Details

sample178.0ms

Algorithm

intervals

Results

104.0ms	109×	body	1280	valid
39.0ms	71×	body	640	valid
11.0ms	33×	body	320	valid
4.0ms	16×	body	160	valid
3.0ms	27×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	21	12
2	21	12

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(sin (- lambda1 lambda2))
3.2b	(cos (- lambda1 lambda2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `sin-sum` `add-cbrt-cube` `add-log-exp`
4×	`sub-neg`
3×	`distribute-rgt-in` `cos-diff` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

7.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
9.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series193.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
100.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify73.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	249	435
1	795	394
2	2920	393
3	5001	393

prune300.0ms

Filtered

67 candidates to 49 candidates (73.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b	(cos (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`cos-diff` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cos-sum` `associate-+r+` `distribute-rgt-neg-out`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `associate-r` `sin-neg` `sum-log` `*-commutative` `flip-+`

Counts

4 → 49

Calls

4 calls:

1.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

series222.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
84.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
102.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify83.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	288	644
1	866	548
2	3228	547
3	5002	547

prune351.0ms

Filtered

61 candidates to 48 candidates (78.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `add-log-exp`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-+r+` `*-commutative` `distribute-rgt-neg-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sin-neg` `sum-log` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
6.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series373.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
86.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
221.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	343	858
1	1180	723
2	5002	722

prune390.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos phi1) 3)
0.4b	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
0.7b	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
1.2b	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
18×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac` `frac-add` `cos-mult`
14×	`associate-*r/`
13×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`frac-times` `pow-unpow` `flip3-+` `flip-+` `add-log-exp`
5×	`flip3--` `flip--` `associate-/l*`
4×	`unpow-prod-down` `cube-prod` `sum-cubes` `sin-mult` `distribute-lft-out`
3×	`cube-div` `pow-pow` `associate-l/` `pow-exp` `associate-/r` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `unpow3` `associate--l+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`

Counts

4 → 112

Calls

4 calls:

3.0ms	(pow (cos phi1) 3)
30.0ms	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
9.0ms	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
12.0ms	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series4.2s

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (cos phi1) 3)
3.7s	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
194.0ms	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
215.0ms	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify54.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1082	4134
1	5002	3888

prune875.0ms

Filtered

124 candidates to 90 candidates (72.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes547.0ms

Accuracy

0% (0.2b 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	49	54
1	49	54

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.2s	3565×	body	1280	valid
1.2s	2349×	body	640	valid
309.0ms	939×	body	320	valid
95.0ms	416×	body	160	valid
79.0ms	730×	body	80	valid
2.0ms	1×	body	2560	valid