Details

sample359.0ms

Algorithm

intervals

Results

209.0ms	106×	body	1280	valid
77.0ms	76×	body	640	valid
23.0ms	40×	body	320	valid
15.0ms	25×	body	80	valid
5.0ms	9×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b	(cos (- lambda1 lambda2))
3.7b	(sin (- lambda1 lambda2))

rewrite69.0ms

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)))))
40.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms	(cos (- lambda1 lambda2))
12.0ms	(sin (- lambda1 lambda2))

series254.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
179.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
27.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

simplify1.7s

Counts: 52 → 52

prune415.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b	(cos (- lambda1 lambda2))

rewrite52.0ms

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)))))
17.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))

series276.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin lambda1) (cos lambda2))
30.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
148.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
28.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts: 61 → 61

prune535.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

13.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
50.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
21.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin lambda1) (sin lambda2))
34.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
326.0ms	(+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
189.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify773.0ms

Counts: 64 → 64

prune647.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (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))))
0.3b	(pow (cos phi1) 3)
0.7b	(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
0.9b	(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite517.0ms

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:

392.0ms	(/ (+ (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))))
7.0ms	(pow (cos phi1) 3)
45.0ms	(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
65.0ms	(- (* (* (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))))
36.0ms	(pow (cos phi1) 3)
206.0ms	(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
231.0ms	(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify2.5s

Counts: 117 → 117

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes1.0s

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.2s

end0.0ms

sample10.5s

Algorithm

intervals

Results

5.9s	3565×	body	1280	valid
2.8s	2327×	body	640	valid
641.0ms	976×	body	320	valid
465.0ms	710×	body	80	valid
222.0ms	422×	body	160	valid