Details

sample262.0ms

Algorithm

intervals

Results

189.0ms	147×	body	1280	valid
44.0ms	62×	body	640	valid
10.0ms	22×	body	320	valid
3.0ms	20×	body	80	valid
1.0ms	5×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
15.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series169.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos phi1) (sin phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify117.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	286	430
1	1077	367
2	4907	367
3	5001	367

prune321.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(cos (- lambda1 lambda2))

rewrite219.0ms

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×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 67

Calls

4 calls:

199.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series197.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos lambda1) (sin lambda2))
42.0ms	(* (cos phi1) (sin phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	331	476
1	1299	404
2	5002	404

prune425.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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

Counts

4 → 87

Calls

4 calls:

7.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
25.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
47.0ms	(* (cos phi1) (sin phi2))
51.0ms	(* (sin lambda1) (sin (- lambda2)))
181.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	510	921
1	2256	799
2	5003	797

prune602.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2))))
0.4b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

18.0ms	(* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2))))
3.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series255.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2))))
75.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
53.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
64.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify79.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	495	652
1	2420	612
2	5001	610

prune623.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes470.0ms

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	49	59
1	49	59

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.0s	4600×	body	1280	valid
1.4s	1966×	body	640	valid
257.0ms	583×	body	320	valid
85.0ms	649×	body	80	valid
62.0ms	202×	body	160	valid