Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	203×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	19×	body	1280	valid
4.0ms	9×	body	320	valid
4.0ms	20×	body	640	valid
0.0ms	5×	body	160	valid

simplify52.0ms

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

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: 22.6b

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))

1.4b

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

17.5b

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

rewrite70.0ms

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:

22.0ms

(/ (/ (* (+ 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)

14.0ms

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

series575.0ms

Counts

3 → 9

Calls

3 calls:

222.0ms

(/ (/ (* (+ 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)

82.0ms

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

simplify98.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	681	1905
1	3622	1789
2	5001	1789

prune331.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 5.1b

Counts

121 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.4b	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
35×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
8×	`flip3-+` `flip-+`
7×	`associate-/r*` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out`
3×	`div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`+-commutative` `flip3--` `div-sub` `pow-prod-down` `sum-log` `*-commutative` `flip--`

Counts

4 → 129

Calls

4 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
23.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
22.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series655.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
224.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
81.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
274.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	657	1569
1	3554	1429
2	5002	1429

prune328.0ms

Filtered

141 candidates to 102 candidates (72.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	140	7	147

Merged error: 5.1b

Counts

147 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.3b	(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.3b	(/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i))))
7.0b	(+ (/ (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

348×	`times-frac`
326×	`*-un-lft-identity`
236×	`add-sqr-sqrt`
162×	`add-cube-cbrt`
108×	`sqrt-prod`
48×	`associate-/r*`
45×	`distribute-lft-out`
37×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
14×	`sqrt-div`
13×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
10×	`flip3-+` `flip-+`
8×	`div-inv`
6×	`associate-/l/` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `flip3--` `div-sub` `sum-log` `flip--`

Counts

4 → 321

Calls

4 calls:

23.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
11.0ms	(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i))))
13.0ms	(/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i))))
1.2s	(+ (/ (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series976.0ms

Counts

4 → 12

Calls

4 calls:

475.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
123.0ms	(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i))))
126.0ms	(/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i))))
252.0ms	(+ (/ (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify86.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1259	6081
1	5002	5789

prune753.0ms

Filtered

333 candidates to 185 candidates (55.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	331	2	333
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	333	7	340

Merged error: 5.1b

Counts

340 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.3b	(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.3b	(/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i))))
7.0b	(+ (/ (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

348×	`times-frac`
326×	`*-un-lft-identity`
236×	`add-sqr-sqrt`
162×	`add-cube-cbrt`
108×	`sqrt-prod`
48×	`associate-/r*`
45×	`distribute-lft-out`
37×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
14×	`sqrt-div`
13×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
10×	`flip3-+` `flip-+`
8×	`div-inv`
6×	`associate-/l/` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `flip3--` `div-sub` `sum-log` `flip--`

Counts

4 → 321

Calls

4 calls:

26.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
11.0ms	(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i))))
12.0ms	(/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i))))
1.2s	(+ (/ (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series982.0ms

Counts

4 → 12

Calls

4 calls:

478.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
129.0ms	(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i))))
120.0ms	(/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i))))
254.0ms	(+ (/ (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (sqrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify88.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1259	6081
1	5002	5789

prune883.0ms

Filtered

333 candidates to 185 candidates (55.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	331	2	333
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	333	7	340

Merged error: 5.1b

Counts

340 → 7

regimes233.0ms

Accuracy

77.1% (1.5b remaining)

Error of 7.3b against oracle of 5.9b and baseline of 12.3b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	36
1	48	36

end0.0ms

sample1.2s

Algorithm

intervals

Results

506.0ms	6365×	body	80	valid
173.0ms	8000×	pre	80	true
146.0ms	559×	body	1280	valid
111.0ms	558×	body	640	valid
53.0ms	329×	body	320	valid
21.0ms	189×	body	160	valid

Details

sample42.0ms

simplify52.0ms

prune3.0ms

localize13.0ms

rewrite70.0ms

series575.0ms

simplify98.0ms

prune331.0ms

localize13.0ms

rewrite75.0ms

series655.0ms

simplify92.0ms

prune328.0ms

localize17.0ms

rewrite1.2s

series976.0ms

simplify86.0ms

prune753.0ms

localize19.0ms

rewrite1.2s

series982.0ms

simplify88.0ms

prune883.0ms

regimes233.0ms

bsearch3.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling