Details

Time bar (total: 12.4s)

sample666.0ms

Algorithm
intervals
Results
424.0ms147×body1280valid
83.0ms69×body640valid
26.0ms25×body320valid
6.0ms10×body160valid
2.0ms6×body80valid

simplify51.0ms

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

prune64.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.8b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.8b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.0b
(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×acos-asin cos-diff sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 61
Calls
4 calls:
0.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
5.0ms
(* 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))))
13.0ms
(cos (- lambda1 lambda2))

series352.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
34.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
20.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
57.0ms
(cos (- lambda1 lambda2))

simplify1.3s

Counts
73 → 73
Iterations
IterNodes
done5002
32470
2731
1294
0168

prune684.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize74.0ms

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 phi2) (sin phi1))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.8b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×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)))
9.0ms
(* (sin phi2) (sin phi1))
5.0ms
(* 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))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
401.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
55.0ms
(* (sin phi2) (sin phi1))
57.0ms
(* 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))))

simplify2.5s

Counts
73 → 73
Iterations
IterNodes
done5000
34595
2798
1256
0126

prune972.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b
(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))))
0.4b
(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
0.5b
(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
0.8b
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×distribute-rgt-in acos-asin distribute-lft-in associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 72
Calls
4 calls:
13.0ms
(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))))
8.0ms
(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
2.0ms
(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

series169.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* R (log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))))
50.0ms
(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
25.0ms
(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
25.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

simplify3.7s

Counts
84 → 84
Iterations
IterNodes
done5001
33041
2645
1196
0114

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.2b

localize2.0ms