Details

Time bar (total: 15.5s)

sample693.0ms

Algorithm
intervals
Results
446.0ms159×body1280valid
75.0ms59×body640valid
20.0ms24×body320valid
6.0ms10×body160valid
1.0msbody80valid

simplify29.0ms

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

prune58.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.3b

localize75.0ms

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)))))
1.1b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
2.6b
(cos (- lambda1 lambda2))

rewrite34.0ms

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:
10.0ms
(* (sin phi2) (sin phi1))
6.0ms
(* 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))))
15.0ms
(cos (- lambda1 lambda2))

series173.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (sin phi2) (sin phi1))
47.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
11.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
44.0ms
(cos (- lambda1 lambda2))

simplify3.4s

Counts
84 → 84
Iterations
IterNodes
done5001
34440
2844
1327
0184

prune819.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi2) (sin phi1))
0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.1b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite32.0ms

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:
18.0ms
(* (sin phi2) (sin phi1))
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
10.0ms
(* 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))))

series510.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin phi2) (sin phi1))
389.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
50.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
21.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.5s

Counts
73 → 73
Iterations
IterNodes
done5000
34686
2802
1256
0126

prune883.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.5b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b
(* R (log (exp (acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1)))))))
0.3b
(exp (acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1)))))
0.8b
(log (exp (acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1))))))
1.1b
(acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1))))

rewrite33.0ms

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 (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1)))))))
3.0ms
(exp (acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1)))))
5.0ms
(log (exp (acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1))))))
1.0ms
(acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1))))

series165.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* R (log (exp (acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1)))))))
73.0ms
(exp (acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1)))))
26.0ms
(log (exp (acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1))))))
24.0ms
(acos (fma (* (cos phi1) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi2) (* (sin phi2) (sin phi1))))

simplify4.7s

Counts
84 → 84
Iterations
IterNodes
done5001
44643
31529
2490
1186
0112

prune1.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.4b

localize3.0ms