Details

Time bar (total: 27.1s)

sample697.0ms

Algorithm
intervals
Results
472.0ms152×body1280valid
96.0ms70×body640valid
25.0ms25×body320valid
5.0ms9×body160valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
01719
12718
23818
34318
done4318

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log cos-sum add-cbrt-cube
9×prod-diff
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cos-diff
2×*-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 74
Calls
4 calls:
56.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
16.0ms
(cos (- lambda1 lambda2))

series291.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
84.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
12.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
38.0ms
(cos (- lambda1 lambda2))

simplify8.1s

Counts
86 → 86
Iterations

Useful iterations: done (8.1s)

IterNodesCost
01961763
13771589
29621325
323201281
438081190
done50011144

prune539.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.3b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×pow-prod-down prod-exp cbrt-unprod
8×add-cube-cbrt *-un-lft-identity
7×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative sin-mult
2×cos-mult unswap-sqr
1×acos-asin frac-times associate-*r/ associate-*l/
Counts
4 → 78
Calls
4 calls:
25.0ms
(* (sin lambda1) (sin lambda2))
102.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
15.0ms
(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (sin lambda1) (sin lambda2))
168.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
116.0ms
(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
21.0ms
(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify4.5s

Counts
90 → 90
Iterations

Useful iterations: 2 (257.0ms)

IterNodesCost
01432023
13031773
210161429
340291429
done50001429

prune811.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.2b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 75
Calls
4 calls:
19.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
30.0ms
(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
1.0ms
(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
10.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series323.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
96.0ms
(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
19.0ms
(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
95.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify3.7s

Counts
87 → 87
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01382024
12911556
28501310
335861309
done50011305

prune823.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 4.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))))))) R)
0.3b
(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))))))
1.2b
(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2)))))))
1.6b
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2)))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 66
Calls
4 calls:
18.0ms
(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))))))) R)
2.0ms
(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))))))
3.0ms
(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2)))))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2)))))

series167.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))))))) R)
50.0ms
(exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2))))))
19.0ms
(log (exp (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2)))))))
26.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (cos phi1) (cos phi2)))))

simplify5.5s

Counts
78 → 78
Iterations

Useful iterations: 5 (1.1s)

IterNodesCost
01002330
11522225
22911971
35141971
48231971
516941969
649561969
done50001969

prune658.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 4.2b

regimes38.0ms