Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

localize16.0ms

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)))

rewrite464.0ms

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:

17.0ms	(* (+ alpha beta) (- beta alpha))
96.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
318.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
25.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series628.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ alpha beta) (- beta alpha))
229.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
278.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
78.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify117.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (20.0ms)

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

prune445.0ms

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)

rewrite409.0ms

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)))
100.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
210.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
57.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series751.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
165.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
229.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
281.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune801.0ms

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)

rewrite2.6s

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:

94.0ms	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
93.0ms	(/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.9s	(* (+ 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))))
535.0ms	(+ (* (+ 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:

177.0ms	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
179.0ms	(/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
347.0ms	(* (+ 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))))
346.0ms	(+ (* (+ 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)

simplify82.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1299	5648
1	5001	5460

prune948.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize21.0ms

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	(* (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))

rewrite832.0ms

Algorithm

rewrite-expression-head

Rules

396×	`times-frac`
316×	`*-un-lft-identity`
202×	`associate-l`
201×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
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` `associate-r`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`frac-times` `associate-r/` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `distribute-neg-frac`
2×	`associate-+l+` `pow-prod-down` `associate-l/` `-commutative`
1×	`+-commutative` `distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `clear-num` `sum-log` `associate-/l/`

Counts

4 → 364

Calls

4 calls:

93.0ms	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
101.0ms	(+ (* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta)) 1.0)
409.0ms	(* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta))
199.0ms	(* (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))

series816.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
277.0ms	(+ (* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta)) 1.0)
184.0ms	(* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta))
178.0ms	(* (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))

simplify92.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2325	5469
1	5001	5326

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.0b

regimes340.0ms

Accuracy

18.9% (5.6b remaining)

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

bsearch92.0ms

Steps

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

simplify2.0ms

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

sample805.0ms

Algorithm

intervals

Results

246.0ms	6313×	body	80	valid
121.0ms	8000×	pre	80	true
101.0ms	629×	body	640	valid
99.0ms	513×	body	1280	valid
41.0ms	332×	body	320	valid
16.0ms	213×	body	160	valid