Details

sample612.0ms

Algorithm

intervals

Results

360.0ms	149×	body	1280	valid
196.0ms	59×	body	640	valid
14.0ms	18×	body	320	valid
7.0ms	25×	body	80	valid
3.0ms	5×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	79
4	79
3	71
2	46
1	27
0	17

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b	(sin (- lambda1 lambda2))
3.7b	(cos (- lambda1 lambda2))

rewrite118.0ms

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` `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 → 60

Calls

4 calls:

32.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
56.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(sin (- lambda1 lambda2))
12.0ms	(cos (- lambda1 lambda2))

series301.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
152.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify882.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1349
1	272
0	116

prune631.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b	(cos (- lambda1 lambda2))

rewrite97.0ms

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×	`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 → 70

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
55.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
24.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series394.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin phi1) (cos phi2))
179.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
133.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5002
2	2002
1	366
0	138

prune953.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (cos lambda1) (cos lambda2)) (sin phi1))
0.3b	(* (* (sin lambda2) (sin lambda1)) (* (sin phi1) (cos phi2)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l`
4×	`associate-l/` `-commutative` `add-log-exp`
3×	`sin-mult`
2×	`sin-cos-mult` `unswap-sqr`
1×	`frac-times` `flip3-+` `associate-*r/` `cos-mult` `flip-+`

Counts

4 → 83

Calls

4 calls:

41.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
9.0ms	(* (sin lambda2) (sin lambda1))
31.0ms	(* (* (cos lambda1) (cos lambda2)) (sin phi1))
69.0ms	(* (* (sin lambda2) (sin lambda1)) (* (sin phi1) (cos phi2)))

series536.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
72.0ms	(* (sin lambda2) (sin lambda1))
123.0ms	(* (* (cos lambda1) (cos lambda2)) (sin phi1))
146.0ms	(* (* (sin lambda2) (sin lambda1)) (* (sin phi1) (cos phi2)))

simplify1.2s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	2374
1	460
0	174

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))))
0.5b	(cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.5b	(cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.5b	(cbrt (+ (* (cos lambda1) (- (sin lambda2))) (* (sin lambda1) (cos lambda2))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

98.0ms	(* (cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))))
15.0ms	(cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
13.0ms	(cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
13.0ms	(cbrt (+ (* (cos lambda1) (- (sin lambda2))) (* (sin lambda1) (cos lambda2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

240.0ms	(* (cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))))
261.0ms	(cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
268.0ms	(cbrt (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
259.0ms	(cbrt (+ (* (cos lambda1) (- (sin lambda2))) (* (sin lambda1) (cos lambda2))))

simplify1.3s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1926
1	415
0	159

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	50
3	50
2	49
1	45
0	30

end0.0ms

sample21.3s

Algorithm

intervals

Results

15.4s	4571×	body	1280	valid
4.4s	1969×	body	640	valid
593.0ms	558×	body	320	valid
228.0ms	685×	body	80	valid
134.0ms	217×	body	160	valid