Details

sample164.0ms

Algorithm

intervals

Results

57.0ms	282×	body	80	valid
24.0ms	39×	body	640	valid
22.0ms	25×	body	1280	valid
11.0ms	26×	body	320	valid
4.0ms	13×	body	160	valid

simplify908.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1037
3	259
2	76
1	34
0	17

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
2.8b	(cos (/ (+ phi2 phi1) 2.0))

rewrite55.0ms

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` `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 → 63

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
14.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
30.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
9.0ms	(cos (/ (+ phi2 phi1) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

637.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
716.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
140.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
33.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify860.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
2	1577
1	359
0	142

prune861.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
26×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`associate-r` `add-cube-cbrt`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3`
2×	`associate-*l/`
1×	`pow-to-exp` `pow-pow` `flip3--` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip--` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

38.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
9.0ms	(cos (/ (+ phi1 phi2) 2.0))

series315.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
49.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
89.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
30.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify1.8s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1961
1	324
0	130

prune917.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize97.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (cos (/ (+ phi2 phi1) 2.0)) 2))
0.5b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
2.8b	(cos (/ (+ phi2 phi1) 2.0))
2.8b	(cos (/ (+ phi1 phi2) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`unpow-prod-down`
6×	`cube-prod`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `pow1/3` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `unpow2` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt (pow (cos (/ (+ phi2 phi1) 2.0)) 2))
3.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
14.0ms	(cos (/ (+ phi2 phi1) 2.0))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series336.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (pow (cos (/ (+ phi2 phi1) 2.0)) 2))
92.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
34.0ms	(cos (/ (+ phi2 phi1) 2.0))
35.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify968.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1075
1	287
0	114

prune777.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi2 phi1) 2.0)) 3)
0.5b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
2.8b	(cos (/ (+ phi1 phi2) 2.0))
2.8b	(cos (/ (+ phi2 phi1) 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`unpow-prod-down` `cube-prod`
6×	`cbrt-prod` `pow1` `pow-unpow` `add-exp-log`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow1/3`

Counts

4 → 75

Calls

4 calls:

3.0ms	(pow (cos (/ (+ phi2 phi1) 2.0)) 3)
5.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
12.0ms	(cos (/ (+ phi1 phi2) 2.0))
9.0ms	(cos (/ (+ phi2 phi1) 2.0))

series217.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (cos (/ (+ phi2 phi1) 2.0)) 3)
94.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 3)
31.0ms	(cos (/ (+ phi1 phi2) 2.0))
30.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify3.0s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1976
1	315
0	106

prune902.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

regimes1.0s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.3s	8313×	body	80	valid
781.0ms	791×	body	1280	valid
745.0ms	1290×	body	640	valid
685.0ms	751×	body	320	valid
630.0ms	351×	body	160	valid