Details

Time bar (total: 24.3s)

sample564.0ms

Algorithm
intervals
Results
314.0ms96×body1280valid
108.0ms65×body640valid
23.0ms20×body320valid
20.0ms65×body80valid
7.0ms10×body160valid

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0221029
1361004
2591004
3641004
done641004

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg prod-diff
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 72
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
9.0ms
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series628.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (sin theta) (sin delta))
226.0ms
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
15.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
298.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify4.3s

Counts
84 → 84
Iterations

Useful iterations: done (4.3s)

IterNodesCost
016449645
135648193
287447812
3268247567
done500245336

prune866.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.7b
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
8×log-prod
7×pow1
6×add-cbrt-cube prod-diff add-exp-log add-log-exp
5×exp-sum
4×expm1-log1p-u log-pow log1p-expm1-u
3×exp-prod fma-neg associate-*r* associate-*l*
2×sub-neg
1×log-div asin-acos flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- sin-mult unswap-sqr
Counts
4 → 74
Calls
4 calls:
10.0ms
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
9.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series694.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
266.0ms
(- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))
214.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify5.9s

Counts
86 → 86
Iterations

Useful iterations: done (5.9s)

IterNodesCost
016370104
133964535
284163778
3250863733
done500059031

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.6b
(log (exp (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×*-un-lft-identity
18×prod-diff add-cube-cbrt
13×log-pow
11×pow1
9×add-log-exp
6×log-prod add-cbrt-cube add-exp-log
4×expm1-log1p-u exp-prod exp-to-pow log1p-expm1-u
3×fma-neg associate-*r* associate-*l* associate--r+
2×distribute-lft-out--
1×asin-acos sub-neg flip3-- diff-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- sin-mult difference-of-squares unswap-sqr
Counts
4 → 88
Calls
4 calls:
15.0ms
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
10.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
4.0ms
(log (exp (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series807.0ms

Counts
4 → 12
Calls
4 calls:
266.0ms
(* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
272.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
255.0ms
(log (exp (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify7.1s

Counts
100 → 100
Iterations

Useful iterations: done (7.0s)

IterNodesCost
017296779
138084178
284781258
3282680925
done500167640

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize129.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.5b
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.5b
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
2.6b
(log (exp (* (sin phi1) (sin (* (* (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1 add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
3×log-prod pow1/3 log-pow
1×exp-prod exp-to-pow rem-log-exp
Counts
4 → 55
Calls
4 calls:
1.0ms
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
6.0ms
(log (exp (* (sin phi1) (sin (* (* (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

series427.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
65.0ms
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
79.0ms
(cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
206.0ms
(log (exp (* (sin phi1) (sin (* (* (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))))

simplify144.0ms

Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
07452872
112949317