Details

sample274.0ms

Algorithm

intervals

Results

196.0ms	157×	body	1280	valid
40.0ms	58×	body	640	valid
7.0ms	15×	body	320	valid
3.0ms	20×	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: 15.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
4.9b	(sin (- lambda1 lambda2))

rewrite113.0ms

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:

31.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
52.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))
14.0ms	(sin (- lambda1 lambda2))

series205.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune429.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.4b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

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` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

12.0ms	(* (cos lambda1) (sin lambda2))
14.0ms	(* (sin lambda1) (cos lambda2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series217.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos lambda1) (sin lambda2))
46.0ms	(* (sin lambda1) (cos lambda2))
101.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	455	787
1	1637	630
2	5002	628

prune547.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite118.0ms

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:

11.0ms	(* (sin lambda1) (cos lambda2))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
47.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
12.0ms	(* (sin lambda1) (sin lambda2))

series337.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin lambda1) (cos lambda2))
125.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
112.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
48.0ms	(* (sin lambda1) (sin lambda2))

simplify53.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	418	830
1	1802	652
2	5001	652

prune554.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (sin lambda1) (sin lambda2))
2.3b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

12.0ms	(* (sin lambda1) (cos lambda2))
46.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
13.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin lambda1) (cos lambda2))
125.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
49.0ms	(* (sin lambda1) (sin lambda2))
54.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify42.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	343	623
1	1254	507
2	5001	507

prune526.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes506.0ms

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	39	39
1	39	39

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.3s	4633×	body	1280	valid
1.4s	1925×	body	640	valid
264.0ms	571×	body	320	valid
91.0ms	650×	body	80	valid
64.0ms	221×	body	160	valid