Details

sample455.0ms

Algorithm

intervals

Results

348.0ms	144×	body	1280	valid
72.0ms	66×	body	640	valid
7.0ms	9×	body	320	valid
7.0ms	30×	body	80	valid
3.0ms	7×	body	160	valid

simplify75.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
4	80
3	77
2	47
1	28
0	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.4b	(cos (- lambda1 lambda2))
1.5b	(sin (- lambda1 lambda2))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

41.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
43.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))
13.0ms	(sin (- lambda1 lambda2))

series276.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
122.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

simplify2.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
3	3372
2	1034
1	436
0	214

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize102.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.4b	(cos (- lambda1 lambda2))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `sin-cos-mult` `flip--`

Counts

4 → 90

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
78.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
46.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))

series451.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (cos phi1) (sin phi2))
209.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
141.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1399
1	506
0	230

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

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

rewrite275.0ms

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×	`expm1-log1p-u` `associate-l/` `-commutative` `insert-posit16` `log1p-expm1-u` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 101

Calls

4 calls:

27.0ms	(* (sin lambda1) (sin lambda2))
108.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
74.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
61.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin lambda1) (sin lambda2))
190.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
188.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
170.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify2.0s

Counts

113 → 113

Iterations

Iter	Nodes
done	5013
2	1695
1	448
0	175

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize101.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))

rewrite39.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `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 → 85

Calls

4 calls:

32.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
1.0ms	(cbrt (sin lambda1))
1.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))

series457.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
108.0ms	(cbrt (sin lambda1))
113.0ms	(cbrt (sin lambda1))
110.0ms	(cbrt (sin lambda1))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	1355
2	474
1	182
0	81

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes846.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample18.7s

Algorithm

intervals

Results

14.3s	4668×	body	1280	valid
3.1s	1963×	body	640	valid
571.0ms	550×	body	320	valid
257.0ms	613×	body	80	valid
107.0ms	206×	body	160	valid