Details

sample557.0ms

Algorithm

intervals

Results

395.0ms	144×	body	1280	valid
97.0ms	66×	body	640	valid
9.0ms	9×	body	320	valid
8.0ms	30×	body	80	valid
4.0ms	7×	body	160	valid

simplify227.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize103.0ms

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))

rewrite269.0ms

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:

89.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
93.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms	(cos (- lambda1 lambda2))
34.0ms	(sin (- lambda1 lambda2))

series472.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
215.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))
52.0ms	(sin (- lambda1 lambda2))

simplify7.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3670
2	1055
1	436
0	214

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize123.0ms

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))

rewrite241.0ms

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:

32.0ms	(* (cos phi1) (sin phi2))
112.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
56.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))

series755.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (cos phi1) (sin phi2))
375.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
225.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
47.0ms	(cos (- lambda1 lambda2))

simplify3.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1397
1	506
0	230

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize242.0ms

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)))

rewrite324.0ms

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))
132.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
79.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
79.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (sin lambda1) (sin lambda2))
342.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
340.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
301.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify3.6s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1733
1	444
0	175

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize261.0ms

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))

rewrite48.0ms

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:

36.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
3.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))
3.0ms	(cbrt (sin lambda1))

series866.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
187.0ms	(cbrt (sin lambda1))
219.0ms	(cbrt (sin lambda1))
196.0ms	(cbrt (sin lambda1))

simplify3.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	1412
2	483
1	182
0	81

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes2.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample18.6s

Algorithm

intervals

Results

13.4s	4668×	body	1280	valid
3.8s	1963×	body	640	valid
623.0ms	550×	body	320	valid
145.0ms	613×	body	80	valid
101.0ms	206×	body	160	valid