Details

sample614.0ms

Algorithm

intervals

Results

470.0ms	158×	body	1280	valid
90.0ms	55×	body	640	valid
25.0ms	22×	body	320	valid
5.0ms	16×	body	80	valid
4.0ms	5×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	73
4	73
3	69
2	45
1	27
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.4b	(cos (- lambda1 lambda2))
2.7b	(sin (- lambda1 lambda2))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

29.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
33.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))
14.0ms	(sin (- lambda1 lambda2))

series241.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
111.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
3	2671
2	792
1	274
0	120

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.5b

localize88.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.1b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.4b	(cos (- lambda1 lambda2))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 74

Calls

4 calls:

14.0ms	(* (sin lambda1) (cos lambda2))
61.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
36.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series385.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin lambda1) (cos lambda2))
181.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
114.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify3.3s

Counts

86 → 86

Iterations

Iter	Nodes
3	4100
2	1164
1	377
0	154

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
0.2b	(* (sin lambda1) (sin lambda2))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`associate-l/` `-commutative` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 93

Calls

4 calls:

53.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
41.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
37.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
18.0ms	(* (sin lambda1) (sin lambda2))

series575.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
130.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
184.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
69.0ms	(* (sin lambda1) (sin lambda2))

simplify4.7s

Counts

105 → 105

Iterations

Iter	Nodes
3	9062
2	1761
1	466
0	169

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize107.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
0.7b	(cbrt (sin lambda2))
0.7b	(cbrt (sin lambda2))
0.7b	(cbrt (sin lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

12.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
1.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))

series548.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
137.0ms	(cbrt (sin lambda2))
136.0ms	(cbrt (sin lambda2))
139.0ms	(cbrt (sin lambda2))

simplify1.8s

Counts

89 → 89

Iterations

Iter	Nodes
4	4117
3	1161
2	416
1	173
0	77

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes675.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
2	39
1	39
0	28

end0.0ms

sample25.5s

Algorithm

intervals

Results

18.1s	4586×	body	1280	valid
5.5s	2023×	body	640	valid
740.0ms	530×	body	320	valid
680.0ms	652×	body	80	valid
168.0ms	209×	body	160	valid