Details

sample18.0ms

Algorithm

intervals

Results

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

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	31	12
1	168	11
2	965	9
3	5001	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize8.0ms

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-log-exp`
3×	`add-sqr-sqrt`
2×	`pow1` `add-cube-cbrt` `flip3--` `-un-lft-identity` `associate-l/` `associate-/r/` `flip--`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

11.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
22.0ms	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

series134.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
79.0ms	(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	342	496
1	1633	364
2	5001	364

prune77.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

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)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-exp-log` `add-cbrt-cube`
22×	`add-sqr-sqrt`
21×	`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`
2×	`flip3--` `frac-2neg` `associate-*l/` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `associate-/r/` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

11.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
17.0ms	(/ 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)

series249.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(- (* (* 2.0 i) (* 2.0 i)) 1.0)
77.0ms	(/ i (/ (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)) i))
117.0ms	(/ (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)) i)

simplify65.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	483	1066
1	2407	906
2	5001	899

prune171.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
22×	`prod-exp` `cbrt-unprod`
12×	`associate-*l/`
10×	`cbrt-undiv` `div-exp`
8×	`frac-times` `associate-/r/`
6×	`add-sqr-sqrt` `flip3--` `flip3-+` `flip--` `flip-+`
4×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-r/`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

2 → 71

Calls

2 calls:

26.0ms	(* (+ (* 2.0 i) (sqrt 1.0)) (- (* 2.0 i) (sqrt 1.0)))
39.0ms	(/ (* i i) (* (* (+ (* 2.0 i) (sqrt 1.0)) (- (* 2.0 i) (sqrt 1.0))) (* 2.0 2.0)))

series367.0ms

Counts

2 → 6

Calls

2 calls:

170.0ms	(* (+ (* 2.0 i) (sqrt 1.0)) (- (* 2.0 i) (sqrt 1.0)))
197.0ms	(/ (* i i) (* (* (+ (* 2.0 i) (sqrt 1.0)) (- (* 2.0 i) (sqrt 1.0))) (* 2.0 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	628	1179
1	3646	850
2	5001	825

prune144.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

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×	`add-log-exp` `sqr-pow`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
4×	`frac-add` `unpow2`
3×	`pow1` `flip3-+` `sum-log` `flip-+`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `div-inv` `inv-pow`
1×	`+-commutative` `associate-+r+`

Counts

3 → 127

Calls

3 calls:

21.0ms	(+ (* 0.00390625 (/ 1 (pow i 4))) (+ (* 0.015625 (/ 1 (pow i 2))) 0.0625))
4.0ms	(/ 1 (pow i 4))
4.0ms	(/ 1 (pow i 2))

series75.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* 0.00390625 (/ 1 (pow i 4))) (+ (* 0.015625 (/ 1 (pow i 2))) 0.0625))
26.0ms	(/ 1 (pow i 4))
20.0ms	(/ 1 (pow i 2))

simplify65.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	474	821
1	2042	726
2	5001	650

prune184.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes20.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch50.0ms

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	39	19
1	39	19

end0.0ms

sample395.0ms

Algorithm

intervals

Results

235.0ms	8000×	body	80	valid
65.0ms	8000×	pre	80	true