Details

sample33.0ms

Algorithm

intervals

Results

15.0ms	203×	body	80	valid
4.0ms	23×	body	640	valid
3.0ms	13×	body	1280	valid
2.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (11.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
1.6b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite7.0ms

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:

5.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series97.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ y (+ y 1.0))
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	203	263
1	708	238
2	3148	232
3	5002	228

prune143.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
8.3b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
19.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series383.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ y 1.0))
98.0ms	(cbrt (+ y 1.0))
118.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
69.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	365	866
1	1251	798
2	5001	736

prune351.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.3b	(* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))
9.6b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

374×	`cbrt-div`
144×	`frac-times`
120×	`flip3-+` `flip-+`
54×	`associate-*r/`
48×	`associate-*l/`
30×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`pow1`
15×	`add-cube-cbrt`
14×	`associate-l`
11×	`add-exp-log`
10×	`pow1/3` `swap-sqr`
8×	`associate-r`
7×	`pow-prod-down` `distribute-lft-out`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus` `fma-udef`

Counts

4 → 190

Calls

4 calls:

7.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
20.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
54.0ms	(* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))
0.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series411.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
114.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
113.0ms	(* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))
65.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify97.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	888	3722
1	2572	3604
2	5002	3507

prune891.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
1.6b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
1.6b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
1.6b	(fma (/ y (+ y 1.0)) (- x 1.0) 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:

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

series517.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
282.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
62.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
56.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	168	405
1	501	355
2	1834	340
3	5002	325

prune193.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

regimes127.0ms

Accuracy

97.2% (0.2b remaining)

Error of 7.4b against oracle of 7.2b and baseline of 14.7b

bsearch114.0ms

Steps

Iters	Range		Point
10	1427003492276683.8	1.7305632411330904e+30	10613960846537648.0
8	-14168364119266.809	-5083001211.319212	-13972044976917.643

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample815.0ms

Algorithm

intervals

Results

322.0ms	6126×	body	80	valid
139.0ms	703×	body	640	valid
97.0ms	372×	body	1280	valid
83.0ms	541×	body	320	valid
26.0ms	258×	body	160	valid