Details

sample49.0ms

Algorithm

intervals

Results

21.0ms	265×	body	80	valid
4.0ms	14×	body	640	valid
3.0ms	10×	body	1280	valid
3.0ms	14×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1620
5	661
4	266
3	103
2	43
1	20
0	11

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.7b	(+ x (/ (* (- y z) (- t x)) (- a z)))
14.0b	(/ (* (- y z) (- t x)) (- a z))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
104×	`*-un-lft-identity`
80×	`times-frac`
40×	`add-cube-cbrt`
35×	`associate-r` `associate-l`
31×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/l*`
13×	`flip3--` `flip--`
10×	`add-cbrt-cube` `add-exp-log`
8×	`frac-times` `associate-/l/`
7×	`*-commutative` `unswap-sqr`
5×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-l/` `associate-r/`
3×	`insert-posit16`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `pow-prod-down` `flip-+` `div-inv` `distribute-lft-out`

Counts

3 → 174

Calls

3 calls:

40.0ms	(* (- y z) (- t x))
149.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
106.0ms	(/ (* (- y z) (- t x)) (- a z))

series481.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (- y z) (- t x))
238.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
193.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify1.9s

Counts

183 → 183

Iterations

Iter	Nodes
done	5006
2	2780
1	766
0	264

prune867.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.2b	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
7.6b	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

2282×	`add-sqr-sqrt`
2203×	`*-un-lft-identity`
1532×	`cbrt-prod` `times-frac`
1351×	`associate-/l*`
1350×	`frac-times`
954×	`add-cube-cbrt`
912×	`associate-/r*`
622×	`distribute-lft-out--`
621×	`difference-of-squares`
532×	`associate-/l/`
375×	`associate-l`
126×	`flip3--` `flip--`
115×	`clear-num`
114×	`frac-2neg`
75×	`associate-*l/`
68×	`add-cbrt-cube`
62×	`cbrt-div`
58×	`associate-/r/`
46×	`associate-r`
44×	`cbrt-undiv`
29×	`div-inv`
25×	`add-exp-log`
21×	`cbrt-unprod` `unswap-sqr`
18×	`associate-*r/`
9×	`div-exp`
6×	`pow1` `prod-exp` `add-log-exp`
4×	`insert-posit16`
3×	`un-div-inv`
2×	`pow1/3` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 1970

Calls

4 calls:

7.0ms	(cbrt (- a z))
7.0ms	(cbrt (- a z))
647.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
1.3s	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (- a z))
216.0ms	(cbrt (- a z))
465.0ms	(* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
214.0ms	(+ x (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))

simplify2.6s

Counts

1982 → 1982

Iterations

Iter	Nodes
done	5001
0	2071

prune10.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.4b

localize80.0ms

Local error

Found 4 expressions with local error:

1.2b	(cbrt (/ (- t x) (cbrt (- a z))))
1.2b	(cbrt (/ (- t x) (cbrt (- a z))))
1.2b	(cbrt (/ (- t x) (cbrt (- a z))))
8.1b	(+ x (* (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

rewrite15.4s

Algorithm

rewrite-expression-head

Rules

228×	`cbrt-prod`
166×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
120×	`times-frac`
70×	`add-cube-cbrt`
60×	`cbrt-div`
45×	`distribute-lft-out--` `difference-of-squares`
24×	`associate-/r*`
15×	`associate-/l*`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `associate-/l/`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`clear-num` `frac-2neg` `pow1/3` `associate-l` `div-inv` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 234

Calls

4 calls:

32.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
34.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
23.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
15.3s	(+ x (* (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

329.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
376.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
337.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
228.0ms	(+ x (* (* (/ (/ (- y z) (cbrt (- a z))) (cbrt (- a z))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

simplify2.2s

Counts

246 → 246

Iterations

Iter	Nodes
done	5000
2	1395
1	571
0	278

prune1.8s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.5b	(* (- y z) (/ (- t x) (- a z)))

rewrite374.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
96×	`add-sqr-sqrt`
51×	`times-frac`
33×	`add-cube-cbrt`
31×	`associate-r` `distribute-lft-out--`
30×	`frac-times`
29×	`difference-of-squares`
22×	`flip3--` `flip--` `associate-/l*`
20×	`associate-/r*`
15×	`associate-*r/`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/l/`
7×	`associate-l`
5×	`pow1` `clear-num` `add-log-exp`
4×	`frac-2neg` `associate-/r/`
3×	`un-div-inv` `insert-posit16` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `div-sub` `pow-prod-down` `*-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

30.0ms	(/ (- t x) (- a z))
190.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
149.0ms	(* (- y z) (/ (- t x) (- a z)))

series495.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(/ (- t x) (- a z))
225.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
187.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify2.1s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	2864
1	687
0	241

prune889.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 2.4b

regimes853.0ms

Accuracy

35.5% (6.2b remaining)

Error of 9.4b against oracle of 3.2b and baseline of 12.8b

bsearch2.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	43
1	43
0	32

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.4s	7739×	body	80	valid
186.0ms	486×	body	640	valid
132.0ms	277×	body	1280	valid
103.0ms	410×	body	320	valid
83.0ms	279×	body	160	valid
3.0ms	6×	body	2560	valid