Details

sample35.0ms

Algorithm

intervals

Results

11.0ms	210×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
2.0ms	16×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	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

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: 23.0b

Counts

2 → 1

localize13.0ms

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))

2.0b

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

19.3b

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

rewrite73.0ms

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:

24.0ms

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

30.0ms

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

series588.0ms

Counts

3 → 9

Calls

3 calls:

231.0ms

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

279.0ms

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

77.0ms

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

simplify95.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (18.0ms)

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

prune332.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	7	121

Merged error: 4.5b

Counts

121 → 7

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))
2.3b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.2b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite120.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
43.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series754.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
167.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
231.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
277.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune795.0ms

Filtered

307 candidates to 199 candidates (64.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	304	3	307
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	306	8	314

Merged error: 4.4b

Counts

314 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.3b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.2b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
3.2b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
274×	`*-un-lft-identity`
195×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
11×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`log-prod` `associate-l` `associate-/r*` `log-pow`
3×	`exp-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `div-sub` `associate-*l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `sum-log` `-commutative` `associate-/l/`

Counts

4 → 271

Calls

4 calls:

20.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
41.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
29.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
27.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series934.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
225.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
271.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
275.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1073	4732
1	5001	4526

prune757.0ms

Filtered

283 candidates to 184 candidates (65.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	282	1	283
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	283	8	291

Merged error: 4.4b

Counts

291 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.3b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.2b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
275×	`*-un-lft-identity`
196×	`add-sqr-sqrt`
133×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`cbrt-prod`
11×	`div-inv`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`associate-l` `associate-/r*`
3×	`unpow-prod-down` `cube-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-div` `frac-times` `cbrt-div` `div-sub` `associate-*l/`
1×	`+-commutative` `cube-mult` `frac-2neg` `pow1/3` `unpow3` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `rem-cbrt-cube` `associate-/l/` `sqr-pow`

Counts

4 → 278

Calls

4 calls:

29.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
21.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
47.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
27.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series969.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
167.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
230.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
285.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify84.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1121	4976
1	5001	4843

prune763.0ms

Filtered

290 candidates to 186 candidates (64.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	286	4	290
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	289	9	298

Merged error: 4.4b

Counts

298 → 9

regimes195.0ms

Accuracy

15.5% (5.6b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 12.5b

bsearch41.0ms

Steps

Iters	Range		Point
5	8.588642662975345e+117	2.204604034550096e+118	1.6509764971427011e+118

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	34
1	50	34

end0.0ms

sample834.0ms

Algorithm

intervals

Results

248.0ms	6331×	body	80	valid
127.0ms	8000×	pre	80	true
113.0ms	513×	body	1280	valid
95.0ms	585×	body	640	valid
42.0ms	365×	body	320	valid
16.0ms	206×	body	160	valid