Details

sample707.0ms

Algorithm

intervals

Results

476.0ms	158×	body	1280	valid
171.0ms	55×	body	640	valid
26.0ms	22×	body	320	valid
5.0ms	16×	body	80	valid
3.0ms	5×	body	160	valid

simplify413.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	80
4	80
3	77
2	47
1	28
0	17

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize88.0ms

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))

rewrite154.0ms

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:

48.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
58.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

series260.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
114.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
29.0ms	(cos (- lambda1 lambda2))
41.0ms	(sin (- lambda1 lambda2))

simplify1.9s

Counts

102 → 102

Iterations

Iter	Nodes
3	3293
2	978
1	425
0	214

prune2.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.5b

localize105.0ms

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))

rewrite186.0ms

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×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 91

Calls

4 calls:

22.0ms	(* (sin lambda1) (cos lambda2))
93.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
49.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

series400.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin lambda1) (cos lambda2))
163.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
138.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
29.0ms	(cos (- lambda1 lambda2))

simplify4.2s

Counts

103 → 103

Iterations

Iter	Nodes
3	4964
2	1357
1	493
0	230

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

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

rewrite247.0ms

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:

105.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
60.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
63.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
17.0ms	(* (sin lambda1) (sin lambda2))

series568.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
153.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
169.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
71.0ms	(* (sin lambda1) (sin lambda2))

simplify4.5s

Counts

113 → 113

Iterations

Iter	Nodes
3	8985
2	1700
1	451
0	175

prune2.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize113.0ms

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))

rewrite21.0ms

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:

15.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
1.0ms	(cbrt (sin lambda2))
1.0ms	(cbrt (sin lambda2))
1.0ms	(cbrt (sin lambda2))

series530.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
122.0ms	(cbrt (sin lambda2))
150.0ms	(cbrt (sin lambda2))
129.0ms	(cbrt (sin lambda2))

simplify2.5s

Counts

97 → 97

Iterations

Iter	Nodes
4	4250
3	1199
2	433
1	180
0	81

prune2.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes549.0ms

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

sample21.4s

Algorithm

intervals

Results

15.9s	4586×	body	1280	valid
3.9s	2023×	body	640	valid
720.0ms	530×	body	320	valid
315.0ms	652×	body	80	valid
204.0ms	209×	body	160	valid