Details

sample285.0ms

Algorithm

intervals

Results

209.0ms	154×	body	1280	valid
45.0ms	57×	body	640	valid
10.0ms	21×	body	320	valid
3.0ms	18×	body	80	valid
2.0ms	6×	body	160	valid

simplify9.0ms

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: 13.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(sin (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))

rewrite38.0ms

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:

8.0ms	(* (sin phi1) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series171.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

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

prune421.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite43.0ms

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` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 87

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
17.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series278.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
125.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify55.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	445	971
1	1607	790
2	5001	789

prune538.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
16.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
52.0ms	(* (sin lambda1) (sin (- lambda2)))
138.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
183.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	529	1209
1	2454	1057
2	5002	1056

prune716.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
3.3b	(log (exp (* (sin lambda1) (sin (- lambda2)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin (- lambda2)))
17.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
2.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin lambda1) (sin (- lambda2)))
128.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
184.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
57.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	549	1631
1	2298	1264
2	5001	1254

prune596.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes779.0ms

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	38	30
1	38	30

end0.0ms

sample8.7s

Algorithm

intervals

Results

6.3s	4625×	body	1280	valid
1.6s	1939×	body	640	valid
300.0ms	571×	body	320	valid
132.0ms	672×	body	80	valid
69.0ms	193×	body	160	valid