Details

sample265.0ms

Algorithm

intervals

Results

186.0ms	154×	body	1280	valid
48.0ms	71×	body	640	valid
12.0ms	27×	body	320	valid
1.0ms	2×	body	160	valid
0.0ms	2×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.3b	(cos (- lambda1 lambda2))

rewrite35.0ms

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:

11.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
13.0ms	(cos (- lambda1 lambda2))

series116.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (sin phi2))
42.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
16.0ms	(cos (- lambda1 lambda2))

simplify69.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (56.0ms)

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

prune575.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite39.0ms

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:

11.0ms	(* (sin phi1) (sin phi2))
18.0ms	(* (sin lambda1) (sin (- lambda2)))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (sin phi2))
48.0ms	(* (sin lambda1) (sin (- lambda2)))
69.0ms	(* (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)))))))

simplify64.0ms

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

prune890.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2)))))))))

rewrite40.0ms

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:

12.0ms	(* (sin phi1) (sin phi2))
17.0ms	(* (sin lambda1) (sin (- lambda2)))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2)))))))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (sin phi2))
47.0ms	(* (sin lambda1) (sin (- lambda2)))
72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))) R)
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2)))))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	288	1180
1	924	1003
2	2500	1003
3	5001	1003

prune933.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))))) R)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2)))))))))
0.6b	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

15.0ms	(* (sin lambda1) (sin (- lambda2)))
18.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2)))))))))
1.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))))

series198.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin lambda1) (sin (- lambda2)))
75.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2)))))))))
54.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (expm1 (log1p (* (sin lambda1) (sin (- lambda2))))))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	257	1666
1	709	1422
2	1996	1404
3	5001	1402

prune869.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.8b

regimes2.3s

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	24
1	36	24

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.9s	4786×	body	1280	valid
1.5s	2166×	body	640	valid
309.0ms	641×	body	320	valid
76.0ms	257×	body	160	valid
29.0ms	144×	body	80	valid
26.0ms	8×	body	2560	valid