Details

Time bar (total: 50.2s)

sample683.0ms

Algorithm
intervals
Results
388.0ms109×body1280valid
187.0ms57×body640valid
27.0ms21×body320valid
23.0ms62×body80valid
6.0ms7×body160valid

simplify545.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25633
36033
done6033

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

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

rewrite83.0ms

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:
25.0ms
(* (sin theta) (sin delta))
39.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms
(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)))))))

series716.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (sin theta) (sin delta))
289.0ms
(* (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))))
329.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.1s

Counts
70 → 70
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01391435
13011369
210721231
done50011229

prune995.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize145.0ms

Local error

Found 4 expressions with local error:

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

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
11×pow1
9×times-frac
8×add-exp-log add-cbrt-cube
6×add-log-exp
5×sin-mult
4×associate-*l/ cos-mult associate-/l/
3×swap-sqr associate-*r* associate-*l* associate-/r* associate-/l*
2×flip3-- associate-/r/ frac-sub flip-- sub-div
1×cbrt-undiv pow2 sub-neg asin-acos sqr-cos frac-2neg flip3-+ pow-plus diff-log div-sub div-exp pow-prod-down prod-exp associate--l+ clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ sqr-sin div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
103.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
39.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
66.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

series2.8s

Counts
4 → 12
Calls
4 calls:
16.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.6s
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
280.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
919.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

simplify3.0s

Counts
96 → 96
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02176055
16265599
232414974
done50004097

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize129.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.4b
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
3.3b
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×sin-sum
8×*-un-lft-identity add-log-exp
6×pow1 add-exp-log distribute-rgt-in acos-asin add-cube-cbrt sub-neg distribute-lft-in add-cbrt-cube associate--r+
5×associate--r-
3×associate-*r* associate-*l*
2×flip3-- diff-log flip-- difference-of-squares
1×times-frac pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult distribute-lft-out-- unswap-sqr
Counts
4 → 67
Calls
4 calls:
132.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
33.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
42.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series740.0ms

Counts
4 → 12
Calls
4 calls:
262.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
15.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
387.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
76.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify1.0s

Counts
79 → 79
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01472555
13262342
211872022
done50011874

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize255.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-log-exp
14×*-un-lft-identity
12×add-cube-cbrt
10×unpow-prod-down
9×pow-unpow
7×pow1 add-exp-log
6×cube-prod sum-log add-cbrt-cube
4×diff-log difference-of-squares sqr-pow
3×pow-to-exp pow-pow pow-exp
2×cube-mult unpow3 rem-cube-cbrt
1×sub-neg flip3-- flip-- associate--r+ distribute-lft-out-- unpow2
Counts
4 → 84
Calls
4 calls:
8.0ms
(pow (sin phi1) 3)
7.0ms
(pow (sin phi1) 3)
2.0s
(- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (pow (sin phi1) 4) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta)))))))))
9.0ms
(pow (sin phi1) 4)

series1.2s

Counts
4 → 12
Calls
4 calls:
51.0ms
(pow (sin phi1) 3)
56.0ms
(pow (sin phi1) 3)
1.0s
(- (pow (cos delta) 2) (+ (* (pow (sin phi1) 3) (* (cos phi1) (* (cos delta) (* (sin delta) (cos theta))))) (+ (* (pow (sin phi1) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin delta) 2)))) (+ (* (pow (sin phi1) 4) (pow (cos delta) 2)) (* (pow (sin phi1) 3) (* (cos phi1) (* (sin delta) (* (cos delta) (cos theta)))))))))
62.0ms
(pow (sin phi1) 4)

simplify2.4s

Counts
96 → 96
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01662878
14822690
223202523
done50022521

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes1.5s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02637
13437
done3437

end0.0ms

sample25.3s

Algorithm
intervals
Results
15.9s3131×body1280valid
4.9s1879×body640valid
1.7s1987×body80valid
1.4s703×body320valid
266.0ms300×body160valid