Details

sample128.0ms

Algorithm

intervals

Results

40.0ms	45×	body	1280	valid
26.0ms	50×	body	640	valid
15.0ms	158×	body	80	valid
11.0ms	30×	body	320	valid
7.0ms	104×	body	80	nan
3.0ms	13×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1961
5	488
4	149
3	52
2	24
1	15
0	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (pow (/ x (+ y x)) x) x)
6.0b	(pow (/ x (+ y x)) x)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
100×	`*-un-lft-identity`
90×	`unpow-prod-down`
70×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/l*`
15×	`distribute-lft-out`
13×	`add-exp-log`
10×	`associate-/r/`
6×	`div-exp` `div-inv`
5×	`flip3-+` `flip-+` `sqr-pow`
4×	`add-cbrt-cube` `pow-exp`
3×	`pow1` `pow-unpow` `associate-/r*`
2×	`pow-to-exp` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `pow-pow` `frac-2neg`

Counts

2 → 139

Calls

2 calls:

40.0ms	(/ (pow (/ x (+ y x)) x) x)
25.0ms	(pow (/ x (+ y x)) x)

series981.0ms

Counts

2 → 6

Calls

2 calls:

608.0ms	(/ (pow (/ x (+ y x)) x) x)
373.0ms	(pow (/ x (+ y x)) x)

simplify1.2s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	2477
1	605
0	263

prune697.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.9b	(pow (/ (cbrt x) (cbrt (+ y x))) x)
1.6b	(pow (* (/ (cbrt x) (cbrt (+ y x))) (/ (cbrt x) (cbrt (+ y x)))) x)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
49×	`unpow-prod-down`
47×	`*-un-lft-identity`
42×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
13×	`pow1`
7×	`pow-pow` `pow-exp`
6×	`pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`add-cbrt-cube` `prod-exp` `add-log-exp`
2×	`pow-to-exp` `cbrt-div` `pow1/3` `associate-/r/` `sqr-pow`
1×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
35.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
41.0ms	(pow (* (/ (cbrt x) (cbrt (+ y x))) (/ (cbrt x) (cbrt (+ y x)))) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt x)
302.0ms	(cbrt x)
409.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
398.0ms	(pow (* (/ (cbrt x) (cbrt (+ y x))) (/ (cbrt x) (cbrt (+ y x)))) x)

simplify1.3s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2573
1	795
0	255

prune599.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.9b	(pow (/ (cbrt x) (cbrt (+ y x))) x)
0.9b	(pow (/ (cbrt x) (cbrt (+ y x))) x)
0.9b	(pow (/ (cbrt x) (cbrt (+ y x))) x)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

144×	`unpow-prod-down`
138×	`cbrt-prod`
126×	`times-frac`
125×	`*-un-lft-identity`
89×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`distribute-lft-out`
13×	`add-exp-log`
9×	`pow-unpow`
7×	`pow1`
6×	`cbrt-div` `pow-exp` `associate-/r/`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `flip-+` `div-inv` `sqr-pow`
1×	`pow1/3`

Counts

4 → 200

Calls

4 calls:

1.0ms	(cbrt x)
15.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
21.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
23.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

271.0ms	(cbrt x)
358.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
437.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)
353.0ms	(pow (/ (cbrt x) (cbrt (+ y x))) x)

simplify972.0ms

Counts

212 → 212

Iterations

Iter	Nodes
done	5000
2	2091
1	655
0	208

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (- y)) x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log` `associate-/l/`
1×	`neg-sub0` `exp-neg` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `exp-diff` `div-exp` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

13.0ms

(/ (exp (- y)) x)

series25.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(/ (exp (- y)) x)

simplify2.6s

Counts

32 → 32

Iterations

Iter	Nodes
done	5002
3	3577
2	483
1	125
0	64

prune147.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes174.0ms

Accuracy

98.1% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 5.9b

bsearch160.0ms

Steps

Iters	Range		Point
9	7.46228068957284e-06	5.1212688054922095	3.9190130617913064
9	-5.514259056545185e+66	-1.3541699186634741e+60	-1.8247882343221416e+60

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	1516×	body	1280	valid
700.0ms	1507×	body	640	valid
402.0ms	4807×	body	80	valid
275.0ms	845×	body	320	valid
215.0ms	3070×	body	80	nan
121.0ms	406×	body	160	valid