Details

sample276.0ms

Algorithm

intervals

Results

194.0ms	150×	body	1280	valid
54.0ms	65×	body	640	valid
8.0ms	19×	body	320	valid
2.0ms	16×	body	80	valid
2.0ms	6×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.0b	(sin (- lambda1 lambda2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `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:

11.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series196.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify107.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune353.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin lambda1) (cos lambda2))
98.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
85.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	348	545
1	1432	476
2	5001	475

prune443.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

4.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
4.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
50.0ms	(* (sin lambda1) (sin lambda2))
111.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
99.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	447	848
1	2015	666
2	5001	665

prune503.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`add-log-exp`
5×	`associate-r`
3×	`associate-r/` `-commutative`
2×	`sin-neg` `cos-mult` `distribute-rgt-neg-out` `sin-cos-mult` `sin-mult`
1×	`+-commutative` `frac-times` `flip3-+` `unsub-neg` `associate-*l/` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

4.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
4.0ms	(* (sin lambda2) (sin lambda1))
16.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
20.0ms	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))
50.0ms	(* (sin lambda2) (sin lambda1))
109.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
98.0ms	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))

simplify57.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	461	807
1	1960	640
2	5002	639

prune449.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes422.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	30
1	40	30

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.4s	4717×	body	1280	valid
1.4s	1883×	body	640	valid
250.0ms	550×	body	320	valid
100.0ms	637×	body	80	valid
61.0ms	213×	body	160	valid