Details

Time bar (total: 59.8s)

sample1.3s

Algorithm
intervals
Results
1.0s111×body1280valid
147.0ms57×body640valid
38.0ms19×body320valid
33.0ms58×body80valid
12.0ms11×body160valid

simplify30.0ms

Counts
1 → 1
Iterations
IterNodes
done55
355
254
135
022

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize126.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (sin delta)) (cos theta))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16
2×*-commutative
1×asin-acos sub-neg flip3-- diff-log flip-- sin-mult unswap-sqr
Counts
4 → 61
Calls
4 calls:
44.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series650.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
14.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
233.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
235.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify3.2s

Counts
73 → 73
Iterations
IterNodes
done5001
33670
2929
1333
0145

prune788.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize164.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(* (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
49×pow1
22×add-cbrt-cube add-exp-log
20×pow-prod-down
16×add-sqr-sqrt
11×prod-exp cbrt-unprod
10×*-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
7×sin-mult
4×pow-sqr *-commutative pow-prod-up insert-posit16 add-log-exp
3×unswap-sqr
2×pow-plus
1×pow2 frac-times swap-sqr associate-*l/ associate-*r/
Counts
4 → 98
Calls
4 calls:
24.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
14.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
14.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
63.0ms
(* (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
260.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
230.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
261.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta))))))
256.0ms
(* (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.9s

Counts
110 → 110
Iterations
IterNodes
done5000
32225
2773
1252
0100

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize159.0ms

Local error

Found 4 expressions with local error:

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

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
20×add-cbrt-cube add-exp-log
18×pow-prod-down
17×add-sqr-sqrt sin-mult
15×*-un-lft-identity add-cube-cbrt
12×times-frac
10×cos-mult
9×prod-exp cbrt-unprod
7×associate-/l/
6×frac-sub add-log-exp
5×associate-*l/ associate-*r/ difference-of-squares
4×associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 associate-/l* sub-div
3×frac-times associate-/r*
2×pow-plus flip3-- associate-/r/ *-commutative flip--
1×pow2 cbrt-undiv sqr-cos clear-num sub-neg frac-2neg flip3-+ diff-log div-sub swap-sqr div-exp associate--l+ flip-+ div-inv unswap-sqr
Counts
4 → 120
Calls
4 calls:
15.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
102.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
50.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
90.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series2.9s

Counts
4 → 12
Calls
4 calls:
297.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.4s
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
319.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
915.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify3.3s

Counts
132 → 132
Iterations
IterNodes
done5007
22728
1760
0267

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize143.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(/ (+ 1/2 (- (* 1/2 (cos (* 2 delta))) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b
(+ 1/2 (- (* 1/2 (cos (* 2 delta))) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
25×*-un-lft-identity
20×add-cbrt-cube add-exp-log
18×pow-prod-down
17×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
9×prod-exp cbrt-unprod add-log-exp
5×sin-mult distribute-lft-out
4×associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16 associate-/l*
3×associate-/r* flip3-+ flip-+
2×associate-+r+ associate-+r- sum-log pow-plus associate-/r/ *-commutative associate-/l/
1×pow2 frac-times cbrt-undiv +-commutative clear-num sub-neg frac-2neg diff-log div-sub swap-sqr div-exp associate-*l/ associate-*r/ div-inv unswap-sqr
Counts
4 → 112
Calls
4 calls:
19.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
64.0ms
(/ (+ 1/2 (- (* 1/2 (cos (* 2 delta))) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
77.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
24.0ms
(+ 1/2 (- (* 1/2 (cos (* 2 delta))) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series2.8s

Counts
4 → 12
Calls
4 calls:
248.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.4s
(/ (+ 1/2 (- (* 1/2 (cos (* 2 delta))) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
305.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
877.0ms
(+ 1/2 (- (* 1/2 (cos (* 2 delta))) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify3.1s

Counts
124 → 124
Iterations
IterNodes
done5000
22445
1689
0251

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes815.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations
IterNodes
done43
143
031

end0.0ms

sample30.7s

Algorithm
intervals
Results
17.8s3194×body1280valid
7.7s1843×body640valid
2.3s694×body320valid
1.9s1984×body80valid
454.0ms285×body160valid