Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
3.0ms	26×	body	640	valid
2.0ms	16×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid

simplify91.0ms

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: 15.4b

Counts

2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.0b	(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)

series102.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ y (+ y 1.0))
65.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify129.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (116.0ms)

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

prune143.0ms

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: 8.0b

Counts

53 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ y 1.0))
0.2b	(cbrt (+ y 1.0))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
10.0b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite22.0ms

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))
11.0ms	(* (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)

series397.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (+ y 1.0))
104.0ms	(cbrt (+ y 1.0))
121.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
67.0ms	(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 (47.0ms)

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

prune326.0ms

Filtered

109 candidates to 79 candidates (72.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	107	12	119

Merged error: 8.0b

Counts

119 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.3b	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
11.9b	(fma (/ (/ y (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (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)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

384×	`cbrt-div`
144×	`frac-times`
120×	`flip3-+` `flip-+`
56×	`cbrt-prod`
52×	`*-un-lft-identity`
48×	`associate-r/` `associate-l/`
44×	`add-sqr-sqrt`
25×	`pow1`
24×	`add-cube-cbrt`
22×	`swap-sqr`
18×	`pow1/3` `associate-r` `associate-l`
12×	`distribute-lft-out` `unswap-sqr`
10×	`add-exp-log`
6×	`pow-prod-down` `pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`fma-udef`

Counts

4 → 236

Calls

4 calls:

11.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
11.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
12.0ms	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
1.0ms	(fma (/ (/ y (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (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)

series451.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
126.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
134.0ms	(* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))
70.0ms	(fma (/ (/ y (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (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)

simplify92.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	545	4234
1	1673	4052
2	5001	3864

prune665.0ms

Filtered

248 candidates to 129 candidates (52.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	246	2	248
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	246	14	260

Merged error: 8.0b

Counts

260 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
0.6b	(* (cbrt y) (cbrt y))
10.7b	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `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 → 78

Calls

4 calls:

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

series722.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt y)
202.0ms	(cbrt y)
237.0ms	(* (cbrt y) (cbrt y))
80.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify143.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	176	413
1	690	365
2	4187	338
3	5001	336

prune223.0ms

Filtered

90 candidates to 70 candidates (77.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	89	15	104

Merged error: 8.0b

Counts

104 → 15

regimes362.0ms

Accuracy

96.9% (0.2b remaining)

Error of 7.6b against oracle of 7.4b and baseline of 15.2b

bsearch116.0ms

Steps

Iters	Range		Point
10	89835997810550.58	4.545211685385971e+31	1.225799455048051e+21
8	-2.898468026705626e+24	-4.390657834609298e+20	-5.3432312811250083e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	20
1	32	20

end0.0ms

sample521.0ms

Algorithm

intervals

Results

188.0ms	6048×	body	80	valid
79.0ms	740×	body	640	valid
58.0ms	388×	body	1280	valid
44.0ms	503×	body	320	valid
18.0ms	321×	body	160	valid

Details

sample21.0ms

simplify91.0ms

prune7.0ms

localize7.0ms

rewrite8.0ms

series102.0ms

simplify129.0ms

prune143.0ms

localize11.0ms

rewrite22.0ms

series397.0ms

simplify58.0ms

prune326.0ms

localize22.0ms

rewrite55.0ms

series451.0ms

simplify92.0ms

prune665.0ms

localize11.0ms

rewrite12.0ms

series722.0ms

simplify143.0ms

prune223.0ms

regimes362.0ms

bsearch116.0ms

simplify2.0ms

end0.0ms

sample521.0ms

Profiling