Details

sample34.0ms

Algorithm

intervals

Results

8.0ms	202×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	21×	body	640	valid
3.0ms	16×	body	1280	valid
2.0ms	13×	body	320	valid
0.0ms	4×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 21.2b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b

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

1.2b

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

19.2b

(/ (* (+ 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:

21.0ms

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

32.0ms

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

series601.0ms

Counts

3 → 9

Calls

3 calls:

237.0ms

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

283.0ms

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

80.0ms

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

simplify92.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

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

prune340.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Merged error: 8.2b

Counts

121 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.3b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
1.9b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.2b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite124.0ms

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:

21.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
13.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
41.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
28.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series763.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
78.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
237.0ms	(* (+ 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)

simplify73.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune686.0ms

Filtered

307 candidates to 200 candidates (65.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	303	4	307
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	307	8	315

Merged error: 8.2b

Counts

315 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
1.9b	(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
7.0b	(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

344×	`times-frac`
273×	`add-sqr-sqrt`
251×	`*-un-lft-identity`
154×	`associate-r`
141×	`add-cube-cbrt`
132×	`sqrt-prod`
100×	`add-exp-log`
56×	`add-cbrt-cube`
38×	`div-exp`
37×	`prod-exp`
31×	`associate-l`
29×	`distribute-lft-out`
25×	`unswap-sqr`
21×	`distribute-lft-out--` `difference-of-squares`
20×	`associate-/r/`
19×	`cbrt-undiv` `cbrt-unprod`
15×	`flip3-+` `flip-+`
13×	`pow1`
10×	`frac-times` `div-inv`
7×	`rec-exp` `1-exp` `associate-r/` `associate-/r`
6×	`sqrt-div` `associate-*l/` `add-log-exp`
4×	`pow-prod-down`
3×	`pow-flip` `associate-/l*`
2×	`*-commutative`
1×	`+-commutative` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `inv-pow`

Counts

4 → 343

Calls

4 calls:

11.0ms	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
114.0ms	(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
46.0ms	(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
50.0ms	(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series822.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
169.0ms	(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
240.0ms	(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
285.0ms	(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify106.0ms

Algorithm

egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1643	7323
1	5002	6721

prune700.0ms

Filtered

355 candidates to 171 candidates (48.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	353	2	355
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	355	8	363

Merged error: 8.2b

Counts

363 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
1.9b	(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
7.0b	(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

344×	`times-frac`
273×	`add-sqr-sqrt`
251×	`*-un-lft-identity`
154×	`associate-r`
141×	`add-cube-cbrt`
132×	`sqrt-prod`
100×	`add-exp-log`
56×	`add-cbrt-cube`
38×	`div-exp`
37×	`prod-exp`
31×	`associate-l`
29×	`distribute-lft-out`
25×	`unswap-sqr`
21×	`distribute-lft-out--` `difference-of-squares`
20×	`associate-/r/`
19×	`cbrt-undiv` `cbrt-unprod`
15×	`flip3-+` `flip-+`
13×	`pow1`
10×	`frac-times` `div-inv`
7×	`rec-exp` `1-exp` `associate-r/` `associate-/r`
6×	`sqrt-div` `associate-*l/` `add-log-exp`
4×	`pow-prod-down`
3×	`pow-flip` `associate-/l*`
2×	`*-commutative`
1×	`+-commutative` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `inv-pow`

Counts

4 → 343

Calls

4 calls:

12.0ms	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
112.0ms	(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
48.0ms	(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
51.0ms	(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series954.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
163.0ms	(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
381.0ms	(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
286.0ms	(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify106.0ms

Algorithm

egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1643	7323
1	5002	6721

prune827.0ms

Filtered

355 candidates to 171 candidates (48.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	350	5	355
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	353	10	363

Merged error: 8.2b

Counts

363 → 10

regimes220.0ms

Accuracy

18.2% (5.2b remaining)

Error of 11.2b against oracle of 6.0b and baseline of 12.3b

bsearch44.0ms

Steps

Iters	Range		Point
5	3.749479162223782e+181	1.156670155801419e+182	7.718884881344612e+181

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	35
1	52	35

end0.0ms

sample835.0ms

Algorithm

intervals

Results

259.0ms	6369×	body	80	valid
131.0ms	8000×	pre	80	true
115.0ms	523×	body	1280	valid
89.0ms	554×	body	640	valid
44.0ms	366×	body	320	valid
15.0ms	188×	body	160	valid