Details

sample296.0ms

Algorithm

intervals

Results

193.0ms	125×	body	1280	valid
52.0ms	68×	body	640	valid
12.0ms	25×	body	320	valid
6.0ms	17×	body	160	valid
3.0ms	21×	body	80	valid

simplify3.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize65.0ms

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))))
2.9b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
10.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))
17.0ms	(sin (- lambda1 lambda2))

series264.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
177.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
34.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

simplify101.0ms

Counts: 52 → 52

prune392.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.9b	(cos (- lambda1 lambda2))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
89.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
9.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms	(cos (- lambda1 lambda2))

series434.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
209.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
169.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
31.0ms	(cos (- lambda1 lambda2))

simplify104.0ms

Counts: 66 → 66

prune502.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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))))))
23.0ms	(* (sin lambda1) (sin lambda2))
106.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
16.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
75.0ms	(* (sin lambda1) (sin lambda2))
225.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
360.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify64.0ms

Counts: 75 → 75

prune542.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
1.0b	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

24.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
3.0ms	(pow (cos phi1) 3)
23.0ms	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
63.0ms	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series2.4s

Counts

4 → 12

Calls

4 calls:

1.8s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
34.0ms	(pow (cos phi1) 3)
310.0ms	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
263.0ms	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify109.0ms

Counts: 87 → 87

prune720.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes909.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify132.0ms

end0.0ms

sample11.4s

Algorithm

intervals

Results

6.9s	3522×	body	1280	valid
3.1s	2401×	body	640	valid
506.0ms	915×	body	320	valid
232.0ms	734×	body	80	valid
149.0ms	428×	body	160	valid