Details

Time bar (total: 39.3s)

sample671.0ms

Algorithm
intervals
Results
367.0ms114×body1280valid
154.0ms63×body640valid
94.0ms32×body320valid
14.0ms40×body80valid
6.0ms7×body160valid

simplify43.0ms

Counts
1 → 1
Iterations
IterNodes
done55
355
254
135
022

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize123.0ms

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)))))))

rewrite56.0ms

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
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
21.0ms
(* (sin theta) (sin delta))
20.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series606.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (sin theta) (sin delta))
239.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
17.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
271.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.3s

Counts
70 → 70
Iterations
IterNodes
done5000
32191
2722
1312
0144

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize189.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
0.4b
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (cbrt (* (* (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))) (* (sin phi1) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))))))
17.5b
(cbrt (* (* (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))) (* (sin phi1) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-log-exp
4×pow1 add-cbrt-cube associate-*l/ add-exp-log add-cube-cbrt sin-mult
3×cbrt-div associate-*r/
2×asin-acos
1×cbrt-prod frac-times sub-neg flip3-- pow1/3 diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 42
Calls
4 calls:
2.0ms
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
2.0ms
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
6.0ms
(- (cos delta) (cbrt (* (* (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))) (* (sin phi1) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))))))
225.0ms
(cbrt (* (* (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))) (* (sin phi1) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))

series577.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
9.0ms
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
297.0ms
(- (cos delta) (cbrt (* (* (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))) (* (sin phi1) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))))))
262.0ms
(cbrt (* (* (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))) (* (sin phi1) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))) (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta)))))))

simplify3.4s

Counts
54 → 54
Iterations
IterNodes
done5012
44801
31725
2541
1220
0109

prune923.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize119.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1))
0.4b
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
0.6b
(- (cos delta) (* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1)))
1.0b
(log (exp (- (cos delta) (* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×add-cbrt-cube add-exp-log add-log-exp
5×log-prod
4×log-pow
3×exp-prod associate-*r* associate-*l*
2×sub-neg exp-sum
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 → 57
Calls
4 calls:
15.0ms
(* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1))
2.0ms
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
5.0ms
(- (cos delta) (* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1)))
9.0ms
(log (exp (- (cos delta) (* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1)))))

series891.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1))
17.0ms
(asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))
316.0ms
(- (cos delta) (* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1)))
310.0ms
(log (exp (- (cos delta) (* (sin (asin (+ (* (sin delta) (* (cos theta) (cos phi1))) (* (sin phi1) (cos delta))))) (sin phi1)))))

simplify3.3s

Counts
69 → 69
Iterations
IterNodes
done5001
43728
31844
2730
1278
0131

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (* (cos theta) (sin phi1)) (* (sin delta) (cos phi1)))))
0.2b
(* (sin theta) (sin delta))
0.2b
(* (cos phi1) (cos phi1))
0.3b
(* (* (cos theta) (sin phi1)) (* (sin delta) (cos phi1)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
20×add-cbrt-cube add-exp-log
14×add-sqr-sqrt
10×*-un-lft-identity pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
7×associate-*r* associate-*l*
4×add-log-exp
3×swap-sqr *-commutative
2×unswap-sqr
1×pow2 sqr-cos pow-plus associate-*r/ pow-sqr cos-mult pow-prod-up sin-cos-mult sin-mult
Counts
4 → 76
Calls
4 calls:
0.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (* (cos theta) (sin phi1)) (* (sin delta) (cos phi1)))))
18.0ms
(* (sin theta) (sin delta))
15.0ms
(* (cos phi1) (cos phi1))
45.0ms
(* (* (cos theta) (sin phi1)) (* (sin delta) (cos phi1)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (* (cos delta) (* (cos phi1) (cos phi1))) (* (* (cos theta) (sin phi1)) (* (sin delta) (cos phi1)))))
64.0ms
(* (sin theta) (sin delta))
25.0ms
(* (cos phi1) (cos phi1))
128.0ms
(* (* (cos theta) (sin phi1)) (* (sin delta) (cos phi1)))

simplify1.7s

Counts
88 → 88
Iterations
IterNodes
done5000
21258
1374
0151

prune674.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes967.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done26
126
019

end0.0ms

sample20.1s

Algorithm
intervals
Results
12.7s3049×body1280valid
4.2s1975×body640valid
1.3s1956×body80valid
985.0ms724×body320valid
315.0ms296×body160valid