Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	188×	body	80	valid
3.0ms	33×	body	640	valid
2.0ms	16×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify78.0ms

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: 16.3b

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)

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)

series91.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ y (+ y 1.0))
57.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (106.0ms)

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

prune132.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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)

rewrite9.0ms

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

series277.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
56.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
51.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
57.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify106.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (97.0ms)

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

prune247.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.0b

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))
12.4b	(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)

series335.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ y 1.0))
93.0ms	(cbrt (+ y 1.0))
98.0ms	(cbrt (+ y 1.0))
54.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (61.0ms)

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

prune238.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

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))
13.1b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (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 (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

series327.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ y 1.0))
88.0ms	(cbrt (+ y 1.0))
91.0ms	(cbrt (+ y 1.0))
59.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	235	669
1	690	597
2	2499	569
3	5001	539

prune267.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

regimes83.0ms

Accuracy

96.9% (0.2b remaining)

Error of 7.3b against oracle of 7.1b and baseline of 15.0b

bsearch78.0ms

Steps

Iters	Range		Point
10	1831.6130620084434	112933556595576.11	111702921412086.14
7	-1.757940421682262e+29	-9.005634263921258e+27	-1.3585420879223014e+28

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	9
1	24	9

end0.0ms

sample436.0ms

Algorithm

intervals

Results

153.0ms	6089×	body	80	valid
64.0ms	744×	body	640	valid
40.0ms	368×	body	1280	valid
35.0ms	495×	body	320	valid
14.0ms	304×	body	160	valid