Details

sample142.0ms

Algorithm

intervals

Results

45.0ms	33×	body	640	valid
36.0ms	271×	body	80	valid
27.0ms	32×	body	1280	valid
8.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1878
4	761
3	231
2	72
1	34
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
2.7b	(cos (/ (+ phi2 phi1) 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
3×	`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×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
19.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms	(cos (/ (+ phi2 phi1) 2))

series848.0ms

Counts

3 → 9

Calls

3 calls:

673.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
149.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
26.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.2s

Counts

65 → 65

Iterations

Iter	Nodes
done	5008
3	3527
2	896
1	307
0	128

prune637.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize44.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
2.7b	(cos (/ (+ phi1 phi2) 2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
3×	`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×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
19.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
20.0ms	(cos (/ (+ phi1 phi2) 2))

series882.0ms

Counts

3 → 9

Calls

3 calls:

740.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
118.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
23.0ms	(cos (/ (+ phi1 phi2) 2))

simplify2.5s

Counts

65 → 65

Iterations

Iter	Nodes
done	5003
3	3590
2	897
1	307
0	127

prune599.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
2.7b	(cos (/ (+ phi2 phi1) 2))
2.7b	(cos (/ (+ phi2 phi1) 2))
2.7b	(cos (/ (+ phi2 phi1) 2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 44

Calls

4 calls:

15.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
8.0ms	(cos (/ (+ phi2 phi1) 2))
15.0ms	(cos (/ (+ phi2 phi1) 2))
13.0ms	(cos (/ (+ phi2 phi1) 2))

series146.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
42.0ms	(cos (/ (+ phi2 phi1) 2))
26.0ms	(cos (/ (+ phi2 phi1) 2))
39.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.2s

Counts

56 → 56

Iterations

Iter	Nodes
done	5013
5	2412
4	739
3	283
2	130
1	80
0	49

prune648.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.3b

localize82.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (log (exp (cos (/ (+ phi2 phi1) 2))))))
2.7b	(cos (/ (+ phi2 phi1) 2))
2.7b	(cos (/ (+ phi2 phi1) 2))
2.7b	(cos (/ (+ phi2 phi1) 2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

14.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (log (exp (cos (/ (+ phi2 phi1) 2))))))
15.0ms	(cos (/ (+ phi2 phi1) 2))
13.0ms	(cos (/ (+ phi2 phi1) 2))
14.0ms	(cos (/ (+ phi2 phi1) 2))

series128.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (log (exp (cos (/ (+ phi2 phi1) 2))))))
28.0ms	(cos (/ (+ phi2 phi1) 2))
42.0ms	(cos (/ (+ phi2 phi1) 2))
25.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.3s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
5	2366
4	705
3	281
2	143
1	89
0	52

prune558.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.3b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 4.0b against oracle of 3.8b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.6s	1236×	body	640	valid
1.5s	8378×	body	80	valid
1.4s	844×	body	1280	valid
460.0ms	722×	body	320	valid
109.0ms	356×	body	160	valid