Details

Time bar (total: 17.9s)

sample280.0ms

Algorithm
intervals
Results
181.0ms108×body1280valid
51.0ms57×body640valid
11.0ms19×body320valid
11.0ms64×body80valid
3.0ms8×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03522
15622
25922
35922
done5922

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×sub-neg asin-acos flip3-- diff-log flip-- sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
30.0ms
(* (* (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))))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (* (cos phi1) (sin delta)) (cos theta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
173.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
202.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify42.0ms

Counts
69 → 69
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0305974
11167862
25002860
done5002860

prune366.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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
(* (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))))))))
0.4b
(* (* (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)))))))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
22×add-exp-log add-cbrt-cube
21×add-sqr-sqrt
19×pow-prod-down
17×add-cube-cbrt *-un-lft-identity
12×times-frac sin-mult
10×prod-exp cbrt-unprod
7×associate-*r* associate-*l* associate-/l/
5×cos-mult
4×pow-sqr pow-prod-up associate-/l* add-log-exp difference-of-squares
3×associate-*r/ associate-*l/ associate-/r* *-commutative frac-sub
2×frac-times pow-plus associate-/r/ sub-div unswap-sqr
1×cbrt-undiv pow2 flip3-- frac-2neg flip3-+ div-sub swap-sqr div-exp clear-num flip-- flip-+ div-inv
Counts
4 → 116
Calls
4 calls:
13.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
15.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
58.0ms
(/ (- (* (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))))))))
51.0ms
(* (* (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)))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
161.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
169.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
863.0ms
(/ (- (* (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))))))))
194.0ms
(* (* (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)))))))

simplify100.0ms

Counts
128 → 128
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
05814066
129123627
250023619
done50023619

prune750.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
54×*-un-lft-identity
32×times-frac
26×add-cube-cbrt
20×difference-of-squares
14×unpow-prod-down
9×add-exp-log pow-unpow distribute-lft-out
8×add-cbrt-cube associate-/l* sqr-pow
7×pow1
6×cube-prod
5×distribute-lft-out-- unpow2
4×associate-/r* add-log-exp
3×pow-to-exp pow-pow pow-exp
2×cube-mult unpow3 associate-/r/ associate-/l/ rem-cube-cbrt
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ div-inv
Counts
4 → 124
Calls
4 calls:
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))))))))) (+ (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))))
4.0ms
(pow (sin phi1) 3)
4.0ms
(pow (sin phi1) 3)
4.0ms
(pow (sin phi1) 4)

series973.0ms

Counts
4 → 12
Calls
4 calls:
876.0ms
(/ (- (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))))))))) (+ (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta)))))))
30.0ms
(pow (sin phi1) 3)
30.0ms
(pow (sin phi1) 3)
36.0ms
(pow (sin phi1) 4)

simplify107.0ms

Counts
136 → 136
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06125793
127605514
250015498
done50015498

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 3)
0.5b
(pow (sin phi1) 4)
0.5b
(pow (sin phi1) 4)
0.5b
(pow (sin phi1) 4)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down pow-unpow
8×pow1 add-exp-log
5×add-cbrt-cube
4×pow-to-exp pow-pow pow-exp add-log-exp sqr-pow
3×cube-prod
1×cube-mult unpow3 rem-cube-cbrt
Counts
4 → 74
Calls
4 calls:
3.0ms
(pow (sin phi1) 3)
3.0ms
(pow (sin phi1) 4)
3.0ms
(pow (sin phi1) 4)
4.0ms
(pow (sin phi1) 4)

series127.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sin phi1) 3)
31.0ms
(pow (sin phi1) 4)
35.0ms
(pow (sin phi1) 4)
31.0ms
(pow (sin phi1) 4)

simplify221.0ms

Counts
86 → 86
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0174298
1695278
24865264
35001264
done5001264

prune775.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes380.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075150
177150
277150
done77150

end0.0ms

sample8.3s

Algorithm
intervals
Results
5.2s3216×body1280valid
1.7s1863×body640valid
480.0ms1950×body80valid
418.0ms698×body320valid
114.0ms273×body160valid