Details

sample73.0ms

Algorithm

intervals

Results

19.0ms	254×	body	80	valid
16.0ms	49×	body	640	valid
13.0ms	29×	body	1280	valid
4.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	17
1	71	17
2	241	17
3	747	17
4	2196	17
5	5001	17

prune4.0ms

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: 40.9b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.3b	(cos (/ (+ phi1 phi2) 2.0))
5.3b	(cos (/ (+ phi1 phi2) 2.0))
37.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
403.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify63.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1312	3623
1	5002	3528

prune419.0ms

Filtered

127 candidates to 77 candidates (60.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	7	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	8	128

Merged error: 27.7b

Counts

128 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

5.3b	(cos (/ (+ phi1 phi2) 2.0))
5.3b	(cos (/ (+ phi1 phi2) 2.0))
27.6b	(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
37.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

60×	`associate-*l/`
47×	`flip3--` `flip--`
42×	`sqrt-div`
40×	`frac-add`
36×	`frac-times`
18×	`associate-*r/`
11×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`times-frac` `associate-/r*` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
21.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series704.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cos (/ (+ phi1 phi2) 2.0))
26.0ms	(cos (/ (+ phi1 phi2) 2.0))
117.0ms	(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
529.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1057	2690
1	5002	2584

prune440.0ms

Filtered

108 candidates to 79 candidates (73.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	108	8	116

Merged error: 27.7b

Counts

116 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

5.3b	(cos (/ (+ phi1 phi2) 2.0))
37.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

384×	`associate-*l/`
288×	`flip3--` `flip--`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
96×	`associate-*r/`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 244

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
22.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2.0))
418.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
410.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
413.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify120.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1266	10063
1	5001	9903

prune1.1s

Filtered

256 candidates to 132 candidates (51.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	256	8	264

Merged error: 27.7b

Counts

264 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

5.3b	(cos (/ (+ phi1 phi2) 2.0))
5.3b	(cos (/ (+ phi1 phi2) 2.0))
6.2b	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
37.5b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
192×	`flip3--` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `exp-diff`
64×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `exp-prod` `exp-sum` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`log-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`rem-sqrt-square` `rem-exp-log`

Counts

4 → 179

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
29.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series897.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
417.0ms	(exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))))
420.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify90.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1513	6939
1	5002	6823

prune613.0ms

Filtered

191 candidates to 98 candidates (51.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	185	6	191
Fresh	0	4	4
Picked	1	0	1
Done	2	1	3
Total	188	11	199

Merged error: 27.7b

Counts

199 → 11

regimes731.0ms

Accuracy

75% (3.4b remaining)

Error of 28.5b against oracle of 25.1b and baseline of 38.8b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	38
1	39	38

end0.0ms

sample2.0s

Algorithm

intervals

Results

636.0ms	8391×	body	80	valid
438.0ms	1322×	body	640	valid
355.0ms	789×	body	1280	valid
171.0ms	711×	body	320	valid
57.0ms	357×	body	160	valid

Details

sample73.0ms

simplify53.0ms

prune4.0ms

localize20.0ms

rewrite44.0ms

series546.0ms

simplify63.0ms

prune419.0ms

localize23.0ms

rewrite47.0ms

series704.0ms

simplify52.0ms

prune440.0ms

localize25.0ms

rewrite93.0ms

series1.3s

simplify120.0ms

prune1.1s

localize21.0ms

rewrite77.0ms

series897.0ms

simplify90.0ms

prune613.0ms

regimes731.0ms

bsearch3.0ms

simplify2.0ms

end0.0ms

sample2.0s

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