Details

sample266.0ms

Algorithm

intervals

Results

192.0ms	148×	body	1280	valid
43.0ms	63×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	20×	body	80	valid
2.0ms	7×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
35.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))
14.0ms	(sin (- lambda1 lambda2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (cos phi2))
94.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify43.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	411	1009
1	1289	778
2	5001	776

prune422.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.1b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 87

Calls

4 calls:

45.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
12.0ms	(* (sin phi1) (cos phi2))
35.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series298.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
43.0ms	(* (sin phi1) (cos phi2))
95.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	477	989
1	1849	806
2	5001	802

prune545.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
12.0ms	(* (sin lambda1) (sin lambda2))
48.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (cos phi2))
121.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
51.0ms	(* (sin lambda1) (sin lambda2))
107.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify57.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	397	830
1	1810	652
2	5001	652

prune565.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate-l`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-r/` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`cos-mult` `sin-cos-mult`
1×	`frac-times` `associate-*l/` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

27.0ms	(* (cos phi2) (* (sin lambda2) (sin lambda1)))
44.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
13.0ms	(* (sin lambda2) (sin lambda1))
65.0ms	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (cos phi2) (* (sin lambda2) (sin lambda1)))
121.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
50.0ms	(* (sin lambda2) (sin lambda1))
108.0ms	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))

simplify52.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	374	836
1	1644	654
2	5001	654

prune482.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes411.0ms

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	42	32
1	42	32

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.0s	4587×	body	1280	valid
1.4s	2017×	body	640	valid
239.0ms	524×	body	320	valid
87.0ms	664×	body	80	valid
58.0ms	208×	body	160	valid