Details

sample270.0ms

Algorithm

intervals

Results

200.0ms	151×	body	1280	valid
44.0ms	62×	body	640	valid
5.0ms	12×	body	320	valid
3.0ms	26×	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: 11.8b

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)))
3.2b	(sin (- lambda1 lambda2))
3.2b	(cos (- lambda1 lambda2))

rewrite33.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

11.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series199.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
23.0ms	(cos (- lambda1 lambda2))

simplify106.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune329.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize34.0ms

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))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(cos (- lambda1 lambda2))

rewrite39.0ms

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` `associate-l/` `-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
17.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series482.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (cos phi2))
328.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	352	681
1	1623	581
2	5001	580

prune460.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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

rewrite48.0ms

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

Counts

4 → 89

Calls

4 calls:

13.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
44.0ms	(* (sin lambda1) (sin lambda2))
108.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify63.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	466	977
1	2206	771
2	5002	771

prune535.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
18.5b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
18.5b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
18.5b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
22×	`sin-cos-mult` `sin-mult`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

31.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
13.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

series911.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
219.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
221.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
220.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	304	1411
1	1196	1254
2	5001	1194

prune614.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes411.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	49
1	42	49

end0.0ms

sample8.1s

Algorithm

intervals

Results

6.0s	4690×	body	1280	valid
1.4s	1876×	body	640	valid
260.0ms	567×	body	320	valid
91.0ms	662×	body	80	valid
56.0ms	205×	body	160	valid