Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	202×	body	80	valid
2.0ms	21×	body	640	valid
1.0ms	10×	body	1280	valid
1.0ms	15×	body	320	valid
0.0ms	8×	body	160	valid

simplify91.0ms

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

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.4b	(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))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series101.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ y (+ y 1.0))
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify124.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	202	264
1	705	238
2	3124	232
3	5002	228

prune100.0ms

Filtered

51 candidates to 40 candidates (21.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	8	52

Merged error: 6.0b

Counts

52 → 8

localize11.0ms

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

rewrite21.0ms

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` `add-cbrt-cube` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `cbrt-unprod` `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` `fma-udef`

Counts

4 → 100

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)

series359.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (+ y 1.0))
93.0ms	(cbrt (+ y 1.0))
110.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
62.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	378	903
1	1306	824
2	5002	745

prune263.0ms

Filtered

112 candidates to 79 candidates (29.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	110	10	120

Merged error: 6.0b

Counts

120 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
10.0b	(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)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

168×	`cbrt-prod`
73×	`*-un-lft-identity`
60×	`cbrt-div`
55×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`swap-sqr`
21×	`associate-r` `associate-l`
18×	`flip3-+` `flip-+` `distribute-lft-out`
12×	`frac-times` `unswap-sqr`
6×	`associate-r/` `associate-l/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `*-commutative`
1×	`fma-udef`

Counts

4 → 160

Calls

4 calls:

12.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
13.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
12.0ms	(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)

series395.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
113.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
109.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
64.0ms	(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)

simplify122.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	291	2247
1	856	2137
2	3524	1957
3	5001	1949

prune485.0ms

Filtered

172 candidates to 111 candidates (35.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	170	12	182

Merged error: 6.0b

Counts

182 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
0.3b	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
9.2b	(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 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))) (cbrt (cbrt (cbrt (+ y 1.0))))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

168×	`cbrt-prod`
73×	`*-un-lft-identity`
60×	`cbrt-div`
55×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`swap-sqr`
21×	`associate-r` `associate-l`
18×	`flip3-+` `flip-+` `distribute-lft-out`
12×	`frac-times` `unswap-sqr`
6×	`associate-r/` `associate-l/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `*-commutative`
1×	`fma-udef`

Counts

4 → 160

Calls

4 calls:

12.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
13.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
13.0ms	(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 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))) (cbrt (cbrt (cbrt (+ y 1.0))))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series407.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
115.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
112.0ms	(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
66.0ms	(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 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))) (cbrt (cbrt (cbrt (+ y 1.0))))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify137.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	299	2364
1	891	2248
2	3832	2095
3	5003	2087

prune564.0ms

Filtered

172 candidates to 111 candidates (35.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	173	11	184

Merged error: 6.0b

Counts

184 → 11

regimes111.0ms

Accuracy

97.6% (0.2b remaining)

Error of 7.5b against oracle of 7.3b and baseline of 14.6b

bsearch71.0ms

Steps

Iters	Range		Point
10	188836.9734675514	2.769850331238764e+21	10818278959049608.0
4	-1.2927900667417545e+22	-7.232876640937852e+21	-7.35642164642662e+21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

end0.0ms

sample466.0ms

Algorithm

intervals

Results

166.0ms	6067×	body	80	valid
67.0ms	731×	body	640	valid
46.0ms	395×	body	1280	valid
35.0ms	503×	body	320	valid
14.0ms	304×	body	160	valid