Details

Time bar (total: 1.0m)

sample807.0ms

Algorithm
intervals
Results
470.0ms89×body1280valid
201.0ms60×body640valid
52.0ms25×body320valid
42.0ms75×body80valid
8.0ms7×body160valid

simplify37.0ms

Counts
1 → 1
Iterations
IterNodes
455
355
254
135
022

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite64.0ms

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* add-log-exp
4×insert-posit16
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 62
Calls
4 calls:
11.0ms
(* (sin theta) (sin delta))
25.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
15.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series553.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin theta) (sin delta))
212.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
12.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
263.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify4.9s

Counts
74 → 74
Iterations
IterNodes
45201
31916
2718
1315
0148

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin delta) (cos theta))
0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (+ (* (cos phi1) (* (sin delta) (cos theta))) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (* (sin phi1) (+ (* (cos phi1) (* (sin delta) (cos theta))) (* (sin phi1) (cos delta)))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
6×add-log-exp
4×associate-*r/ insert-posit16
3×pow-prod-down prod-exp *-commutative cbrt-unprod sin-cos-mult unswap-sqr
2×distribute-rgt-in distribute-lft-in associate--r+
1×sub-neg flip3-+ flip3-- diff-log frac-add flip-+ flip-- sin-mult
Counts
4 → 79
Calls
4 calls:
22.0ms
(* (sin delta) (cos theta))
13.0ms
(* (sin theta) (sin delta))
83.0ms
(* (sin phi1) (+ (* (cos phi1) (* (sin delta) (cos theta))) (* (sin phi1) (cos delta))))
13.0ms
(- (cos delta) (* (sin phi1) (+ (* (cos phi1) (* (sin delta) (cos theta))) (* (sin phi1) (cos delta)))))

series576.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (sin delta) (cos theta))
68.0ms
(* (sin theta) (sin delta))
208.0ms
(* (sin phi1) (+ (* (cos phi1) (* (sin delta) (cos theta))) (* (sin phi1) (cos delta))))
225.0ms
(- (cos delta) (* (sin phi1) (+ (* (cos phi1) (* (sin delta) (cos theta))) (* (sin phi1) (cos delta)))))

simplify5.8s

Counts
91 → 91
Iterations
IterNodes
37114
21629
1510
0184

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (sin phi1) (* (sin phi1) (cos delta)))
0.2b
(* (sin phi1) (* (cos phi1) (* (sin delta) (cos theta))))
0.6b
(- (cos delta) (+ (* (sin phi1) (* (cos phi1) (* (sin delta) (cos theta)))) (* (sin phi1) (* (sin phi1) (cos delta)))))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity pow-prod-down prod-exp cbrt-unprod
9×associate-*l* add-log-exp
8×add-cube-cbrt
5×associate-*r*
4×insert-posit16
3×associate-*r/ *-commutative
2×diff-log sin-cos-mult
1×sum-log sub-neg flip3-- flip-- sin-mult associate--r+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 80
Calls
4 calls:
21.0ms
(* (sin theta) (sin delta))
46.0ms
(* (sin phi1) (* (sin phi1) (cos delta)))
70.0ms
(* (sin phi1) (* (cos phi1) (* (sin delta) (cos theta))))
94.0ms
(- (cos delta) (+ (* (sin phi1) (* (cos phi1) (* (sin delta) (cos theta)))) (* (sin phi1) (* (sin phi1) (cos delta)))))

series540.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sin theta) (sin delta))
65.0ms
(* (sin phi1) (* (sin phi1) (cos delta)))
142.0ms
(* (sin phi1) (* (cos phi1) (* (sin delta) (cos theta))))
271.0ms
(- (cos delta) (+ (* (sin phi1) (* (cos phi1) (* (sin delta) (cos theta)))) (* (sin phi1) (* (sin phi1) (cos delta)))))

simplify6.5s

Counts
92 → 92
Iterations
IterNodes
310507
21868
1473
0185

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (+ (* (cos phi1) (log (exp (* (sin delta) (cos theta))))) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (* (sin phi1) (+ (* (cos phi1) (log (exp (* (sin delta) (cos theta))))) (* (sin phi1) (cos delta)))))
2.4b
(log (exp (* (sin delta) (cos theta))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×add-log-exp
6×associate-*r* associate-*l*
4×insert-posit16
3×log-prod log-pow
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod associate--r+ unswap-sqr
1×exp-prod sub-neg flip3-+ flip3-- exp-to-pow diff-log rem-log-exp flip-+ flip-- sin-mult
Counts
4 → 73
Calls
4 calls:
23.0ms
(* (sin theta) (sin delta))
33.0ms
(* (sin phi1) (+ (* (cos phi1) (log (exp (* (sin delta) (cos theta))))) (* (sin phi1) (cos delta))))
6.0ms
(- (cos delta) (* (sin phi1) (+ (* (cos phi1) (log (exp (* (sin delta) (cos theta))))) (* (sin phi1) (cos delta)))))
4.0ms
(log (exp (* (sin delta) (cos theta))))

series527.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin theta) (sin delta))
183.0ms
(* (sin phi1) (+ (* (cos phi1) (log (exp (* (sin delta) (cos theta))))) (* (sin phi1) (cos delta))))
245.0ms
(- (cos delta) (* (sin phi1) (+ (* (cos phi1) (log (exp (* (sin delta) (cos theta))))) (* (sin phi1) (cos delta)))))
50.0ms
(log (exp (* (sin delta) (cos theta))))

simplify4.6s

Counts
85 → 85
Iterations
IterNodes
37559
21391
1438
0166

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes633.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
230
130
021

end0.0ms

sample26.0s

Algorithm
intervals
Results
15.6s3154×body1280valid
5.6s1833×body640valid
2.2s679×body320valid
1.8s2026×body80valid
473.0ms308×body160valid