Details

Time bar (total: 30.0s)

sample337.0ms

Algorithm
intervals
Results
169.0ms110×body1280valid
69.0ms79×body640valid
53.0ms16×body160valid
17.0ms29×body320valid
4.0ms22×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01420
12020
22120
done2120

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize84.0ms

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))

rewrite126.0ms

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:
65.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
21.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms
(sin (- lambda1 lambda2))
15.0ms
(cos (- lambda1 lambda2))

series369.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
178.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
41.0ms
(sin (- lambda1 lambda2))
35.0ms
(cos (- lambda1 lambda2))

simplify3.7s

Counts
67 → 67
Iterations

Useful iterations: 3 (564.0ms)

IterNodesCost
0112733
1247711
2658647
31474645
43013645
done5000645

prune428.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 1.2b

localize89.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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
3×cos-diff
2×cos-sum associate-+r+ *-commutative sin-cos-mult
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in flip3-+ associate-*l/ sum-log flip-+ unswap-sqr
Counts
4 → 61
Calls
4 calls:
26.0ms
(* (sin lambda1) (cos lambda2))
55.0ms
(* (* (sin lambda1) (cos lambda2)) (cos phi2))
11.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(cos (- lambda1 lambda2))

series353.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (sin lambda1) (cos lambda2))
121.0ms
(* (* (sin lambda1) (cos lambda2)) (cos phi2))
153.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))

simplify4.2s

Counts
73 → 73
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
0133773
1310752
2939662
32592654
done5000654

prune583.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
3×*-commutative
2×sin-cos-mult unswap-sqr
1×+-commutative flip3-+ associate-*l/ sum-log flip-+ sin-mult
Counts
4 → 68
Calls
4 calls:
17.0ms
(* (sin lambda1) (cos lambda2))
19.0ms
(* (sin lambda1) (sin lambda2))
31.0ms
(* (* (sin lambda1) (cos lambda2)) (cos phi2))
13.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series502.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (sin lambda1) (cos lambda2))
101.0ms
(* (sin lambda1) (sin lambda2))
105.0ms
(* (* (sin lambda1) (cos lambda2)) (cos phi2))
245.0ms
(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify3.4s

Counts
80 → 80
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
0135830
1329807
21073703
33495697
done5001697

prune788.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

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-*r/ sum-log cos-mult sum-cubes flip-- flip-+ distribute-lft-out
Counts
4 → 74
Calls
4 calls:
28.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3))
4.0ms
(pow (cos phi1) 3)
23.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
49.0ms
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

series714.0ms

Counts
4 → 12
Calls
4 calls:
326.0ms
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3))
54.0ms
(pow (cos phi1) 3)
155.0ms
(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
179.0ms
(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify1.2s

Counts
86 → 86
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01461188
13801047
21404935
done5001934

prune682.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes799.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03888
15388
done5388

end0.0ms

sample11.1s

Algorithm
intervals
Results
6.9s3516×body1280valid
2.8s2346×body640valid
588.0ms988×body320valid
160.0ms740×body80valid
148.0ms410×body160valid