Details

Time bar (total: 43.4s)

sample934.0ms

Algorithm
intervals
Results
446.0ms15×body320valid
333.0ms150×body1280valid
114.0ms59×body640valid
7.0ms12×body160valid
5.0ms20×body80valid

simplify123.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
12724
24624
37124
47224
done7224

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b
(cos (- lambda1 lambda2))
4.0b
(sin (- lambda1 lambda2))

rewrite144.0ms

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×sub-neg cos-sum sin-sum *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 60
Calls
4 calls:
43.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
56.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms
(cos (- lambda1 lambda2))
22.0ms
(sin (- lambda1 lambda2))

series336.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
145.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms
(cos (- lambda1 lambda2))
47.0ms
(sin (- lambda1 lambda2))

simplify7.2s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0116760
1258748
2816644
32194642
43730642
done5000642

prune575.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos phi2))
0.2b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b
(cos (- lambda1 lambda2))

rewrite164.0ms

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*
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×cos-diff associate-*l/ *-commutative
2×cos-sum sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in flip--
Counts
4 → 70
Calls
4 calls:
24.0ms
(* (sin phi1) (cos phi2))
63.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
35.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
38.0ms
(cos (- lambda1 lambda2))

series527.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (sin phi1) (cos phi2))
237.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
175.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
30.0ms
(cos (- lambda1 lambda2))

simplify3.4s

Counts
82 → 82
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
01311039
13211026
21110888
33637880
done5001880

prune646.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin lambda1) (sin (- lambda2)))
0.2b
(* (sin phi1) (cos phi2))
0.2b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-exp-log add-cbrt-cube
12×associate-*r*
11×add-cube-cbrt *-un-lft-identity
10×associate-*l*
6×pow-prod-down prod-exp sin-cos-mult cbrt-unprod
5×sin-mult
4×frac-times associate-*r/ cos-mult *-commutative add-log-exp
3×flip3-- associate-*l/ flip-- unswap-sqr
2×distribute-rgt-in sub-neg distribute-lft-in frac-sub sub-div
1×sin-neg distribute-rgt-neg-out
Counts
4 → 90
Calls
4 calls:
17.0ms
(* (sin lambda1) (sin (- lambda2)))
16.0ms
(* (sin phi1) (cos phi2))
97.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
144.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

series725.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (sin lambda1) (sin (- lambda2)))
87.0ms
(* (sin phi1) (cos phi2))
215.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
318.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))

simplify1.4s

Counts
102 → 102
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01961702
14941655
218901417
done50001384

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda2) (sin lambda2))
0.2b
(* (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda1) (* (* (sin lambda2) (sin lambda2)) (sin lambda1)))) (* (sin phi1) (cos phi2)))
0.3b
(/ (* (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda1) (* (* (sin lambda2) (sin lambda2)) (sin lambda1)))) (* (sin phi1) (cos phi2))) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
0.4b
(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

rewrite817.0ms

Algorithm
rewrite-expression-head
Rules
55×pow1
43×associate-*l/
32×add-exp-log add-cbrt-cube
31×associate-*r/
29×cos-mult
22×sin-mult
21×pow-prod-down
19×frac-times
16×sin-cos-mult
15×prod-exp cbrt-unprod associate-/l/
13×add-sqr-sqrt
12×frac-sub
11×add-cube-cbrt *-un-lft-identity
8×sub-div
7×associate-*l*
5×associate-*r* pow-sqr pow-prod-up
4×flip3-- swap-sqr flip-- add-log-exp
3×cbrt-undiv times-frac pow-plus div-exp associate-/r* associate-/r/ *-commutative
2×pow2
1×frac-2neg flip3-+ frac-add clear-num flip-+ sqr-sin div-inv associate-/l* unswap-sqr
Counts
4 → 138
Calls
4 calls:
26.0ms
(* (sin lambda2) (sin lambda2))
410.0ms
(* (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda1) (* (* (sin lambda2) (sin lambda2)) (sin lambda1)))) (* (sin phi1) (cos phi2)))
301.0ms
(/ (* (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda1) (* (* (sin lambda2) (sin lambda2)) (sin lambda1)))) (* (sin phi1) (cos phi2))) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
71.0ms
(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (sin lambda2) (sin lambda2))
329.0ms
(* (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda1) (* (* (sin lambda2) (sin lambda2)) (sin lambda1)))) (* (sin phi1) (cos phi2)))
648.0ms
(/ (* (- (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (sin lambda1) (* (* (sin lambda2) (sin lambda2)) (sin lambda1)))) (* (sin phi1) (cos phi2))) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))
82.0ms
(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

simplify1.9s

Counts
150 → 150
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02654289
17613703
229553004
done50002996

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03263
14363
done4363

end0.0ms

sample20.4s

Algorithm
intervals
Results
15.3s4584×body1280valid
3.5s1973×body640valid
588.0ms593×body320valid
230.0ms654×body80valid
116.0ms196×body160valid