Details

Time bar (total: 19.3s)

sample508.0ms

Algorithm
intervals
Results
325.0ms152×body1280valid
67.0ms70×body640valid
18.0ms25×body320valid
3.0ms9×body160valid

simplify24.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01719
12619
23319
33519
done3519

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b
(cos (- lambda1 lambda2))

rewrite41.0ms

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:
14.0ms
(* (sin phi1) (sin phi2))
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))

series190.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (sin phi1) (sin phi2))
55.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
44.0ms
(cos (- lambda1 lambda2))

simplify4.1s

Counts
67 → 67
Iterations

Useful iterations: 3 (357.0ms)

IterNodesCost
01111035
11981027
2435893
3686887
4916887
51536887
63401887
done5000887

prune526.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 64
Calls
4 calls:
20.0ms
(* (sin lambda1) (sin lambda2))
23.0ms
(* (sin phi1) (sin phi2))
16.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series274.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (sin lambda1) (sin lambda2))
80.0ms
(* (sin phi1) (sin phi2))
105.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.3s

Counts
76 → 76
Iterations

Useful iterations: 2 (134.0ms)

IterNodesCost
01331410
12591401
26661173
311761173
415731173
524901173
done50011173

prune751.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 4.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
3.6b
(log (exp (* (sin lambda1) (sin lambda2))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
5×add-log-exp
3×log-prod log-pow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin exp-prod exp-to-pow rem-log-exp sin-mult
Counts
4 → 59
Calls
4 calls:
40.0ms
(* (sin phi1) (sin phi2))
14.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
9.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (sin phi1) (sin phi2))
128.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
31.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
85.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

simplify3.0s

Counts
71 → 71
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01201473
12181370
25431146
39371146
412591146
525241146
done50011144

prune669.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (sin lambda1) (sin lambda2)) 3)
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
1.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
27.7b
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×pow1 add-exp-log add-cbrt-cube
8×cbrt-prod add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod sin-mult rem-cube-cbrt sqr-pow
1×acos-asin pow-to-exp cbrt-div pow1/3 *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 67
Calls
4 calls:
12.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
14.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
5.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
9.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series295.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
132.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
25.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
65.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify3.4s

Counts
79 → 79
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01341690
12851474
28321254
334251254
done50011250

prune510.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 4.2b

regimes24.0ms