1.0 y))
133.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
99.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
71.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify2.7s

Counts

122 → 122

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	242	2627
1	513	2470
2	1321	1800
3	4154	1710
done	5000	1700

prune384.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.7b	(- 1.0 (/ (- x y) (- 1.0 y)))
6.0b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
6.0b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
6.0b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`log-prod`
15×	`*-un-lft-identity`
8×	`difference-of-squares`
7×	`pow1` `add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`rem-log-exp` `log-pow`
1×	`sub-neg` `diff-log` `div-sub` `associate--r-`

Counts

4 → 67

Calls

4 calls:

54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
49.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
33.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
63.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
149.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
143.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
126.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify2.8s

Counts

79 → 79

Iterations

Useful iterations: 3 (260.0ms)

Iter	Nodes	Cost
0	91	1427
1	195	1376
2	458	1229
3	1237	1223
4	4597	1223
done	5000	1223

prune540.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* (- x y) (+ (/ (- x y) (- 1.0 y)) 1.0)) (- 1.0 y))
1.7b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
9.3b	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
11.1b	(log (+ (/ (* (- x y) (+ (/ (- x y) (- 1.0 y)) 1.0)) (- 1.0 y)) (* 1.0 1.0)))

rewrite504.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
50×	`difference-of-squares`
36×	`unpow-prod-down` `log-prod` `cube-prod`
32×	`*-un-lft-identity`
21×	`times-frac`
20×	`sqr-pow`
12×	`distribute-lft-out--`
11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-cube-cbrt` `associate-/l/`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-/r*`
4×	`frac-times` `log-div` `flip3-+` `flip-+`
2×	`difference-cubes` `cbrt-undiv` `associate-r/` `div-exp` `rem-log-exp` `associate-l/` `associate-/r/` `log-pow`
1×	`sub-neg` `frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 135

Calls

4 calls:

104.0ms	(/ (* (- x y) (+ (/ (- x y) (- 1.0 y)) 1.0)) (- 1.0 y))
108.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
177.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
109.0ms	(log (+ (/ (* (- x y) (+ (/ (- x y) (- 1.0 y)) 1.0)) (- 1.0 y)) (* 1.0 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (* (- x y) (+ (/ (- x y) (- 1.0 y)) 1.0)) (- 1.0 y))
308.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
509.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
254.0ms	(log (+ (/ (* (- x y) (+ (/ (- x y) (- 1.0 y)) 1.0)) (- 1.0 y)) (* 1.0 1.0)))

simplify1.6s

Counts

147 → 147

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	289	4015
1	727	3772
2	2493	3546
done	5000	3538

prune703.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes241.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 16.9b

bsearch1.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	49
1	28	49
done	28	49

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	5699×	body	80	valid
356.0ms	835×	body	1280	valid
331.0ms	769×	body	640	valid
249.0ms	3664×	body	80	nan
158.0ms	371×	body	1280	nan
133.0ms	385×	body	640	nan
88.0ms	456×	body	320	valid
33.0ms	194×	body	320	nan
31.0ms	241×	body	160	valid
15.0ms	132×	body	160	nan