Details

sample365.0ms

Algorithm

intervals

Results

231.0ms	118×	body	1280	valid
77.0ms	71×	body	640	valid
22.0ms	35×	body	320	valid
4.0ms	23×	body	80	valid
4.0ms	9×	body	160	valid

simplify19.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.2b	(cos (- lambda1 lambda2))
4.3b	(sin (- lambda1 lambda2))

rewrite109.0ms

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:

52.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
10.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

series308.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
153.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
31.0ms	(cos (- lambda1 lambda2))
40.0ms	(sin (- lambda1 lambda2))

simplify1.2s

Counts: 67 → 67

prune417.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.5b	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
4.3b	(sin (- lambda1 lambda2))

rewrite106.0ms

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

Counts

4 → 50

Calls

4 calls:

64.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
18.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms	(sin (- lambda1 lambda2))

series331.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
30.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
193.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
26.0ms	(sin (- lambda1 lambda2))

simplify2.4s

Counts: 62 → 62

prune443.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

37.0ms	(* (* (cos phi2) (sin lambda1)) (cos lambda2))
1.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
19.0ms	(* (cos phi2) (sin lambda1))
9.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (* (cos phi2) (sin lambda1)) (cos lambda2))
47.0ms	(atan2 (+ (* (* (cos phi2) (sin lambda1)) (cos lambda2)) (* (cos phi2) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
78.0ms	(* (cos phi2) (sin lambda1))
204.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify864.0ms

Counts: 66 → 66

prune621.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

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

rewrite467.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

384.0ms	(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
11.0ms	(pow (cos phi1) 3)
34.0ms	(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
34.0ms	(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)) (+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))) (* (cos phi1) (cos phi1))))
55.0ms	(pow (cos phi1) 3)
164.0ms	(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
201.0ms	(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify2.4s

Counts: 117 → 117

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes805.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.5s

end0.0ms

sample12.1s

Algorithm

intervals

Results

6.4s	3601×	body	1280	valid
3.7s	2296×	body	640	valid
682.0ms	941×	body	320	valid
608.0ms	416×	body	160	valid
124.0ms	746×	body	80	valid