Details

sample259.0ms

Algorithm

intervals

Results

185.0ms	163×	body	1280	valid
49.0ms	67×	body	640	valid
6.0ms	16×	body	320	valid
2.0ms	7×	body	160	valid
0.0ms	3×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.6b	(cos (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 72

Calls

4 calls:

4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
7.0ms	(cos (- lambda1 lambda2))

series123.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (sin phi2))
43.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
22.0ms	(cos (- lambda1 lambda2))

simplify63.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	323	995
1	789	819
2	2620	818
3	5002	793

prune355.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin (- lambda2)))
4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin lambda1) (sin (- lambda2)))
48.0ms	(* (sin phi1) (sin phi2))
73.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	292	1092
1	949	951
2	2618	927
3	5002	927

prune492.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.1b	(acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin (- lambda2)))
4.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0ms	(acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series196.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin lambda1) (sin (- lambda2)))
44.0ms	(* (sin phi1) (sin phi2))
77.0ms	(* (acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
18.0ms	(acos (+ (log1p (expm1 (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	291	1180
1	953	1027
2	2628	1003
3	5001	1003

prune539.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3)))))) R)
0.3b	(pow (* (sin lambda1) (sin (* -1 lambda2))) 3)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3))))))
25.1b	(cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `mul-1-neg` `pow1/3` `cube-neg` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3)))))) R)
4.0ms	(pow (* (sin lambda1) (sin (* -1 lambda2))) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3))))))
3.0ms	(cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3))

series221.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3)))))) R)
75.0ms	(pow (* (sin lambda1) (sin (* -1 lambda2))) 3)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3))))))
56.0ms	(cbrt (pow (* (sin lambda1) (sin (* -1 lambda2))) 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	305	1246
1	1128	1101
2	5001	1088

prune463.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.6b

regimes1.1s

Accuracy

0% (0.3b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	30
1	38	30

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.0s	4779×	body	1280	valid
1.5s	2141×	body	640	valid
305.0ms	681×	body	320	valid
78.0ms	270×	body	160	valid
19.0ms	128×	body	80	valid
17.0ms	5×	body	2560	valid