Details

sample359.0ms

Algorithm

intervals

Results

224.0ms	114×	body	1280	valid
73.0ms	74×	body	640	valid
17.0ms	25×	body	320	valid
10.0ms	24×	body	80	valid
9.0ms	19×	body	160	valid

simplify18.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b	(sin (- lambda1 lambda2))
4.0b	(cos (- lambda1 lambda2))

rewrite81.0ms

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:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms	(sin (- lambda1 lambda2))
51.0ms	(cos (- lambda1 lambda2))

series254.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
167.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
41.0ms	(sin (- lambda1 lambda2))
33.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts: 52 → 52

prune409.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.9b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b	(cos (- lambda1 lambda2))

rewrite53.0ms

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×	`cos-diff` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 49

Calls

4 calls:

13.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
20.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(cos (- lambda1 lambda2))

series295.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin lambda1) (cos lambda2))
15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
175.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
33.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts: 61 → 61

prune508.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos 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)))
0.8b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

rewrite81.0ms

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`
4×	`associate-+r+`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sin-neg` `sum-log` `distribute-rgt-neg-out` `sin-cos-mult` `flip-+` `sin-mult`

Counts

4 → 61

Calls

4 calls:

24.0ms	(* (sin lambda1) (cos 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)))))))
33.0ms	(* (sin lambda1) (sin (- lambda2)))
20.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin lambda1) (cos lambda2))
39.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
69.0ms	(* (sin lambda1) (sin (- lambda2)))
397.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify1.9s

Counts: 73 → 73

prune671.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize102.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1)))
0.6b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
0.6b	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
1.4b	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

rewrite773.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

579.0ms	(* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1)))
41.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
60.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
87.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

series3.2s

Counts

4 → 12

Calls

4 calls:

682.0ms	(* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1)))
1.9s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
330.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
344.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

simplify637.0ms

Counts: 111 → 111

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

regimes1.0s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.5s

end0.0ms

sample11.4s

Algorithm

intervals

Results

6.4s	3568×	body	1280	valid
2.7s	2328×	body	640	valid
955.0ms	920×	body	320	valid
488.0ms	704×	body	80	valid
246.0ms	480×	body	160	valid