Details

sample163.0ms

Algorithm

intervals

Results

94.0ms	105×	body	1280	valid
39.0ms	81×	body	640	valid
10.0ms	33×	body	320	valid
3.0ms	14×	body	160	valid
2.0ms	23×	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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize20.0ms

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))))
2.5b	(sin (- lambda1 lambda2))
2.6b	(cos (- lambda1 lambda2))

rewrite22.0ms

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)))))
6.0ms	(+ (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:

9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify67.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (59.0ms)

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

prune451.0ms

Filtered

81 candidates to 55 candidates (67.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.6b

localize28.0ms

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))))
2.6b	(cos (- lambda1 lambda2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

17.0ms	(* (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))

series268.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
12.0ms	(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))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	427	1128
1	1340	942
2	5001	940

prune451.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u`
3×	`fma-def`
2×	`sub-neg` `associate-+r+` `associate-r/` `prod-diff` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `sin-mult`

Counts

4 → 76

Calls

4 calls:

17.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms	(* (sin 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))))))
5.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
48.0ms	(* (sin lambda1) (sin lambda2))
17.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
219.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	374	1090
1	1513	949
2	5002	941

prune458.0ms

Filtered

88 candidates to 68 candidates (77.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
0.6b	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
0.8b	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-udef`
2×	`exp-sum`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 51

Calls

4 calls:

1.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
0.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
1.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

series699.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
14.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))))
201.0ms	(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
201.0ms	(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

simplify43.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	175	956
1	400	822
2	1295	817
3	5001	817

prune329.0ms

Filtered

63 candidates to 49 candidates (77.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes469.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	22
1	27	22

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.1s	3506×	body	1280	valid
1.2s	2356×	body	640	valid
337.0ms	972×	body	320	valid
91.0ms	424×	body	160	valid
78.0ms	742×	body	80	valid