Details

sample174.0ms

Algorithm

intervals

Results

99.0ms	114×	body	1280	valid
44.0ms	76×	body	640	valid
8.0ms	23×	body	320	valid
4.0ms	17×	body	160	valid
3.0ms	26×	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: 0.5b

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)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b	(cos (- lambda1 lambda2))
2.7b	(sin (- lambda1 lambda2))

rewrite31.0ms

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))))
10.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series137.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
89.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify121.0ms

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

prune238.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b	(cos (- lambda1 lambda2))

rewrite79.0ms

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`
3×	`distribute-rgt-in` `cos-diff` `sub-neg` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+` `associate-*r/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

56.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
9.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
12.0ms	(cos (- lambda1 lambda2))

series235.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
87.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms	(cos (- lambda1 lambda2))

simplify119.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	289	748
1	1037	659
2	4438	658
3	5002	658

prune318.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.4b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

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)))))))
57.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
15.0ms	(* (sin lambda1) (sin (- lambda2)))
9.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

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)))))))
119.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
47.0ms	(* (sin lambda1) (sin (- lambda2)))
199.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	366	1039
1	1388	913
2	5002	902

prune374.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
0.4b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
0.6b	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
1.6b	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
22×	`cos-mult`
18×	`associate-*r/`
16×	`associate-/r/`
15×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
14×	`frac-add`
10×	`flip3--` `flip--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `sin-mult` `add-log-exp`
7×	`pow1`
5×	`sum-cubes` `distribute-lft-out` `associate-/l*`
4×	`cube-div` `associate-*l/` `associate--l+` `frac-sub` `sub-div`
3×	`sub-neg` `pow-unpow` `flip3-+` `associate-/r*` `flip-+`
2×	`distribute-rgt-in` `pow-pow` `distribute-lft-in` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `diff-log` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

334.0ms	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
18.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 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))

series5.2s

Counts

4 → 12

Calls

4 calls:

3.8s	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
1.0s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
180.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
236.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

simplify60.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1250	5024
1	5001	4746

prune868.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes537.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	78
1	44	78

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.2s	3598×	body	1280	valid
1.2s	2345×	body	640	valid
315.0ms	950×	body	320	valid
91.0ms	417×	body	160	valid
76.0ms	690×	body	80	valid