Details

sample21.0ms

Algorithm

intervals

Results

5.0ms	203×	body	80	valid
4.0ms	13×	body	1280	valid
2.0ms	23×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 12.5b

Counts

2 → 2

localize6.0ms

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

series94.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ y (+ y 1.0))
59.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify114.0ms

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

prune144.0ms

Filtered

51 candidates to 40 candidates (78.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	42	9	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	43	10	53

Merged error: 6.5b

Counts

53 → 10

localize11.0ms

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)

rewrite20.0ms

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:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
10.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
1.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series352.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (+ y 1.0))
93.0ms	(cbrt (+ y 1.0))
107.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
58.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (41.0ms)

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

prune313.0ms

Filtered

109 candidates to 79 candidates (72.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	106	13	119

Merged error: 6.5b

Counts

119 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
8.8b	(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)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
9.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
11.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
1.0ms	(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)

series383.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (+ y 1.0))
113.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
111.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
62.0ms	(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)

simplify68.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	483	1106
1	1632	1020
2	5001	963

prune387.0ms

Filtered

112 candidates to 82 candidates (73.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	112	13	125

Merged error: 6.5b

Counts

125 → 13

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)

rewrite4.0ms

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

series290.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
59.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
54.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (56.0ms)

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

prune162.0ms

Filtered

55 candidates to 51 candidates (92.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	56	12	68

Merged error: 6.5b

Counts

68 → 12

regimes266.0ms

Accuracy

97.2% (0.2b remaining)

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

bsearch82.0ms

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	23	9
1	23	9

end0.0ms

sample686.0ms

Algorithm

intervals

Results

273.0ms	372×	body	1280	valid
160.0ms	6126×	body	80	valid
65.0ms	703×	body	640	valid
37.0ms	541×	body	320	valid
13.0ms	258×	body	160	valid