Details

sample160.0ms

Algorithm

intervals

Results

71.0ms	395×	body	80	valid
40.0ms	406×	body	80	nan

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	518
1	37	518
2	83	518
3	234	518
4	651	518
5	1468	518
6	3225	518
done	5000	518

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`associate-+l+` `add-cbrt-cube` `add-exp-log`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-*l/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `associate-+l-` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

65.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
36.0ms	(* (- x 0.5) (log x))
28.0ms	(- (* (- x 0.5) (log x)) x)
75.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

704.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
400.0ms	(* (- x 0.5) (log x))
601.0ms	(- (* (- x 0.5) (log x)) x)
133.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.9s

Counts

110 → 110

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	216	35388
1	525	33084
2	1468	32519
done	5001	32039

prune890.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize93.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `add-log-exp`
3×	`associate-/r` `pow1/3` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
61.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series971.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt x)
278.0ms	(cbrt x)
285.0ms	(cbrt x)
127.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.2s

Counts

74 → 74

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	97	21113
1	224	19261
2	639	19023
3	2513	18383
done	5010	18383

prune736.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize92.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
5.1b	(pow x 1/3)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/r` `unpow-prod-down` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `div-exp` `pow-exp` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
4.0ms	(pow x 1/3)
62.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series959.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(cbrt x)
306.0ms	(cbrt x)
266.0ms	(pow x 1/3)
116.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify4.1s

Counts

81 → 81

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	124	24344
1	303	20469
2	819	20348
3	3195	19598
done	5003	19557

prune694.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize118.0ms

Local error

Found 4 expressions with local error:

5.1b	(pow x 1/3)
5.1b	(pow x 1/3)
5.1b	(pow x 1/3)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow-unpow` `unpow-prod-down` `times-frac` `add-exp-log`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-to-exp` `associate-/r` `pow-pow` `unpow1/3` `pow-exp` `associate-/l` `sqr-pow`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 83

Calls

4 calls:

2.0ms	(pow x 1/3)
2.0ms	(pow x 1/3)
2.0ms	(pow x 1/3)
44.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series807.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(pow x 1/3)
240.0ms	(pow x 1/3)
250.0ms	(pow x 1/3)
126.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.5s

Counts

95 → 95

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	111	30806
1	281	23119
2	783	22998
3	2981	22028
done	5007	21905

prune956.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

regimes661.0ms

Accuracy

88.5% (0.3b remaining)

Error of 4.0b against oracle of 3.8b and baseline of 6.0b

bsearch46.0ms

Steps

Iters	Range		Point
3	8958292526974556.0	13148629152164846.0	11293960185246276.0

simplify16.0ms

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	44	1930
1	58	1930
done	58	1930

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.0s	11597×	body	80	nan
1.6s	11601×	body	80	valid