Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	256×	pre	80	true

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (30.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
13.4b	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

rewrite35.0ms

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:

12.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
22.0ms	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

series138.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
80.0ms	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (46.0ms)

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

prune99.0ms

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)
0.5b	(/ i (/ (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)) i))
12.3b	(/ (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)) i)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

12.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
18.0ms	(/ i (/ (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)) i))
21.0ms	(/ (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)) i)

series449.0ms

Counts

3 → 9

Calls

3 calls:

248.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
82.0ms	(/ i (/ (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)) i))
119.0ms	(/ (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)) i)

simplify76.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	534	1135
1	2701	958
2	5003	947

prune203.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 1 expressions with local error:

13.4b

(/ (* 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)))

series89.0ms

Counts

1 → 3

Calls

1 calls:

88.0ms

(/ (* 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

prune45.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 124

Calls

3 calls:

0.0ms	(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
4.0ms	(/ 1 (pow i 4))
4.0ms	(/ 1 (pow i 2))

series76.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
26.0ms	(/ 1 (pow i 4))
16.0ms	(/ 1 (pow i 2))

simplify37.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	300	623
1	1163	535
2	5001	459

prune199.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 16.0b

bsearch43.0ms

Steps

Iters	Range		Point
9	0.46820136545482216	278469639.75496256	206.90965650935013

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	29	14

end0.0ms

sample398.0ms

Algorithm

intervals

Results

233.0ms	8000×	body	80	valid
66.0ms	8000×	pre	80	true