Details

sample975.0ms

Algorithm

intervals

Results

824.0ms	148×	body	1280	valid
85.0ms	61×	body	640	valid
16.0ms	19×	body	320	valid
6.0ms	21×	body	80	valid
6.0ms	7×	body	160	valid

simplify67.0ms

Counts

1 → 1

Iterations

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

prune51.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (cos phi1))
0.2b	(* (cos (- lambda1 lambda2)) (* (cos phi2) (sin phi1)))
4.6b	(cos (- lambda1 lambda2))
4.6b	(sin (- lambda1 lambda2))

rewrite69.0ms

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-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`cos-sum` `sub-neg` `sin-sum` `*-commutative`
1×	`cos-diff` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

9.0ms	(* (sin phi2) (cos phi1))
40.0ms	(* (cos (- lambda1 lambda2)) (* (cos phi2) (sin phi1)))
10.0ms	(cos (- lambda1 lambda2))
9.0ms	(sin (- lambda1 lambda2))

series286.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin phi2) (cos phi1))
165.0ms	(* (cos (- lambda1 lambda2)) (* (cos phi2) (sin phi1)))
19.0ms	(cos (- lambda1 lambda2))
27.0ms	(sin (- lambda1 lambda2))

simplify3.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
3	4961
2	916
1	263
0	122

prune687.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin phi2) (cos phi1))
0.2b	(* (cos (- lambda1 lambda2)) (* (cos phi2) (sin phi1)))
4.6b	(cos (- lambda1 lambda2))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
17.0ms	(* (sin phi2) (cos phi1))
44.0ms	(* (cos (- lambda1 lambda2)) (* (cos phi2) (sin phi1)))
27.0ms	(cos (- lambda1 lambda2))

series358.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin lambda1) (cos lambda2))
58.0ms	(* (sin phi2) (cos phi1))
198.0ms	(* (cos (- lambda1 lambda2)) (* (cos phi2) (sin phi1)))
21.0ms	(cos (- lambda1 lambda2))

simplify800.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1252
1	325
0	144

prune843.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize111.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `associate-l`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `unswap-sqr`
2×	`associate-*l/` `sin-cos-mult`
1×	`distribute-lft-neg-out` `neg-mul-1` `flip3--` `flip--`

Counts

4 → 84

Calls

4 calls:

16.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin phi2) (cos phi1))
13.0ms	(* (- (sin lambda2)) (sin lambda1))
75.0ms	(* (- (* (cos lambda1) (cos lambda2)) (* (- (sin lambda2)) (sin lambda1))) (* (cos phi2) (sin phi1)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin lambda1) (cos lambda2))
58.0ms	(* (sin phi2) (cos phi1))
75.0ms	(* (- (sin lambda2)) (sin lambda1))
293.0ms	(* (- (* (cos lambda1) (cos lambda2)) (* (- (sin lambda2)) (sin lambda1))) (* (cos phi2) (sin phi1)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	2032
1	460
0	181

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
0.5b	(pow (* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))) 3)
19.8b	(cbrt (pow (* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))) 3))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`cbrt-prod`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`cube-div` `associate-l`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `sin-mult` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `pow-pow` `flip3-+` `frac-add` `pow-exp` `cos-mult` `flip-+` `rem-cube-cbrt`
2×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
87.0ms	(* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
69.0ms	(pow (* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))) 3)
40.0ms	(cbrt (pow (* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))) 3))

series1.1s

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sin lambda1) (sin lambda2))
277.0ms	(* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
497.0ms	(pow (* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))) 3)
262.0ms	(cbrt (pow (* (sin phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))) 3))

simplify2.0s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
2	3346
1	594
0	189

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes808.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample20.3s

Algorithm

intervals

Results

14.9s	4551×	body	1280	valid
3.7s	2024×	body	640	valid
652.0ms	555×	body	320	valid
191.0ms	206×	body	160	valid
180.0ms	664×	body	80	valid