Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	200×	body	80	valid
5.0ms	24×	body	640	valid
2.0ms	10×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid

simplify6.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
14	4751
13	4132
12	3553
11	3096
10	2562
9	1993
8	1617
7	1069
6	543
5	259
4	129
3	73
2	33
1	16
0	8

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

25.0ms	(/ y (+ 1.0 y))
1.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

series226.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(/ y (+ 1.0 y))
148.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

simplify4.0s

Counts

51 → 51

Iterations

Iter	Nodes
done	5002
3	2799
2	752
1	214
0	94

prune432.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

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:

2.0ms	(cbrt (fma (- x 1.0) (/ y (+ 1.0 y)) 1.0))
1.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
1.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
1.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

573.0ms	(cbrt (fma (- x 1.0) (/ y (+ 1.0 y)) 1.0))
201.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
176.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)
159.0ms	(fma (- x 1.0) (/ y (+ 1.0 y)) 1.0)

simplify3.2s

Counts

55 → 55

Iterations

Iter	Nodes
done	5004
3	1735
2	508
1	179
0	76

prune712.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y y) y)
4.0b	(fma (- x 1.0) (* (/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y)))) 1.0)
7.5b	(/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y)))
14.9b	(* (/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y))))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`pow1`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`add-exp-log` `add-cbrt-cube`
14×	`associate-l`
6×	`pow-plus` `associate-r` `pow-prod-up`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `pow2` `frac-times` `flip3-+` `associate-r/` `div-exp` `pow-sqr` `-commutative` `flip-+` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow3` `associate-*l/` `clear-num` `fma-udef`

Counts

4 → 109

Calls

4 calls:

73.0ms	(* (* y y) y)
1.0ms	(fma (- x 1.0) (* (/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y)))) 1.0)
11.0ms	(/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y)))
212.0ms	(* (/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y))))

series875.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (* y y) y)
330.0ms	(fma (- x 1.0) (* (/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y)))) 1.0)
258.0ms	(/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y)))
183.0ms	(* (/ y (fma (* 1.0 1.0) 1.0 (* (* y y) y))) (+ (* 1.0 1.0) (- (* y y) (* 1.0 y))))

simplify4.6s

Counts

121 → 121

Iterations

Iter	Nodes
done	5002
2	2774
1	638
0	191

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1.0 (- (/ 1 y) (/ x y)) x)
0.0b	(- (/ 1 y) (/ x y))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

257×	`times-frac`
210×	`add-sqr-sqrt`
207×	`*-un-lft-identity`
193×	`add-cube-cbrt`
169×	`prod-diff`
32×	`div-inv`
13×	`fma-neg`
6×	`difference-of-squares`
5×	`distribute-lft-out--`
4×	`add-log-exp`
3×	`distribute-rgt-out--`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `fma-udef` `sub-div`

Counts

2 → 222

Calls

2 calls:

1.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)
75.0ms	(- (/ 1 y) (/ x y))

series130.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)
58.0ms	(- (/ 1 y) (/ x y))

simplify4.7s

Counts

228 → 228

Iterations

Iter	Nodes
done	5000
3	4252
2	1530
1	710
0	315

prune974.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes264.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.1b

bsearch195.0ms

Steps

Iters	Range		Point
9	14127485.489807976	332285973929163.2	180419841.13710186
10	-822849273294.6077	-1.963203309137196e-05	-150725849.0902553

simplify8.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

518.0ms	6140×	body	80	valid
192.0ms	698×	body	640	valid
170.0ms	363×	body	1280	valid
138.0ms	503×	body	320	valid
113.0ms	296×	body	160	valid