Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	206×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify2.8s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize21.0ms

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)))
10.2b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite59.0ms

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:

17.0ms	(* (- 1.0 x) y)
19.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
21.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series220.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* (- 1.0 x) y)
103.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
78.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.5s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1286
1	346
0	128

prune369.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite72.0ms

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:

55.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
8.0ms	(/ y (+ y 1.0))
4.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series197.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
48.0ms	(/ y (+ y 1.0))
88.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1637
1	425
0	157

prune466.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
2.1b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
2.1b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
2.1b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 84

Calls

4 calls:

45.0ms	(* (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
6.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
4.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
4.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series928.0ms

Counts

4 → 12

Calls

4 calls:

608.0ms	(* (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
93.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
126.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
102.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify2.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	3383
2	854
1	287
0	119

prune567.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
0.1b	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
2.1b	(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
10.2b	(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

49×	`frac-times`
43×	`pow1`
42×	`add-cbrt-cube` `add-exp-log`
29×	`associate-*l/`
26×	`flip3--` `flip--`
21×	`prod-exp` `cbrt-unprod`
17×	`pow-prod-down` `associate-*r/`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
5×	`difference-of-squares`
4×	`pow-sqr` `pow-prod-up` `associate-/l*`
3×	`associate-/r*`
2×	`flip3-+` `pow-plus` `associate-/r/` `flip-+` `associate-/l/`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative` `div-inv`

Counts

4 → 139

Calls

4 calls:

10.0ms	(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
127.0ms	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
14.0ms	(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
45.0ms	(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

series764.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
67.0ms	(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
107.0ms	(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
519.0ms	(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

simplify2.6s

Counts

151 → 151

Iterations

Iter	Nodes
done	5006
2	4015
1	825
0	251

prune818.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes239.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.6b

bsearch124.0ms

Steps

Iters	Range		Point
10	0.778402845272117	1913856845736365.8	214825219.74745002
10	-454307648390.4797	-8.1353853441046	-205884948.09812093

simplify9.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample1.5s

Algorithm

intervals

Results

844.0ms	6068×	body	80	valid
220.0ms	747×	body	640	valid
91.0ms	357×	body	1280	valid
79.0ms	530×	body	320	valid
30.0ms	298×	body	160	valid