Details

Time bar (total: 14.0s)

sample756.0ms

Algorithm
intervals
Results
531.0ms162×body1280valid
89.0ms63×body640valid
17.0ms18×body320valid
7.0msbody160valid
2.0msbody80valid

simplify90.0ms

Counts
1 → 1
Iterations
IterNodes
done46
446
344
238
127
017

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi2) (sin phi1))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.5b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.2b
(cos (- lambda1 lambda2))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×cos-sum
prod-diff
pow1 add-cbrt-cube add-exp-log
associate-*r* associate-*l*
expm1-log1p-u log1p-expm1-u add-log-exp
pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
acos-asin cos-diff sub-neg sin-mult
Counts
4 → 72
Calls
4 calls:
22.0ms
(* (sin phi2) (sin phi1))
7.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
23.0ms
(cos (- lambda1 lambda2))

series170.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (sin phi2) (sin phi1))
34.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
12.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
29.0ms
(cos (- lambda1 lambda2))

simplify3.2s

Counts
84 → 84
Iterations
IterNodes
done5001
34440
2844
1327
0184

prune820.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.2b
(* (sin lambda1) (sin lambda2))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.5b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
associate-*r* associate-*l*
expm1-log1p-u log1p-expm1-u add-log-exp
pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
acos-asin fma-udef sin-mult
Counts
4 → 61
Calls
4 calls:
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
25.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series572.0ms

Counts
4 → 12
Calls
4 calls:
426.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
71.0ms
(* (sin lambda1) (sin lambda2))
60.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
14.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.8s

Counts
73 → 73
Iterations
IterNodes
done5000
34913
2880
1258
0127

prune955.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
log-prod exp-prod
pow1 log-pow
associate-*r*
add-cbrt-cube add-exp-log
add-log-exp
expm1-log1p-u log1p-expm1-u
distribute-rgt-in acos-asin distribute-lft-in associate-*l*
exp-diff
log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 72
Calls
4 calls:
21.0ms
(* R (log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
5.0ms
(log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
2.0ms
(exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
1.0ms
(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

series135.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* R (log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
21.0ms
(log (exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
44.0ms
(exp (acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
26.0ms
(acos (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

simplify3.2s

Counts
84 → 84
Iterations
IterNodes
done5000
43226
31288
2430
1175
0105

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.9b

localize1.0ms