Details

sample177.0ms

Algorithm

intervals

Results

100.0ms	111×	body	1280	valid
46.0ms	85×	body	640	valid
10.0ms	30×	body	320	valid
2.0ms	11×	body	160	valid
2.0ms	19×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	21	12
2	21	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
9.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series133.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
90.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms	(cos (- lambda1 lambda2))
19.0ms	(sin (- lambda1 lambda2))

simplify117.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	205	421
1	508	375
2	1327	374
3	3685	374
4	5002	374

prune255.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.5b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
3.6b	(sin (- lambda1 lambda2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
4×	`associate-+r+`
3×	`sub-neg` `associate-r` `associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `sin-sum`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sin-neg` `sum-log` `sin-diff` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

15.0ms	(* (sin lambda1) (sin (- lambda2)))
0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
10.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
10.0ms	(sin (- lambda1 lambda2))

series290.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin lambda1) (sin (- lambda2)))
15.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
206.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
19.0ms	(sin (- lambda1 lambda2))

simplify85.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	285	712
1	845	629
2	3301	618
3	5002	618

prune349.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`associate-+r+`
3×	`sub-neg` `associate-r` `associate-l` `sin-mult`
2×	`distribute-rgt-in` `distribute-lft-in` `cos-mult`
1×	`+-commutative` `flip3--` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sin-neg` `sum-log` `*-commutative` `distribute-rgt-neg-out` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `sub-div` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

18.0ms	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
17.0ms	(* (sin lambda1) (sin (- lambda2)))
9.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
18.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
50.0ms	(* (sin lambda1) (sin (- lambda2)))
207.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify120.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	370	937
1	1173	827
2	4892	801
3	5001	801

prune376.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
0.3b	(pow (cos phi1) 3)
0.6b	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
0.8b	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`pow-unpow`
4×	`cube-div` `unpow-prod-down` `cube-prod` `associate-*r/` `associate--l+`
3×	`sub-neg` `pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `flip3--` `distribute-lft-in` `unpow3` `cos-mult` `flip--` `sin-mult` `sqr-pow`
1×	`+-commutative` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `sum-cubes` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `sub-div`

Counts

4 → 78

Calls

4 calls:

19.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
3.0ms	(pow (cos phi1) 3)
35.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
66.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.0s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
25.0ms	(pow (cos phi1) 3)
189.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
194.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

simplify101.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	673	1163
1	3208	1028
2	5002	1024

prune465.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes568.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	69
1	47	69

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.2s	3541×	body	1280	valid
1.3s	2402×	body	640	valid
320.0ms	942×	body	320	valid
91.0ms	397×	body	160	valid
76.0ms	718×	body	80	valid