Details

sample270.0ms

Algorithm

intervals

Results

198.0ms	147×	body	1280	valid
41.0ms	57×	body	640	valid
8.0ms	18×	body	320	valid
4.0ms	27×	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

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(sin (- lambda1 lambda2))
4.4b	(cos (- lambda1 lambda2))

rewrite41.0ms

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`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series175.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos phi1) (sin phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	443	1004
1	1340	773
2	5001	771

prune397.0ms

Filtered

97 candidates to 62 candidates (63.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.4b	(cos (- lambda1 lambda2))

rewrite40.0ms

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×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sin-cos-mult` `flip-+`

Counts

4 → 86

Calls

4 calls:

14.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
4.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
45.0ms	(* (cos phi1) (sin phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	512	984
1	1910	801
2	5001	797

prune546.0ms

Filtered

98 candidates to 70 candidates (71.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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*`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
111.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
48.0ms	(* (sin lambda1) (sin lambda2))
98.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	429	827
1	1850	649
2	5001	647

prune555.0ms

Filtered

107 candidates to 65 candidates (60.7%)

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
20.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos phi1) (sin phi2))
45.0ms	(* (sin lambda1) (sin lambda2))
101.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
113.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	444	783
1	1893	620
2	5002	620

prune525.0ms

Filtered

104 candidates to 67 candidates (64.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes418.0ms

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	42	32
1	42	32

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.4s	4569×	body	1280	valid
1.5s	2015×	body	640	valid
258.0ms	549×	body	320	valid
99.0ms	669×	body	80	valid
58.0ms	198×	body	160	valid