Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	205×	body	80	valid
2.0ms	22×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	10×	body	320	valid
0.0ms	8×	body	160	valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (12.0ms)

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

prune7.0ms

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: 12.3b

Counts

2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.2b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite8.0ms

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:

6.0ms	(/ y (+ y 1.0))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series96.0ms

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 (108.0ms)

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

prune138.0ms

Filtered

51 candidates to 40 candidates (78.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	41	10	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	42	11	53

Merged error: 8.7b

Counts

53 → 11

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 (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite12.0ms

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:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
1.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series360.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (+ y 1.0))
100.0ms	(cbrt (+ y 1.0))
98.0ms	(cbrt (+ y 1.0))
58.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify104.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (87.0ms)

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

prune266.0ms

Filtered

70 candidates to 62 candidates (88.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	69	12	81

Merged error: 8.7b

Counts

81 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
9.0b	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

rewrite6.0ms

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

series708.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt y)
215.0ms	(cbrt y)
205.0ms	(cbrt y)
83.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (46.0ms)

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

prune217.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	60	13	73

Merged error: 8.7b

Counts

73 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
8.8b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite6.0ms

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

series713.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt y)
201.0ms	(cbrt y)
203.0ms	(cbrt y)
93.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (55.0ms)

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

prune177.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	61	13	74

Merged error: 8.7b

Counts

74 → 13

regimes313.0ms

Accuracy

97.3% (0.2b remaining)

Error of 7.6b against oracle of 7.4b and baseline of 15.1b

bsearch133.0ms

Steps

Iters	Range		Point
11	7.358553961982732e+28	9.91620148864009e+48	1.9204227606463456e+29
7	-2.5065033830167604e+30	-1.2514886377233823e+29	-5.690547167924476e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample523.0ms

Algorithm

intervals

Results

183.0ms	6090×	body	80	valid
87.0ms	713×	body	640	valid
55.0ms	398×	body	1280	valid
45.0ms	498×	body	320	valid
17.0ms	301×	body	160	valid