Details

sample264.0ms

Algorithm

intervals

Results

187.0ms	145×	body	1280	valid
49.0ms	71×	body	640	valid
8.0ms	18×	body	320	valid
2.0ms	16×	body	80	valid
2.0ms	6×	body	160	valid

simplify10.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.4b	(sin (- lambda1 lambda2))
4.5b	(cos (- lambda1 lambda2))

rewrite44.0ms

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:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(sin (- lambda1 lambda2))
8.0ms	(cos (- lambda1 lambda2))

series191.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

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

prune438.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (sin lambda1) (cos lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.5b	(cos (- lambda1 lambda2))

rewrite31.0ms

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/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (sin lambda1) (cos lambda2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series202.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos lambda1) (sin (- lambda2)))
45.0ms	(* (sin lambda1) (cos lambda2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify52.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	463	817
1	1702	656
2	5001	654

prune558.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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

Counts

4 → 92

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos lambda1) (sin (- lambda2)))
45.0ms	(* (sin lambda1) (cos lambda2))
45.0ms	(* (sin lambda1) (sin lambda2))
172.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify75.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	527	847
1	2499	740
2	5001	740

prune648.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(log1p (* (sin lambda1) (cos lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite32.0ms

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

Counts

4 → 82

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(log1p (* (sin lambda1) (cos lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
21.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (cos lambda2))
70.0ms	(log1p (* (sin lambda1) (cos lambda2)))
46.0ms	(* (sin lambda1) (sin lambda2))
175.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify70.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	465	782
1	2189	683
2	5002	680

prune561.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes468.0ms

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	40	30
1	40	30

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.0s	4572×	body	1280	valid
1.4s	1952×	body	640	valid
284.0ms	583×	body	320	valid
100.0ms	686×	body	80	valid
66.0ms	207×	body	160	valid