Details

sample260.0ms

Algorithm

intervals

Results

187.0ms	148×	body	1280	valid
42.0ms	63×	body	640	valid
8.0ms	18×	body	320	valid
2.0ms	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

localize35.0ms

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))

rewrite80.0ms

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))
37.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))
14.0ms	(sin (- lambda1 lambda2))

series186.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin phi1) (cos phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

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

prune415.0ms

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))

rewrite110.0ms

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:

46.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
12.0ms	(* (sin phi1) (cos phi2))
36.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series304.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
45.0ms	(* (sin phi1) (cos phi2))
98.0ms	(* (* (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

prune549.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
20.0ms	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
93.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
16.0ms	(* (sin lambda1) (sin (- lambda2)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin phi1) (cos phi2))
93.0ms	(- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
201.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
58.0ms	(* (sin lambda1) (sin (- lambda2)))

simplify64.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	453	1165
1	2098	1016
2	5001	1009

prune643.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.6b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1`
34×	`add-exp-log` `add-cbrt-cube`
27×	`pow-prod-down`
18×	`prod-exp` `cbrt-unprod`
7×	`cos-mult`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
3×	`distribute-rgt-neg-out` `sin-mult`
2×	`cube-div` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `associate-r/` `associate-r` `associate-l` `associate-l/` `sin-neg` `*-commutative` `sqr-pow`
1×	`pow2` `swap-sqr` `cube-neg`

Counts

4 → 118

Calls

4 calls:

11.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
52.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
43.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
12.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series326.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
120.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))
62.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
68.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify88.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	489	755
1	2479	700
2	5001	698

prune644.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes344.0ms

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	46	56
1	46	56

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.1s	4587×	body	1280	valid
1.4s	2017×	body	640	valid
257.0ms	524×	body	320	valid
92.0ms	664×	body	80	valid
63.0ms	208×	body	160	valid