Details

sample268.0ms

Algorithm

intervals

Results

199.0ms	162×	body	1280	valid
42.0ms	56×	body	640	valid
8.0ms	18×	body	320	valid
2.0ms	14×	body	80	valid
2.0ms	6×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite32.0ms

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:

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

series173.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (cos phi2))
85.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- 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

prune393.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

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)))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
10×	`prod-diff`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `fma-neg` `diff-log` `associate-*l/` `flip--` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
5.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
14.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series246.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
95.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	450	871
1	1598	711
2	5002	709

prune498.0ms

Filtered

93 candidates to 63 candidates (67.7%)

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

rewrite45.0ms

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

Counts

4 → 94

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
5.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
25.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
92.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
52.0ms	(* (sin lambda1) (sin (- lambda2)))
179.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	534	1109
1	2437	978
2	5002	977

prune669.0ms

Filtered

106 candidates to 79 candidates (74.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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

Counts

4 → 88

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
0.0ms	(fma (sin lambda1) (cos lambda2) (- (* (cos lambda1) (sin lambda2))))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
29.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
97.0ms	(fma (sin lambda1) (cos lambda2) (- (* (cos lambda1) (sin lambda2))))
53.0ms	(* (sin lambda1) (sin (- lambda2)))
188.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	468	1030
1	2136	902
2	5001	900

prune569.0ms

Filtered

100 candidates to 75 candidates (75.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes426.0ms

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	43	43
1	45	43
2	45	43

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.4s	4608×	body	1280	valid
1.4s	1931×	body	640	valid
280.0ms	606×	body	320	valid
88.0ms	659×	body	80	valid
57.0ms	196×	body	160	valid