Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	213×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	17×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	2×	body	160	valid

simplify51.0ms

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: 20.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.4b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

18.9b

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `flip--`
2×	`frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 111

Calls

3 calls:

20.0ms

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

33.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

14.0ms

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

series572.0ms

Counts

3 → 9

Calls

3 calls:

224.0ms

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

268.0ms

(+ (/ (/ (* (+ 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)))

simplify90.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	681	1905
1	3622	1789
2	5003	1789

prune330.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.0b	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.4b	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

1250×	`times-frac`
1055×	`*-un-lft-identity`
619×	`add-sqr-sqrt`
461×	`add-cube-cbrt`
218×	`distribute-lft-out`
96×	`associate-/l*`
79×	`distribute-lft-out--` `difference-of-squares`
60×	`associate-/r/`
33×	`div-inv`
30×	`associate-/r*`
26×	`flip3--` `flip--`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`pow1` `flip3-+` `flip-+`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log`

Counts

4 → 645

Calls

4 calls:

11.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
38.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
118.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series692.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
228.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
78.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
272.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify151.0ms

Algorithm

egg-herbie

Counts

657 → 657

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1783	13720
1	5001	13481

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.1b	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.1b	(* (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.1b	(+ (* (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

345×	`times-frac`
304×	`*-un-lft-identity`
239×	`add-sqr-sqrt`
147×	`add-cube-cbrt`
89×	`associate-l`
50×	`add-exp-log`
46×	`distribute-lft-out`
32×	`add-cbrt-cube`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/r*`
24×	`associate-/r/`
22×	`div-exp`
18×	`associate-r`
13×	`cbrt-undiv` `div-inv`
12×	`prod-exp`
10×	`flip3--` `flip--`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `cbrt-unprod` `add-log-exp`
4×	`flip3-+` `flip-+` `associate-/l/`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `un-div-inv` `*-commutative`

Counts

4 → 323

Calls

4 calls:

12.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
15.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
54.0ms	(* (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms	(+ (* (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series704.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
80.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
227.0ms	(* (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
281.0ms	(+ (* (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

335 → 335

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1275	4811
1	5002	4488

prune846.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
0.1b	(* (* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b	(/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
2.1b	(+ (* (* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

249×	`times-frac`
176×	`add-sqr-sqrt`
172×	`*-un-lft-identity`
154×	`add-exp-log`
120×	`add-cube-cbrt`
86×	`associate-r`
67×	`prod-exp`
58×	`div-exp`
50×	`add-cbrt-cube`
21×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
20×	`rec-exp` `1-exp`
18×	`associate-/r/`
17×	`cbrt-unprod`
16×	`cbrt-undiv`
12×	`pow1` `frac-times` `associate-*l/`
10×	`div-inv`
8×	`flip3-+` `flip-+`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`associate-*r/` `pow-prod-down` `un-div-inv` `distribute-lft-out`
3×	`associate-/l*`
2×	`*-commutative`
1×	`+-commutative` `pow-flip` `frac-2neg` `clear-num` `sum-log` `inv-pow`

Counts

4 → 304

Calls

4 calls:

32.0ms	(* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
32.0ms	(* (* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
12.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
30.0ms	(+ (* (* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series664.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
231.0ms	(* (* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
77.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
280.0ms	(+ (* (* (+ alpha beta) (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1314	4115
1	5001	3618

prune716.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.2b

regimes136.0ms

Accuracy

8.8% (5.6b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 12.0b

bsearch74.0ms

Steps

Iters	Range		Point
9	3.088617839269422e+142	1.495088011218417e+148	1.4714840476837656e+148

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	27
1	49	27

end0.0ms

sample820.0ms

Algorithm

intervals

Results

245.0ms	6396×	body	80	valid
137.0ms	8000×	pre	80	true
96.0ms	499×	body	1280	valid
91.0ms	574×	body	640	valid
42.0ms	341×	body	320	valid
14.0ms	190×	body	160	valid