Details

sample180.0ms

Algorithm

intervals

Results

119.0ms	123×	body	1280	valid
30.0ms	59×	body	640	valid
9.0ms	27×	body	320	valid
5.0ms	21×	body	160	valid
3.0ms	26×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	23	12
2	23	12

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b	(sin (- lambda1 lambda2))
4.4b	(cos (- lambda1 lambda2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`prod-diff`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum` `sin-sum`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cos-diff` `fma-def`
2×	`sub-neg` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 69

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series150.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
101.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

simplify69.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	365	1011
1	800	787
2	2597	784
3	5002	735

prune311.0ms

Filtered

81 candidates to 55 candidates (67.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.4b	(cos (- lambda1 lambda2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

13.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(cos (- lambda1 lambda2))

series275.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
16.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	458	1104
1	1634	916
2	5001	912

prune451.0ms

Filtered

84 candidates to 65 candidates (77.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `sin-mult`

Counts

4 → 72

Calls

4 calls:

15.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
4.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
19.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
46.0ms	(* (sin lambda1) (sin lambda2))
216.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	406	1066
1	1792	923
2	5002	913

prune495.0ms

Filtered

84 candidates to 67 candidates (79.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos phi1) 3)
0.4b	(pow (cos phi2) 3)
0.5b	(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
1.3b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow` `cube-prod`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`fma-udef`

Counts

4 → 85

Calls

4 calls:

1.0ms	(pow (cos phi1) 3)
1.0ms	(pow (cos phi2) 3)
1.0ms	(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (cos phi1) 3)
28.0ms	(pow (cos phi2) 3)
108.0ms	(pow (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) 3)
214.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (- (cos phi1)))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	320	616
1	1404	530
2	5001	516

prune506.0ms

Filtered

97 candidates to 56 candidates (57.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes492.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	49
1	40	49

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.2s	3539×	body	1280	valid
1.2s	2380×	body	640	valid
330.0ms	924×	body	320	valid
101.0ms	433×	body	160	valid
79.0ms	724×	body	80	valid