Details

Time bar (total: 39.1s)

sample604.0ms

Algorithm
intervals
Results
429.0ms164×body1280valid
67.0ms55×body640valid
25.0ms26×body320valid
5.0ms10×body160valid
0.0ms1×body80valid

simplify45.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01719
12619
23319
33519
done3519

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize409.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.3b
(cos (- lambda1 lambda2))

rewrite106.0ms

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*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×cos-sum *-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
77.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
14.0ms
(cos (- lambda1 lambda2))

series294.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
68.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
25.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
50.0ms
(cos (- lambda1 lambda2))

simplify8.1s

Counts
69 → 69
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01211225
12621213
28101035
321211033
436111033
done50011033

prune502.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.5b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
0.2b
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.3b
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-exp-log add-cbrt-cube
17×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity cos-mult
5×associate-*r* associate-*l*
4×add-log-exp
3×*-commutative
2×frac-times associate-*r/ associate-*l/ sin-mult
1×acos-asin unswap-sqr
Counts
4 → 76
Calls
4 calls:
16.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
80.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
75.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series557.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
204.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
215.0ms
(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
42.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify1.6s

Counts
88 → 88
Iterations

Useful iterations: 2 (349.0ms)

IterNodesCost
01672204
14201939
216211567
done50011567

prune752.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b
(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
0.8b
(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
1.3b
(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod cos-mult
5×add-log-exp
4×log-pow
3×acos-asin frac-times log-prod associate-*r/ associate-*r* pow-prod-down prod-exp cbrt-unprod
2×flip3-+ exp-diff frac-add flip-+ sin-mult
1×distribute-rgt-in log-div distribute-lft-in rem-log-exp associate-*l* associate-*l/ *-commutative rem-exp-log
Counts
4 → 63
Calls
4 calls:
88.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms
(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
9.0ms
(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
3.0ms
(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

series463.0ms

Counts
4 → 12
Calls
4 calls:
326.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
72.0ms
(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
42.0ms
(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
23.0ms
(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

simplify1.4s

Counts
75 → 75
Iterations

Useful iterations: 2 (322.0ms)

IterNodesCost
01612258
14182201
216041871
done50001871

prune733.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.5b
(asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))
1.0b
(- (/ PI 2) (asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1 add-exp-log add-cbrt-cube
9×*-un-lft-identity
7×add-cube-cbrt
6×associate-*r* cos-mult add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×frac-times associate-*r/ sin-mult
2×asin-acos flip3-+ frac-add *-commutative flip-+ difference-of-squares
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in times-frac diff-log associate-*l/ flip-- distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 70
Calls
4 calls:
24.0ms
(* (sin lambda1) (sin lambda2))
111.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
4.0ms
(asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))
28.0ms
(- (/ PI 2) (asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (sin lambda1) (sin lambda2))
318.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
24.0ms
(asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))
76.0ms
(- (/ PI 2) (asin (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))

simplify1.5s

Counts
82 → 82
Iterations

Useful iterations: 2 (399.0ms)

IterNodesCost
01892127
14992017
218281809
done50011809

prune610.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 4.1b

regimes2.1s

Accuracy

0% (0.6b remaining)

Error of 4.2b against oracle of 3.5b and baseline of 4.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02630
13430
done3430

end0.0ms

sample18.0s

Algorithm
intervals
Results
13.5s4728×body1280valid
3.0s2153×body640valid
794.0ms718×body320valid
145.0ms269×body160valid
85.0ms7×body2560valid
74.0ms127×body80valid