Details

sample35.0ms

Algorithm

intervals

Results

9.0ms	204×	body	80	valid
5.0ms	256×	pre	80	true
3.0ms	19×	body	640	valid
3.0ms	15×	body	1280	valid
2.0ms	12×	body	320	valid
0.0ms	6×	body	160	valid

simplify54.0ms

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 (100.0%)

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: 24.4b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.1b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.6b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite528.0ms

Algorithm

rewrite-expression-head

Rules

4105×	`*-un-lft-identity`
2223×	`distribute-lft-out`
1938×	`times-frac`
818×	`associate-l`
781×	`add-sqr-sqrt`
493×	`add-cube-cbrt`
360×	`associate-r`
141×	`associate-/l*`
72×	`*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
49×	`associate-/l/`
22×	`associate-/r*` `associate-/r/`
19×	`flip3-+` `flip-+`
18×	`add-exp-log` `add-cbrt-cube`
11×	`div-inv` `add-log-exp`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`flip3--` `flip--`
4×	`pow1` `associate-r/` `associate-l/` `sum-log`
3×	`+-commutative` `frac-2neg` `clear-num`
2×	`associate-+l+` `prod-exp` `cbrt-unprod`

Counts

4 → 1239

Calls

4 calls:

10.0ms	(+ (+ alpha beta) (* 2.0 i))
72.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
282.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series650.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ alpha beta) (* 2.0 i))
241.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
294.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
90.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify251.0ms

Algorithm

egg-herbie

Counts

1251 → 1251

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1445	21741
1	5002	21606

prune910.0ms

Filtered

1251 candidates to 286 candidates (77.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	1241	10	1251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1242	10	1252

Merged error: 6.5b

Counts

1252 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.1b	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

2698×	`*-un-lft-identity`
1482×	`distribute-lft-out`
1135×	`times-frac`
350×	`add-sqr-sqrt`
339×	`add-cube-cbrt`
329×	`associate-l`
278×	`associate-r`
159×	`associate-/l*`
122×	`frac-times`
77×	`associate-/l/`
67×	`associate-/r*`
62×	`flip3--` `flip--`
61×	`associate-*r/`
46×	`associate-/r/`
29×	`flip3-+` `flip-+`
23×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`clear-num`
9×	`frac-2neg`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
5×	`un-div-inv`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`associate-*l/` `distribute-lft-out--`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `difference-of-squares`

Counts

4 → 906

Calls

4 calls:

15.0ms	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
36.0ms	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
113.0ms	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
192.0ms	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series682.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
170.0ms	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
245.0ms	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
198.0ms	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify162.0ms

Algorithm

egg-herbie

Counts

918 → 918

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1354	11966
1	5002	11815

prune1.0s

Filtered

918 candidates to 261 candidates (71.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	911	7	918
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	919	9	928

Merged error: 6.5b

Counts

928 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
0.1b	(cbrt (pow (+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
3.1b	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite659.0ms

Algorithm

rewrite-expression-head

Rules

1435×	`*-un-lft-identity`
779×	`distribute-lft-out`
583×	`times-frac`
278×	`associate-r`
196×	`add-sqr-sqrt`
185×	`add-cube-cbrt`
179×	`associate-l`
122×	`frac-times`
117×	`associate-/l*`
62×	`flip3--` `flip--`
61×	`associate-*r/`
57×	`associate-/l/`
45×	`associate-/r*`
24×	`associate-/r/`
16×	`flip3-+` `flip-+`
14×	`add-exp-log` `add-cbrt-cube`
12×	`unpow-prod-down` `div-inv`
11×	`cbrt-prod`
8×	`clear-num`
7×	`pow1`
6×	`frac-2neg` `add-log-exp`
5×	`un-div-inv`
4×	`pow-unpow` `distribute-lft-out--`
3×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`unpow3` `associate-*l/` `rem-cbrt-cube` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `sum-log` `*-commutative` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 548

Calls

4 calls:

159.0ms	(pow (+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
156.0ms	(cbrt (pow (+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
107.0ms	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
178.0ms	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series952.0ms

Counts

4 → 12

Calls

4 calls:

337.0ms	(pow (+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
188.0ms	(cbrt (pow (+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
238.0ms	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
189.0ms	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify115.0ms

Algorithm

egg-herbie

Counts

560 → 560

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1347	6707
1	5001	6614

prune733.0ms

Filtered

560 candidates to 184 candidates (67.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	551	9	560
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	559	10	569

Merged error: 6.5b

Counts

569 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.1b	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.5b	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

2698×	`*-un-lft-identity`
1482×	`distribute-lft-out`
1135×	`times-frac`
350×	`add-sqr-sqrt`
339×	`add-cube-cbrt`
329×	`associate-l`
278×	`associate-r`
159×	`associate-/l*`
122×	`frac-times`
77×	`associate-/l/`
67×	`associate-/r*`
62×	`flip3--` `flip--`
61×	`associate-*r/`
46×	`associate-/r/`
29×	`flip3-+` `flip-+`
23×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`clear-num`
9×	`frac-2neg`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
5×	`un-div-inv`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`associate-*l/` `distribute-lft-out--`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `difference-of-squares`

Counts

4 → 906

Calls

4 calls:

15.0ms	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
35.0ms	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
109.0ms	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
182.0ms	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series693.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i)))
188.0ms	(/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
245.0ms	(* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
191.0ms	(+ (* (- beta alpha) (/ (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify175.0ms

Algorithm

egg-herbie

Counts

918 → 918

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1354	11966
1	5002	11815

prune911.0ms

Filtered

918 candidates to 263 candidates (71.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	918	0	918
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	918	10	928

Merged error: 6.5b

Counts

928 → 10

regimes229.0ms

Accuracy

0% (6.4b remaining)

Error of 12.6b against oracle of 6.2b and baseline of 12.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	15
1	25	15

end0.0ms

sample928.0ms

Algorithm

intervals

Results

282.0ms	6320×	body	80	valid
148.0ms	8000×	pre	80	true
116.0ms	531×	body	1280	valid
109.0ms	573×	body	640	valid
53.0ms	378×	body	320	valid
17.0ms	198×	body	160	valid