Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	209×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	20×	body	1280	valid
1.0ms	7×	body	640	valid
1.0ms	12×	body	160	valid
1.0ms	8×	body	320	valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	14
1	107	14
2	479	14
3	2315	14
4	5002	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: 23.6b

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))

3.0b

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
83×	`*-un-lft-identity`
43×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`fma-def`
24×	`associate-/r/`
20×	`distribute-lft-out`
17×	`add-exp-log` `add-cbrt-cube`
16×	`flip3-+` `flip-+`
12×	`div-inv`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 159

Calls

3 calls:

20.0ms

(/ (/ (* (+ 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)

21.0ms

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

series582.0ms

Counts

3 → 9

Calls

3 calls:

230.0ms

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

269.0ms

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

82.0ms

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

simplify101.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	701	1971
1	3740	1800
2	5001	1782

prune494.0ms

Filtered

168 candidates to 131 candidates (78.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	158	10	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Merged error: 5.2b

Counts

169 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.3b	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.2b	(fma (/ (/ (+ 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)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

490×	`times-frac`
410×	`*-un-lft-identity`
284×	`add-sqr-sqrt`
228×	`add-cube-cbrt`
156×	`sqrt-prod`
63×	`distribute-lft-out`
42×	`associate-/l*`
28×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
19×	`div-inv`
18×	`add-exp-log`
17×	`associate-/r*`
16×	`add-cbrt-cube`
11×	`flip3-+` `flip-+`
9×	`div-exp`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num`
1×	`flip3--` `1-exp` `flip--` `fma-udef`

Counts

4 → 402

Calls

4 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
22.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
22.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.0ms	(fma (/ (/ (+ 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)

series682.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
145.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
224.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
236.0ms	(fma (/ (/ (+ 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)

simplify254.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1283	7520
1	5001	6992

prune855.0ms

Filtered

414 candidates to 212 candidates (51.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	409	5	414
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	412	12	424

Merged error: 5.2b

Counts

424 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
0.3b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.2b	(fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

295×	`times-frac`
259×	`*-un-lft-identity`
189×	`add-sqr-sqrt`
141×	`add-cube-cbrt`
108×	`sqrt-prod`
35×	`distribute-lft-out`
25×	`associate-/l*`
24×	`distribute-lft-out--` `difference-of-squares`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`cbrt-prod`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
10×	`div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `cube-prod` `associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`cube-mult` `pow1/3` `unpow3` `rem-cbrt-cube` `fma-udef` `sqr-pow`

Counts

4 → 285

Calls

4 calls:

2.0ms	(cbrt (pow (fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
17.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
22.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.0ms	(fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series806.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt (pow (fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
139.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
219.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
223.0ms	(fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify143.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1039	6098
1	4721	5801
2	5001	5800

prune793.0ms

Filtered

297 candidates to 168 candidates (56.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	295	2	297
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	299	10	309

Merged error: 5.2b

Counts

309 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.4b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.1b	(fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

313×	`times-frac`
261×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
151×	`add-cube-cbrt`
118×	`sqrt-prod`
30×	`distribute-lft-out`
27×	`associate-r`
24×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
22×	`add-exp-log` `associate-/r/`
16×	`add-cbrt-cube`
14×	`associate-/r*`
13×	`flip3-+` `flip-+`
11×	`div-inv`
8×	`pow1`
7×	`div-exp`
6×	`sqrt-div`
5×	`cbrt-undiv` `unswap-sqr`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `div-sub` `associate-*l/` `clear-num` `cbrt-unprod`
1×	`sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 317

Calls

4 calls:

20.0ms	(* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
26.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.0ms	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.0ms	(fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series716.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
224.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
122.0ms	(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
232.0ms	(fma (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify87.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1187	5841
1	5001	5432

prune847.0ms

Filtered

329 candidates to 184 candidates (55.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	328	1	329
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	328	11	339

Merged error: 5.2b

Counts

339 → 11

regimes232.0ms

Accuracy

19.5% (5.2b remaining)

Error of 10.9b against oracle of 5.7b and baseline of 12.2b

bsearch80.0ms

Steps

Iters	Range		Point
9	1.3602877512310623e+165	4.876217483973988e+170	7.579467408578127e+165

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	33
1	46	33

end0.0ms

sample991.0ms

Algorithm

intervals

Results

309.0ms	6389×	body	80	valid
173.0ms	8000×	pre	80	true
137.0ms	519×	body	1280	valid
106.0ms	566×	body	640	valid
47.0ms	315×	body	320	valid
22.0ms	211×	body	160	valid