Details

sample188.0ms

Algorithm

intervals

Results

58.0ms	265×	body	80	valid
52.0ms	46×	body	640	valid
33.0ms	22×	body	1280	valid
11.0ms	17×	body	320	valid
4.0ms	8×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
5	2141
4	757
3	225
2	66
1	32
0	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

244×	`*-un-lft-identity`
130×	`associate-*l/`
97×	`flip3--` `flip--`
76×	`associate-l`
72×	`swap-sqr`
68×	`distribute-lft-out--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
51×	`sqrt-prod`
48×	`distribute-lft-out`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
4×	`insert-posit16` `add-log-exp`
3×	`associate-r`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr`

Counts

4 → 167

Calls

4 calls:

73.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
31.0ms	(cos (/ (+ phi1 phi2) 2))
48.0ms	(cos (/ (+ phi1 phi2) 2))
1.5s	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series822.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
39.0ms	(cos (/ (+ phi1 phi2) 2))
44.0ms	(cos (/ (+ phi1 phi2) 2))
622.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.1s

Counts

179 → 179

Iterations

Iter	Nodes
done	5001
1	1294
0	448

prune782.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.3b

localize98.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2))))
2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
38×	`*-un-lft-identity`
32×	`associate-*r/`
23×	`associate-l`
15×	`sqrt-prod`
12×	`distribute-lft-out`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `distribute-lft-out--`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube` `log-pow` `insert-posit16` `add-log-exp`
3×	`log-prod` `exp-prod`
2×	`rem-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 125

Calls

4 calls:

21.0ms	(log (exp (cos (/ (+ phi1 phi2) 2))))
49.0ms	(cos (/ (+ phi1 phi2) 2))
26.0ms	(cos (/ (+ phi1 phi2) 2))
1.5s	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series620.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(log (exp (cos (/ (+ phi1 phi2) 2))))
26.0ms	(cos (/ (+ phi1 phi2) 2))
43.0ms	(cos (/ (+ phi1 phi2) 2))
527.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.0s

Counts

137 → 137

Iterations

Iter	Nodes
done	5003
1	1324
0	446

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.3b

localize128.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
2.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite9.4s

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
36×	`*-un-lft-identity`
32×	`associate-*r/`
23×	`associate-l`
15×	`sqrt-prod`
12×	`distribute-lft-out`
7×	`distribute-lft-out--`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 116

Calls

4 calls:

26.0ms	(cos (/ (+ phi1 phi2) 2))
36.0ms	(cos (/ (+ phi1 phi2) 2))
39.0ms	(cos (/ (+ phi1 phi2) 2))
9.2s	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(cos (/ (+ phi1 phi2) 2))
39.0ms	(cos (/ (+ phi1 phi2) 2))
36.0ms	(cos (/ (+ phi1 phi2) 2))
575.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2)))))) (cbrt (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
1	1273
0	428

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.0b

localize119.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos (/ (+ phi1 phi2) 2))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite4.8s

Algorithm

rewrite-expression-head

Rules

384×	`associate-*l/`
288×	`flip3--` `flip--`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
100×	`*-un-lft-identity`
96×	`associate-*r/`
69×	`associate-l`
45×	`sqrt-prod`
36×	`distribute-lft-out`
21×	`distribute-lft-out--`
10×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 284

Calls

4 calls:

53.0ms	(cos (/ (+ phi1 phi2) 2))
1.6s	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
1.5s	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
1.5s	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

series2.0s

Counts

4 → 12

Calls

4 calls:

41.0ms	(cos (/ (+ phi1 phi2) 2))
629.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
695.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
619.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.3s

Counts

296 → 296

Iterations

Iter	Nodes
done	5000
1	1298
0	425

prune3.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.0b

regimes865.0ms

Accuracy

33.4% (8.7b remaining)

Error of 32.8b against oracle of 24.1b and baseline of 37.1b

bsearch186.0ms

Steps

Iters	Range		Point
9	5.0875015420834634e-30	1.4423693549975343e-20	1.400742996618376e-20

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.8s	8345×	body	80	valid
1.7s	783×	body	1280	valid
1.4s	1197×	body	640	valid
544.0ms	687×	body	320	valid
157.0ms	343×	body	160	valid