Details

sample45.0ms

Algorithm

intervals

Results

11.0ms	202×	body	80	valid
8.0ms	17×	body	1280	valid
5.0ms	256×	pre	80	true
4.0ms	21×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	8×	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

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: 22.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (- beta alpha))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.5b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.7b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity` `times-frac`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `associate-/r/` `flip-+`
12×	`distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`associate-r/` `associate-l` `associate-l/`
3×	`prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

8.0ms	(* (+ alpha beta) (- beta alpha))
19.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
13.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (+ alpha beta) (- beta alpha))
69.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
89.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify117.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	767	2103
1	4353	1976
2	5001	1976

prune305.0ms

Filtered

156 candidates to 112 candidates (28.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	146	10	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	10	157

Merged error: 5.5b

Counts

157 → 10

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))
2.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.4b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite112.0ms

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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
18.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
38.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series212.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
41.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
66.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
90.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune598.0ms

Filtered

307 candidates to 200 candidates (34.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	300	7	307
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	307	10	317

Merged error: 5.5b

Counts

317 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
2.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.4b	(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
11.1b	(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
135×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
90×	`associate-r`
65×	`add-cube-cbrt`
23×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
12×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
10×	`cube-div` `associate-/r/`
9×	`pow1`
8×	`cbrt-prod`
6×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`cbrt-div` `div-inv`
4×	`associate-l` `pow-exp` `rem-cube-cbrt`
3×	`pow-unpow` `associate-*r/` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow1/3` `sum-log` `*-commutative` `rem-cbrt-cube`

Counts

4 → 182

Calls

4 calls:

25.0ms	(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
39.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.0ms	(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
3.0ms	(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

series2.2s

Counts

4 → 12

Calls

4 calls:

2.0s	(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
68.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
87.0ms	(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
72.0ms	(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1001	2763
1	5001	2615

prune414.0ms

Filtered

194 candidates to 130 candidates (33.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	191	3	194
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	194	10	204

Merged error: 5.5b

Counts

204 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
2.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.4b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
137×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
90×	`associate-r`
69×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
7×	`pow1`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`div-inv`
4×	`cube-div` `associate-l`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-mult` `frac-times` `cbrt-div` `unpow3` `associate-*l/` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `pow-prod-down` `pow-exp` `sum-log` `-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 176

Calls

4 calls:

26.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
26.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
39.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series486.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
87.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
66.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
89.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	973	3074
1	5001	2918

prune360.0ms

Filtered

188 candidates to 119 candidates (36.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	182	6	188
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	185	13	198

Merged error: 5.5b

Counts

198 → 13

regimes443.0ms

Accuracy

12.6% (5.6b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 12.3b

bsearch22.0ms

Steps

Iters	Range		Point
6	1.3159735598486673e+108	7.686346090059962e+108	7.594028729264956e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	48	27

end0.0ms

sample1.2s

Algorithm

intervals

Results

351.0ms	6360×	body	80	valid
168.0ms	8000×	pre	80	true
137.0ms	510×	body	1280	valid
123.0ms	562×	body	640	valid
59.0ms	357×	body	320	valid
22.0ms	211×	body	160	valid

Details

sample45.0ms

simplify51.0ms

prune3.0ms

localize13.0ms

rewrite76.0ms

series184.0ms

simplify117.0ms

prune305.0ms

localize13.0ms

rewrite112.0ms

series212.0ms

simplify74.0ms

prune598.0ms

localize16.0ms

rewrite83.0ms

series2.2s

simplify51.0ms

prune414.0ms

localize16.0ms

rewrite128.0ms

series486.0ms

simplify58.0ms

prune360.0ms

regimes443.0ms

bsearch22.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling