Details

sample247.0ms

Algorithm

intervals

Results

175.0ms	158×	body	1280	valid
41.0ms	67×	body	640	valid
9.0ms	21×	body	320	valid
3.0ms	1×	body	2560	valid
2.0ms	6×	body	160	valid
1.0ms	4×	body	80	valid

simplify15.0ms

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: 15.3b

localize25.0ms

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)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.3b	(cos (- lambda1 lambda2))

rewrite17.0ms

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:

5.0ms	(* (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)))))
5.0ms	(cos (- lambda1 lambda2))

series125.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (sin phi2))
51.0ms	(* (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)))))
18.0ms	(cos (- lambda1 lambda2))

simplify64.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (55.0ms)

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

prune348.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite17.0ms

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:

4.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
5.0ms	(* (sin lambda1) (sin (- lambda2)))
5.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
51.0ms	(* (sin lambda1) (sin (- lambda2)))
48.0ms	(* (sin phi1) (sin phi2))
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify62.0ms

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

prune485.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
3.7b	(log (exp (* (sin lambda1) (sin (- lambda2)))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin (- lambda2)))
5.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
3.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin lambda1) (sin (- lambda2)))
45.0ms	(* (sin phi1) (sin phi2))
18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))))
56.0ms	(log (exp (* (sin lambda1) (sin (- lambda2)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	261	701
1	759	613
2	2145	607
3	5002	607

prune514.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2))))))))) R)
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (sin phi2))
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))))

rewrite17.0ms

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:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2))))))))) R)
5.0ms	(* (sin lambda1) (sin (- lambda2)))
5.0ms	(* (sin phi1) (sin phi2))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2))))))))) R)
52.0ms	(* (sin lambda1) (sin (- lambda2)))
47.0ms	(* (sin phi1) (sin phi2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log1p (expm1 (* (sin lambda1) (sin (- lambda2)))))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	288	1180
1	959	1003
2	2579	1003
3	5001	1003

prune444.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.4b

regimes824.0ms

Accuracy

0% (0.3b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	20
1	32	20

end0.0ms

sample7.7s

Algorithm

intervals

Results

5.6s	4821×	body	1280	valid
1.4s	2018×	body	640	valid
319.0ms	729×	body	320	valid
86.0ms	287×	body	160	valid
48.0ms	14×	body	2560	valid
20.0ms	133×	body	80	valid