Details

sample298.0ms

Algorithm

intervals

Results

208.0ms	138×	body	1280	valid
58.0ms	72×	body	640	valid
11.0ms	19×	body	320	valid
4.0ms	23×	body	80	valid
1.0ms	4×	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: 11.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.2b	(sin (- lambda1 lambda2))
2.2b	(cos (- lambda1 lambda2))

rewrite46.0ms

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:

7.0ms	(* (sin phi1) (cos phi2))
16.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series239.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin phi1) (cos phi2))
135.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(sin (- lambda1 lambda2))
26.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	411	1009
1	1289	778
2	5001	776

prune386.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.2b	(cos (- lambda1 lambda2))

rewrite29.0ms

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

Counts

4 → 86

Calls

4 calls:

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

series196.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (cos lambda2))
43.0ms	(* (sin phi1) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	430	792
1	1533	636
2	5001	634

prune561.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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*`
6×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `sin-mult` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

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

series286.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin phi1) (cos phi2))
43.0ms	(* (sin phi1) (cos phi2))
94.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
108.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify51.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	368	836
1	1642	658
2	5001	658

prune544.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
22.2b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
22.2b	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
22.2b	(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×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `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 → 90

Calls

4 calls:

32.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
11.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
12.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

series890.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
217.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
211.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
214.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	312	1499
1	1230	1339
2	5002	1279

prune672.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes409.0ms

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	42	49
1	42	49

end0.0ms

sample9.0s

Algorithm

intervals

Results

6.6s	4656×	body	1280	valid
1.6s	1909×	body	640	valid
305.0ms	564×	body	320	valid
118.0ms	659×	body	80	valid
74.0ms	212×	body	160	valid