Details

sample259.0ms

Algorithm

intervals

Results

190.0ms	151×	body	1280	valid
43.0ms	62×	body	640	valid
5.0ms	12×	body	320	valid
3.0ms	26×	body	80	valid
2.0ms	5×	body	160	valid

simplify17.0ms

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: 11.8b

localize24.0ms

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))

rewrite42.0ms

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))
7.0ms	(cos (- lambda1 lambda2))

series199.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (39.0ms)

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

prune401.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize38.0ms

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))

rewrite41.0ms

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×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 87

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
16.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
133.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
93.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify51.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	445	971
1	1607	790
2	5001	789

prune519.0ms

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	(* (- (* (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)))

rewrite53.0ms

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:

16.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
47.0ms	(* (sin lambda1) (sin lambda2))
111.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
101.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify60.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	443	1009
1	1980	806
2	5001	806

prune541.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

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))))

rewrite67.0ms

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:

30.0ms	(* (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))))
11.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

series923.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))
225.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
218.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
222.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

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

prune667.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes415.0ms

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	39	48
1	39	48

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.1s	4690×	body	1280	valid
1.4s	1876×	body	640	valid
261.0ms	567×	body	320	valid
104.0ms	662×	body	80	valid
66.0ms	205×	body	160	valid