Details

Time bar (total: 33.1s)

sample829.0ms

Algorithm
intervals
Results
466.0ms159×body1280valid
110.0ms23×body320valid
91.0ms61×body640valid
6.0ms8×body160valid
2.0ms5×body80valid

simplify52.0ms

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: 17.4b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.7b
(cos (- lambda1 lambda2))

rewrite68.0ms

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*
4×add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 55
Calls
4 calls:
20.0ms
(* (sin phi1) (sin phi2))
15.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
26.0ms
(cos (- lambda1 lambda2))

series648.0ms

Counts
4 → 12
Calls
4 calls:
478.0ms
(* (sin phi1) (sin phi2))
99.0ms
(* (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)))))
46.0ms
(cos (- lambda1 lambda2))

simplify3.9s

Counts
67 → 67
Iterations

Useful iterations: 3 (371.0ms)

IterNodesCost
01111035
11981027
2435893
3686887
4916887
51536887
63401887
done5000887

prune456.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.4b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

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×cos-mult
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add flip-+ unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/
Counts
4 → 72
Calls
4 calls:
15.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
98.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series530.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (sin phi1) (sin phi2))
153.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
287.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
22.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.4s

Counts
84 → 84
Iterations

Useful iterations: 2 (318.0ms)

IterNodesCost
01802014
14841991
218621677
done50001677

prune755.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.3b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite136.0ms

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:
93.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
25.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
7.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
31.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
69.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
24.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.4s

Counts
75 → 75
Iterations

Useful iterations: 2 (292.0ms)

IterNodesCost
01572258
14132201
216011871
done50011871

prune742.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.5b
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
1.8b
(log (exp (* (sin phi1) (sin phi2))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
11×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* cos-mult
5×add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×frac-times log-prod associate-*r/ log-pow
2×flip3-+ frac-add *-commutative flip-+ sin-mult
1×distribute-rgt-in acos-asin exp-prod exp-to-pow distribute-lft-in rem-log-exp associate-*l/ unswap-sqr
Counts
4 → 67
Calls
4 calls:
14.0ms
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
101.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
7.0ms
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
10.0ms
(log (exp (* (sin phi1) (sin phi2))))

series551.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
323.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
26.0ms
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
74.0ms
(log (exp (* (sin phi1) (sin phi2))))

simplify1.5s

Counts
79 → 79
Iterations

Useful iterations: 2 (328.0ms)

IterNodesCost
01712077
14491960
217561650
done50001650

prune651.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 2.2b

regimes938.0ms

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02428
13228
done3228

end0.0ms

sample17.4s

Algorithm
intervals
Results
12.7s4750×body1280valid
3.1s2123×body640valid
684.0ms679×body320valid
132.0ms289×body160valid
81.0ms146×body80valid
65.0ms14×body2560valid