Details

Time bar (total: 42.6s)

sample597.0ms

Algorithm
intervals
Results
330.0ms97×body1280valid
160.0ms64×body640valid
35.0ms31×body320valid
25.0ms54×body80valid
8.0ms10×body160valid

simplify64.0ms

Counts
1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

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))))))
0.3b
(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)))))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
12.0ms
(* (sin theta) (sin delta))
30.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
34.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series570.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (sin theta) (sin delta))
226.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
18.0ms
(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)))))))

simplify1.4s

Counts
70 → 70

prune638.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
17×pow-prod-down
16×add-exp-log add-cbrt-cube
10×sin-mult
8×prod-exp cbrt-unprod
6×add-log-exp
5×cos-mult
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-sqr pow-prod-up
3×associate-*r/ associate-*l/ frac-sub
2×frac-times asin-acos pow-plus sub-div
1×pow2 sub-neg sqr-cos flip3-- diff-log swap-sqr associate-*r* associate-*l* associate--l+ *-commutative flip-- difference-of-squares
Counts
4 → 72
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
84.0ms
(- (* (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))))))))
83.0ms
(* (* (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)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
16.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
736.0ms
(- (* (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))))))))
293.0ms
(* (* (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)))))))

simplify1.2s

Counts
84 → 84

prune810.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize148.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(pow (sin phi1) 3)
0.4b
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
0.5b
(pow (sin phi1) 4)

rewrite4.5s

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-log-exp
11×*-un-lft-identity
9×add-cube-cbrt
7×unpow-prod-down
6×pow1 add-exp-log pow-unpow
5×add-cbrt-cube
4×difference-of-squares
3×diff-log cube-prod sum-log sqr-pow
2×pow-to-exp pow-pow pow-exp
1×cube-mult sub-neg asin-acos flip3-- unpow3 flip-- associate--r+ distribute-lft-out-- unpow2 rem-cube-cbrt
Counts
4 → 68
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(pow (sin phi1) 3)
4.5s
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
8.0ms
(pow (sin phi1) 4)

series756.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
59.0ms
(pow (sin phi1) 3)
623.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
56.0ms
(pow (sin phi1) 4)

simplify1.0s

Counts
80 → 80

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(pow (pow (sin phi1) (sqrt 4)) (sqrt 4))
0.4b
(pow (sin phi1) 3)
0.4b
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (pow (sin phi1) (sqrt 4)) (sqrt 4)) (pow (cos delta) 2)))))

rewrite4.6s

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×unpow-prod-down
13×*-un-lft-identity add-log-exp
11×add-cube-cbrt
9×pow-unpow
7×add-exp-log
5×pow1 pow-exp add-cbrt-cube
4×difference-of-squares sqr-pow
3×pow-to-exp diff-log cube-prod sum-log sqrt-prod
2×pow-pow
1×cube-mult sub-neg asin-acos flip3-- unpow3 flip-- associate--r+ distribute-lft-out-- unpow2 rem-cube-cbrt
Counts
4 → 77
Calls
4 calls:
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms
(pow (pow (sin phi1) (sqrt 4)) (sqrt 4))
7.0ms
(pow (sin phi1) 3)
4.6s
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (pow (sin phi1) (sqrt 4)) (sqrt 4)) (pow (cos delta) 2)))))

series825.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
53.0ms
(pow (pow (sin phi1) (sqrt 4)) (sqrt 4))
56.0ms
(pow (sin phi1) 3)
706.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (pow (sin phi1) (sqrt 4)) (sqrt 4)) (pow (cos delta) 2)))))

simplify944.0ms

Counts
89 → 89

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes928.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.7s

end0.0ms

sample17.8s

Algorithm
intervals
Results
10.9s3122×body1280valid
4.0s1847×body640valid
1.1s749×body320valid
987.0ms1973×body80valid
235.0ms309×body160valid