Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	32	12
1	172	11
2	974	9
3	5001	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
11.9b	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
9×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
4×	`add-sqr-sqrt` `add-log-exp`
3×	`add-cube-cbrt` `*-un-lft-identity` `prod-diff`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-*l/` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`sub-neg` `frac-2neg` `times-frac` `fma-neg` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `difference-of-squares`

Counts

2 → 48

Calls

2 calls:

8.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
14.0ms	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
81.0ms	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	390	550
1	1886	402
2	5001	398

prune103.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
0.1b	(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
11.6b	(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
31×	`times-frac`
26×	`add-exp-log` `add-cbrt-cube`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-l`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares`
7×	`associate-r`
5×	`pow1` `add-log-exp`
4×	`associate-/r*` `associate-/r/` `unswap-sqr`
3×	`expm1-log1p-u` `flip3--` `prod-diff` `flip--` `log1p-expm1-u` `div-inv` `associate-/l*`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 109

Calls

3 calls:

8.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
16.0ms	(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
9.0ms	(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

series209.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
78.0ms	(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
79.0ms	(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	594	1142
1	2820	976
2	5001	959

prune234.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

11.9b

(/ (* i i) (* (fma (* 2.0 i) (* 2.0 i) (- 1.0)) (* 2.0 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log` `add-cbrt-cube`
9×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
1×	`pow1` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `frac-2neg` `-un-lft-identity` `times-frac` `clear-num` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

9.0ms

(/ (* i i) (* (fma (* 2.0 i) (* 2.0 i) (- 1.0)) (* 2.0 2.0)))

series92.0ms

Counts

1 → 3

Calls

1 calls:

92.0ms

(/ (* i i) (* (fma (* 2.0 i) (* 2.0 i) (- 1.0)) (* 2.0 2.0)))

simplify36.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	262	383
1	1292	263
2	5001	263

prune48.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.015625 (/ 1 (pow i 2)) 0.0625)
0.0b	(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
0.2b	(/ 1 (pow i 4))
0.4b	(/ 1 (pow i 2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`add-exp-log`
15×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 134

Calls

4 calls:

1.0ms	(fma 0.015625 (/ 1 (pow i 2)) 0.0625)
1.0ms	(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
5.0ms	(/ 1 (pow i 4))
5.0ms	(/ 1 (pow i 2))

series118.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma 0.015625 (/ 1 (pow i 2)) 0.0625)
30.0ms	(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
27.0ms	(/ 1 (pow i 4))
16.0ms	(/ 1 (pow i 2))

simplify39.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	310	683
1	1198	587
2	5001	511

prune241.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.5b

bsearch36.0ms

Steps

Iters	Range		Point
7	69.979237422269	3396.5660583078065	248.47326712178204

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	29	14

end0.0ms

sample412.0ms

Algorithm

intervals

Results

243.0ms	8000×	body	80	valid
68.0ms	8000×	pre	80	true