Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	207×	body	80	valid
3.0ms	15×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	9×	body	160	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (10.0ms)

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: 11.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.9b	(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)

series89.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ y (+ y 1.0))
55.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (108.0ms)

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

prune129.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

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))
8.5b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite8.0ms

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:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
2.0ms	(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)

series314.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (+ y 1.0))
87.0ms	(cbrt (+ y 1.0))
90.0ms	(cbrt (+ y 1.0))
52.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (64.0ms)

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

prune237.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize15.0ms

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))
8.5b	(fma (/ (/ y (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite8.0ms

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:

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

series322.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ y 1.0))
90.0ms	(cbrt (+ y 1.0))
87.0ms	(cbrt (+ y 1.0))
56.0ms	(fma (/ (/ y (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	237	656
1	682	593
2	2421	578
3	5002	549

prune296.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
8.5b	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

rewrite3.0ms

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

series611.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt y)
177.0ms	(cbrt y)
182.0ms	(cbrt y)
71.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	104	277
1	278	244
2	1012	231
3	5002	227

prune171.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

regimes102.0ms

Accuracy

97.5% (0.2b remaining)

Error of 7.2b against oracle of 7.0b and baseline of 15.3b

bsearch86.0ms

Steps

Iters	Range		Point
8	1.1431332651762801e+24	2.2737699151718684e+27	5.359213104125442e+25
9	-1.9437229314865982e+38	-3.944269144284268e+32	-2.076632712489761e+33

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	12
1	25	12

end0.0ms

sample773.0ms

Algorithm

intervals

Results

306.0ms	6072×	body	80	valid
141.0ms	734×	body	640	valid
94.0ms	389×	body	1280	valid
73.0ms	514×	body	320	valid
27.0ms	291×	body	160	valid