Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	195×	body	80	valid
2.0ms	24×	body	640	valid
1.0ms	11×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	14×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

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: 14.3b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.5b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite16.0ms

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:

14.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series85.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ y (+ y 1.0))
49.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify104.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (99.0ms)

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

prune137.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize12.0ms

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))
10.6b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

4.0ms	(cbrt (+ y 1.0))
4.0ms	(cbrt (+ y 1.0))
4.0ms	(cbrt (+ y 1.0))
0.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series309.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ y 1.0))
85.0ms	(cbrt (+ y 1.0))
85.0ms	(cbrt (+ y 1.0))
53.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	235	565
1	699	515
2	2697	493
3	5001	461

prune265.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.8b

localize10.0ms

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))
11.1b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

4.0ms	(cbrt (+ y 1.0))
4.0ms	(cbrt (+ y 1.0))
8.0ms	(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)

series306.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ y 1.0))
86.0ms	(cbrt (+ y 1.0))
85.0ms	(cbrt (+ y 1.0))
48.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	230	552
1	657	500
2	2252	479
3	5001	448

prune255.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
10.3b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

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

series596.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt y)
176.0ms	(cbrt y)
183.0ms	(cbrt y)
60.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	104	277
1	282	243
2	1092	232
3	5002	228

prune176.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

regimes121.0ms

Accuracy

97.2% (0.2b remaining)

Error of 7.7b against oracle of 7.5b and baseline of 14.7b

bsearch67.0ms

Steps

Iters	Range		Point
10	202115485668.4307	2.3320142913441958e+21	29987682850388436.0
5	-5.282105409381724e+16	-15982864723585738.0	-1.823668018094434e+16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	12
1	25	12

end0.0ms

sample477.0ms

Algorithm

intervals

Results

150.0ms	6066×	body	80	valid
68.0ms	744×	body	640	valid
42.0ms	384×	body	1280	valid
33.0ms	510×	body	320	valid
13.0ms	296×	body	160	valid