Details

sample166.0ms

Algorithm

intervals

Results

51.0ms	256×	body	80	valid
32.0ms	40×	body	640	valid
31.0ms	25×	body	320	valid
20.0ms	19×	body	1280	valid
6.0ms	16×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
6	5440
5	1878
4	761
3	231
2	72
1	34
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
3.4b	(cos (/ (+ phi2 phi1) 2))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
12.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
37.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
19.0ms	(cos (/ (+ phi2 phi1) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

577.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
601.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
135.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
34.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.7s

Counts

79 → 79

Iterations

Iter	Nodes
3	3897
2	1082
1	359
0	144

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ phi2 phi1) 2)))
3.4b	(cos (/ (+ phi2 phi1) 2))
3.4b	(cos (/ (+ phi2 phi1) 2))
3.4b	(cos (/ (+ phi2 phi1) 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ phi2 phi1) 2)))
8.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))
18.0ms	(cos (/ (+ phi2 phi1) 2))

series218.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (cos (/ (+ phi2 phi1) 2)))
40.0ms	(cos (/ (+ phi2 phi1) 2))
38.0ms	(cos (/ (+ phi2 phi1) 2))
32.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.3s

Counts

56 → 56

Iterations

Iter	Nodes
6	2049
5	1116
4	666
3	300
2	147
1	88
0	49

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(log1p (cbrt (cos (/ (+ phi2 phi1) 2))))
3.4b	(cos (/ (+ phi2 phi1) 2))
3.4b	(cos (/ (+ phi2 phi1) 2))
3.4b	(cos (/ (+ phi2 phi1) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

5×	`expm1-log1p-u`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`log1p-udef` `log1p-expm1`

Counts

4 → 42

Calls

4 calls:

0.0ms	(log1p (cbrt (cos (/ (+ phi2 phi1) 2))))
8.0ms	(cos (/ (+ phi2 phi1) 2))
8.0ms	(cos (/ (+ phi2 phi1) 2))
14.0ms	(cos (/ (+ phi2 phi1) 2))

series293.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(log1p (cbrt (cos (/ (+ phi2 phi1) 2))))
27.0ms	(cos (/ (+ phi2 phi1) 2))
22.0ms	(cos (/ (+ phi2 phi1) 2))
23.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.5s

Counts

54 → 54

Iterations

Iter	Nodes
7	3410
6	1535
5	968
4	625
3	305
2	156
1	94
0	52

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.5b

localize110.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ 1 (cbrt (cos (/ (+ phi2 phi1) 2))))
3.4b	(cos (/ (+ phi2 phi1) 2))
3.4b	(cos (/ (+ phi2 phi1) 2))
3.4b	(cos (/ (+ phi2 phi1) 2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 48

Calls

4 calls:

4.0ms	(+ 1 (cbrt (cos (/ (+ phi2 phi1) 2))))
8.0ms	(cos (/ (+ phi2 phi1) 2))
7.0ms	(cos (/ (+ phi2 phi1) 2))
12.0ms	(cos (/ (+ phi2 phi1) 2))

series229.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ 1 (cbrt (cos (/ (+ phi2 phi1) 2))))
32.0ms	(cos (/ (+ phi2 phi1) 2))
22.0ms	(cos (/ (+ phi2 phi1) 2))
37.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.4s

Counts

60 → 60

Iterations

Iter	Nodes
4	2017
3	917
2	371
1	146
0	62

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.5b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	17
1	17
0	14

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.8s	8322×	body	80	valid
1.6s	1296×	body	640	valid
1.3s	758×	body	1280	valid
1.0s	752×	body	320	valid
251.0ms	372×	body	160	valid