Details

Time bar (total: 23.3s)

sample289.0ms

Algorithm
intervals
Results
127.0ms110×body1280valid
68.0ms79×body640valid
65.0ms29×body320valid
5.0ms16×body160valid
3.0ms22×body80valid

simplify27.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b
(sin (- lambda1 lambda2))
3.4b
(cos (- lambda1 lambda2))

rewrite121.0ms

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:
56.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
37.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms
(sin (- lambda1 lambda2))
14.0ms
(cos (- lambda1 lambda2))

series315.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
193.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms
(sin (- lambda1 lambda2))
33.0ms
(cos (- lambda1 lambda2))

simplify1.3s

Counts
67 → 67

prune461.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b
(cos (- lambda1 lambda2))

rewrite165.0ms

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 cos-diff sub-neg distribute-lft-in
2×cos-sum associate-+r+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative flip3-- flip3-+ sum-log sin-cos-mult flip-- flip-+
Counts
4 → 66
Calls
4 calls:
25.0ms
(* (sin lambda1) (cos lambda2))
102.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms
(cos (- lambda1 lambda2))

series518.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (sin lambda1) (cos lambda2))
212.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
199.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
35.0ms
(cos (- lambda1 lambda2))

simplify766.0ms

Counts
78 → 78

prune687.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×+-commutative flip3-- flip3-+ sum-log sin-cos-mult flip-- flip-+ sin-mult
Counts
4 → 73
Calls
4 calls:
19.0ms
(* (sin lambda1) (cos lambda2))
120.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
24.0ms
(* (sin lambda1) (sin lambda2))
10.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series587.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin lambda1) (cos lambda2))
225.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
84.0ms
(* (sin lambda1) (sin lambda2))
213.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify787.0ms

Counts
85 → 85

prune651.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
0.4b
(pow (cos phi1) 3)
0.7b
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
1.9b
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
10×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt add-log-exp
6×pow-unpow
4×unpow-prod-down pow-pow cube-prod pow-exp rem-cube-cbrt
3×pow-prod-down prod-exp cbrt-unprod
2×cube-mult pow-to-exp unpow3 sqr-pow
1×+-commutative cube-div sub-neg flip3-- flip3-+ diff-log associate-*l/ sum-log cos-mult sum-cubes flip-- flip-+ distribute-lft-out
Counts
4 → 74
Calls
4 calls:
33.0ms
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
4.0ms
(pow (cos phi1) 3)
29.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
56.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series678.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(+ (pow (cos phi1) 3) (pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3))
32.0ms
(pow (cos phi1) 3)
177.0ms
(pow (* (* (cos lambda1) (cos lambda2)) (cos phi2)) 3)
184.0ms
(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify1.3s

Counts
86 → 86

prune724.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes800.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.9s

end0.0ms

sample10.6s

Algorithm
intervals
Results
5.5s3516×body1280valid
3.3s2346×body640valid
726.0ms988×body320valid
404.0ms740×body80valid
188.0ms410×body160valid