Details

Time bar (total: 9.0s)

sample169.0ms

Algorithm
intervals
Results
102.0ms112×body1280valid
35.0ms76×body640valid
10.0ms30×body320valid
3.0ms28×body80valid
2.0ms10×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12112
22112
done2112

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b
(sin (- lambda1 lambda2))
3.4b
(cos (- lambda1 lambda2))

rewrite58.0ms

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:
27.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms
(sin (- lambda1 lambda2))
10.0ms
(cos (- lambda1 lambda2))

series204.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (cos phi2) (sin (- lambda1 lambda2)))
105.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify72.0ms

Counts
67 → 67
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0249435
1795394
22920393
35001393
done5001393

prune250.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.3b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
3.4b
(sin (- lambda1 lambda2))

rewrite59.0ms

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×sin-sum *-commutative sin-mult
1×+-commutative sub-neg flip3-+ associate-*l/ sum-log sin-diff flip-+ unswap-sqr
Counts
4 → 59
Calls
4 calls:
28.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
11.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
10.0ms
(sin (- lambda1 lambda2))

series282.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
48.0ms
(* (sin lambda1) (sin lambda2))
128.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms
(sin (- lambda1 lambda2))

simplify39.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0289472
11273405
25001404
done5001404

prune346.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.3b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite50.0ms

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 sin-mult
1×+-commutative flip3-+ associate-*l/ sum-log flip-+ unswap-sqr
Counts
4 → 56
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
28.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
11.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
84.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
49.0ms
(* (sin lambda1) (sin lambda2))
130.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify41.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0309736
11280625
25002624
done5002624

prune362.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
0.3b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity add-log-exp
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
4×log-prod log-pow
3×associate-*r* associate-*l*
2×exp-sum sum-log rem-exp-log
1×+-commutative flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
15.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
11.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))))
44.0ms
(* (sin lambda1) (sin lambda2))
128.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
132.0ms
(log (exp (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))

simplify100.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0248604
1925534
23624532
35001532
done5001532

prune355.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes453.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03727
13727
done3727

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.1s3528×body1280valid
1.2s2384×body640valid
318.0ms947×body320valid
95.0ms422×body160valid
74.0ms719×body80valid