Details

sample164.0ms

Algorithm

intervals

Results

50.0ms	30×	body	1280	valid
47.0ms	275×	body	80	valid
28.0ms	37×	body	640	valid
12.0ms	22×	body	320	valid
4.0ms	11×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
5	2001
4	757
3	225
2	66
1	32
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
4.0b	(cos (/ (+ phi1 phi2) 2))
4.0b	(cos (/ (+ phi1 phi2) 2))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite115.0ms

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-cbrt-cube` `add-exp-log`
5×	`associate-l`
4×	`insert-posit16` `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 → 119

Calls

4 calls:

23.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
9.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
70.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
22.0ms	(cos (/ (+ phi1 phi2) 2))
24.0ms	(cos (/ (+ phi1 phi2) 2))
502.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.1s

Counts

131 → 131

Iterations

Iter	Nodes
done	2000
2	2000
1	1296
0	446

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.5b

localize60.0ms

Local error

Found 4 expressions with local error:

4.0b	(cos (/ (+ phi1 phi2) 2))
4.0b	(cos (/ (+ phi1 phi2) 2))
4.0b	(cos (/ (+ phi1 phi2) 2))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

290×	`associate-*l/`
198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
74×	`associate-*r/`
72×	`cbrt-div` `cos-mult`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 176

Calls

4 calls:

15.0ms	(cos (/ (+ phi1 phi2) 2))
10.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
191.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series649.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cos (/ (+ phi1 phi2) 2))
27.0ms	(cos (/ (+ phi1 phi2) 2))
30.0ms	(cos (/ (+ phi1 phi2) 2))
547.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.1s

Counts

188 → 188

Iterations

Iter	Nodes
done	2000
1	2000
0	831

prune5.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.0b

localize53.0ms

Local error

Found 4 expressions with local error:

4.0b	(cos (/ (+ phi1 phi2) 2))
4.0b	(cos (/ (+ phi1 phi2) 2))
4.0b	(cos (/ (+ phi1 phi2) 2))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

176×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 104

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2))
8.0ms	(cos (/ (+ phi1 phi2) 2))
16.0ms	(cos (/ (+ phi1 phi2) 2))
428.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(cos (/ (+ phi1 phi2) 2))
23.0ms	(cos (/ (+ phi1 phi2) 2))
31.0ms	(cos (/ (+ phi1 phi2) 2))
608.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	2002
2	2002
1	1273
0	427

prune2.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 22.0b

localize83.0ms

Local error

Found 4 expressions with local error:

4.0b	(cos (/ (+ phi1 phi2) 2))
4.0b	(cos (/ (+ phi1 phi2) 2))
4.0b	(cos (/ (+ phi1 phi2) 2))
34.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite504.0ms

Algorithm

rewrite-expression-head

Rules

2240×	`associate-*l/`
1408×	`frac-times`
1344×	`flip3--` `flip--`
1296×	`cbrt-div`
642×	`sqrt-div`
640×	`frac-add`
560×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 680

Calls

4 calls:

11.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
7.0ms	(cos (/ (+ phi1 phi2) 2))
398.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cos (/ (+ phi1 phi2) 2))
38.0ms	(cos (/ (+ phi1 phi2) 2))
24.0ms	(cos (/ (+ phi1 phi2) 2))
601.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify4.2s

Counts

692 → 692

Iterations

Iter	Nodes
done	2914
0	2914

prune23.8s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 22.0b

regimes1.9s

Accuracy

56.8% (6.2b remaining)

Error of 28.8b against oracle of 22.6b and baseline of 36.9b

bsearch3.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.9s	8237×	body	80	valid
1.6s	1315×	body	640	valid
1.1s	775×	body	1280	valid
637.0ms	713×	body	320	valid
180.0ms	358×	body	160	valid