Details

sample281.0ms

Algorithm

intervals

Results

203.0ms	145×	body	1280	valid
44.0ms	62×	body	640	valid
7.0ms	16×	body	320	valid
3.0ms	26×	body	80	valid
2.0ms	7×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))
2.7b	(sin (- lambda1 lambda2))

rewrite93.0ms

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))
34.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))
13.0ms	(sin (- lambda1 lambda2))

series164.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
79.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))
18.0ms	(sin (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (33.0ms)

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

prune383.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))

rewrite104.0ms

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:

11.0ms	(* (cos phi1) (sin phi2))
41.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
34.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series250.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos phi1) (sin phi2))
116.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
81.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(cos (- lambda1 lambda2))

simplify52.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (44.0ms)

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

prune608.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite139.0ms

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` `associate-l/` `-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3-+` `flip-+`

Counts

4 → 97

Calls

4 calls:

41.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
11.0ms	(* (sin lambda1) (sin lambda2))
40.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
44.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
40.0ms	(* (sin lambda1) (sin lambda2))
97.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
86.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify66.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	477	1027
1	2206	822
2	5001	820

prune587.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

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` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `flip3-+` `associate-r/` `associate-l/` `flip-+` `sin-mult` `unswap-sqr`
2×	`frac-add` `cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 92

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
42.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
12.0ms	(* (sin lambda1) (sin lambda2))
56.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (cos phi1) (sin phi2))
114.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
39.0ms	(* (sin lambda1) (sin lambda2))
149.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify73.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	579	1014
1	2808	885
2	5001	883

prune540.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes475.0ms

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	47	52
1	47	52

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.1s	4647×	body	1280	valid
1.4s	1937×	body	640	valid
257.0ms	543×	body	320	valid
85.0ms	666×	body	80	valid
58.0ms	207×	body	160	valid