Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	205×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	16×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	8×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (- beta alpha))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.6b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity` `times-frac`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `associate-/r/` `flip-+`
12×	`distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`associate-r/` `associate-l` `associate-l/`
3×	`prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

18.0ms	(* (+ alpha beta) (- beta alpha))
94.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
304.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (+ alpha beta) (- beta alpha))
218.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
266.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
79.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify119.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	767	2103
1	4353	1976
2	5003	1976

prune419.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.9b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.9b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

22.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
97.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
204.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
54.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series731.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
164.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
223.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
267.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune812.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.9b	(* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
3.9b	(+ (* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

348×	`times-frac`
320×	`*-un-lft-identity`
172×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
61×	`distribute-lft-out`
58×	`associate-r`
52×	`associate-/r/`
32×	`flip3-+` `flip-+`
30×	`associate-/l*`
26×	`div-inv`
25×	`distribute-lft-out--`
21×	`distribute-rgt-out--`
16×	`add-exp-log` `add-cbrt-cube`
9×	`difference-of-squares`
8×	`frac-times` `associate-/r*`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in` `associate-r/` `associate-l*`
3×	`flip3--` `frac-sub` `flip--` `sub-div`
2×	`frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 299

Calls

4 calls:

90.0ms	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
90.0ms	(/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0s	(* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
525.0ms	(+ (* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
177.0ms	(/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
337.0ms	(* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
336.0ms	(+ (* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify79.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1302	5648
1	5002	5460

prune922.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
4.0b	(+ (* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta)) 1.0)
5.1b	(* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta))
5.3b	(* (+ alpha beta) (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite802.0ms

Algorithm

rewrite-expression-head

Rules

396×	`times-frac`
316×	`*-un-lft-identity`
201×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
140×	`associate-l`
70×	`associate-r`
66×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
63×	`distribute-lft-out`
42×	`associate-/r/`
26×	`flip3-+` `flip-+`
21×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/l*`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`frac-times` `prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
3×	`associate-r/` `associate-l/` `distribute-neg-frac`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative`
1×	`+-commutative` `distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `clear-num` `sum-log` `associate-/l/`

Counts

4 → 362

Calls

4 calls:

90.0ms	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
98.0ms	(+ (* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta)) 1.0)
397.0ms	(* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta))
193.0ms	(* (+ alpha beta) (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series807.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
267.0ms	(+ (* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta)) 1.0)
180.0ms	(* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta))
188.0ms	(* (+ alpha beta) (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify96.0ms

Algorithm

egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2200	5400
1	5002	5259

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.0b

regimes321.0ms

Accuracy

18.9% (5.6b remaining)

Error of 11.2b against oracle of 5.6b and baseline of 12.5b

bsearch85.0ms

Steps

Iters	Range		Point
8	3.594603974860845e+173	6.302835922400278e+177	6.191224408848943e+177

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	51
1	66	51
2	70	51
3	70	51

end0.0ms

sample817.0ms

Algorithm

intervals

Results

253.0ms	6313×	body	80	valid
123.0ms	8000×	pre	80	true
106.0ms	513×	body	1280	valid
99.0ms	629×	body	640	valid
39.0ms	332×	body	320	valid
16.0ms	213×	body	160	valid