Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	198×	body	80	valid
2.0ms	27×	body	640	valid
2.0ms	14×	body	1280	valid
1.0ms	9×	body	320	valid
0.0ms	8×	body	160	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (14.0ms)

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: 13.9b

Counts

2 → 2

localize12.0ms

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)

series103.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ y (+ y 1.0))
59.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify124.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (118.0ms)

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

prune157.0ms

Filtered

51 candidates to 40 candidates (78.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	39	12	51
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	41	12	53

Merged error: 8.1b

Counts

53 → 12

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))
10.4b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (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:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
8.0ms	(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)

series370.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (+ y 1.0))
104.0ms	(cbrt (+ y 1.0))
104.0ms	(cbrt (+ y 1.0))
59.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify99.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (82.0ms)

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

prune531.0ms

Filtered

70 candidates to 62 candidates (88.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	69	13	82

Merged error: 8.1b

Counts

82 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
2.2b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
2.2b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
2.2b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 72

Calls

4 calls:

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

series307.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
58.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
62.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify129.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	203	822
1	713	736
2	3312	647
3	5001	632

prune294.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	84	13	97

Merged error: 8.1b

Counts

97 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (cbrt (+ y 1.0)))
10.2b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

19×	`cbrt-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `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 → 61

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
4.0ms	(cbrt (cbrt (+ y 1.0)))
1.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series354.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ y 1.0))
93.0ms	(cbrt (+ y 1.0))
98.0ms	(cbrt (cbrt (+ y 1.0)))
63.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify143.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	362	717
1	1100	649
2	4509	627
3	5001	620

prune331.0ms

Filtered

73 candidates to 65 candidates (89.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	74	12	86

Merged error: 8.1b

Counts

86 → 12

regimes116.0ms

Accuracy

96.7% (0.2b remaining)

Error of 7.6b against oracle of 7.3b and baseline of 14.8b

bsearch100.0ms

Steps

Iters	Range		Point
9	1.1581638671359371e+19	2.3534274151300485e+26	4.147177003063489e+24
8	-3.934899403699163e+52	-1.2131416731721854e+50	-2.1718162890186172e+50

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample460.0ms

Algorithm

intervals

Results

154.0ms	6110×	body	80	valid
69.0ms	698×	body	640	valid
46.0ms	377×	body	1280	valid
34.0ms	507×	body	320	valid
14.0ms	308×	body	160	valid