Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	199×	body	80	valid
3.0ms	26×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	10×	body	1280	valid
0.0ms	3×	body	160	valid

simplify6.3s

Counts

1 → 1

Iterations

Useful iterations: 4 (19.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	72	11
4	137	10
5	243	10
6	316	10
7	381	10
8	417	10
9	499	10
10	573	10
11	582	10
12	601	10
13	640	10
14	740	10
15	1002	10
16	1312	10
17	1800	10
18	2290	10
19	2369	10
20	2375	10
done	2375	10

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
13×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv`

Counts

2 → 58

Calls

2 calls:

12.0ms	(/ (- x 1.0) (+ y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series97.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (- x 1.0) (+ y 1.0))
66.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.3s

Counts

64 → 64

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	114	834
1	277	799
2	678	745
3	1667	740
4	4688	736
done	5001	736

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series418.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
62.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
65.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
66.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.0s

Counts

55 → 55

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	76	843
1	182	832
2	462	731
3	1264	695
4	4038	674
done	5001	674

prune196.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0))
4.0b	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`cbrt-div` `flip3-+` `flip-+` `fma-udef`
1×	`+-commutative` `fma-def` `pow1/3` `sum-log`

Counts

4 → 49

Calls

4 calls:

8.0ms	(cbrt (+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0))
8.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series442.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(cbrt (+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0))
71.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)
68.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
67.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify1.2s

Counts

61 → 61

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	104	1049
1	264	998
2	713	897
3	2168	845
done	5000	843

prune236.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
1.4b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.1b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `prod-diff`
24×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
5×	`pow1` `associate-l` `distribute-lft-out` `add-log-exp`
4×	`flip3-+` `associate-l/` `associate-/r` `flip-+` `div-inv`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-r` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `unswap-sqr`

Counts

3 → 102

Calls

3 calls:

10.0ms	(* (- 1.0 x) y)
13.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
10.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series157.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* (- 1.0 x) y)
73.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
50.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.0s

Counts

111 → 111

Iterations

Useful iterations: 2 (343.0ms)

Iter	Nodes	Cost
0	202	2757
1	523	2323
2	1931	1851
done	5000	1851

prune216.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes130.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch93.0ms

Steps

Iters	Range		Point
8	28638621.607503247	50024088429.266525	212488777.89840698
10	-7.884632933156152e+16	-925426.909356872	-198843285.26894423

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	19	41
1	26	31
done	26	31

end0.0ms

sample481.0ms

Algorithm

intervals

Results

167.0ms	6133×	body	80	valid
70.0ms	719×	body	640	valid
43.0ms	347×	body	1280	valid
43.0ms	515×	body	320	valid
19.0ms	286×	body	160	valid