Details

Time bar (total: 39.9s)

sample617.0ms

Algorithm
intervals
Results
330.0ms97×body1280valid
177.0ms64×body640valid
39.0ms31×body320valid
20.0ms54×body80valid
8.0ms10×body160valid

simplify80.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25533
35833
done5833

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize66.0ms

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)))))))

rewrite68.0ms

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))
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))))
8.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series610.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (sin theta) (sin delta))
233.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
10.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
286.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify6.0s

Counts
70 → 70
Iterations

Useful iterations: 3 (696.0ms)

IterNodesCost
01391435
12881368
27091231
317151229
448041229
done50001229

prune727.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize90.0ms

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)) (* (pow (sin phi1) 2) (* (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
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube add-log-exp
3×swap-sqr associate-*r* associate-*l* sin-mult
2×asin-acos associate-*r/ cos-mult
1×pow2 sub-neg sqr-cos flip3-- pow-plus diff-log pow-prod-down prod-exp associate--l+ pow-sqr *-commutative pow-prod-up frac-sub flip-- cbrt-unprod sqr-sin sub-div unswap-sqr
Counts
4 → 58
Calls
4 calls:
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
68.0ms
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
35.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
11.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
826.0ms
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
199.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify1.2s

Counts
70 → 70
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01462808
13582451
210682065
done50001672

prune949.0ms

Pruning

12 alts after pruning (12 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) (+ (* (sin delta) (+ (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (* (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))) 2))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))
0.5b
(pow (sin phi1) 4)

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×*-un-lft-identity
9×add-cube-cbrt add-log-exp
7×unpow-prod-down
6×pow1 add-exp-log pow-unpow
5×add-cbrt-cube
4×difference-of-squares
3×cube-prod sqr-pow
2×pow-to-exp pow-pow diff-log pow-exp
1×cube-mult sub-neg asin-acos flip3-- unpow3 sum-log flip-- associate--r+ distribute-lft-out-- unpow2 rem-cube-cbrt
Counts
4 → 67
Calls
4 calls:
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms
(pow (sin phi1) 3)
310.0ms
(- (pow (cos delta) 2) (+ (* (sin delta) (+ (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (* (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))) 2))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))
8.0ms
(pow (sin phi1) 4)

series812.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
60.0ms
(pow (sin phi1) 3)
681.0ms
(- (pow (cos delta) 2) (+ (* (sin delta) (+ (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (* (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))) 2))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))
54.0ms
(pow (sin phi1) 4)

simplify1.1s

Counts
79 → 79
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01772264
14362139
213541979
done50001956

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize136.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (pow (cos delta) 2) (+ (* (sin delta) (+ (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))
0.4b
(pow (pow (sin phi1) 3) 3)
0.5b
(pow (sin phi1) 4)
6.0b
(cbrt (pow (pow (sin phi1) 3) 3))

rewrite740.0ms

Algorithm
rewrite-expression-head
Rules
40×unpow-prod-down
36×cube-prod
30×cbrt-prod
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
9×add-log-exp
8×sqr-pow
7×add-exp-log
6×cube-mult pow-unpow unpow3
5×pow1 pow-exp add-cbrt-cube
4×difference-of-squares
3×pow-to-exp
2×pow-pow diff-log
1×sub-neg flip3-- pow1/3 sum-log flip-- rem-cbrt-cube associate--r+ distribute-lft-out-- unpow2 rem-cube-cbrt
Counts
4 → 118
Calls
4 calls:
711.0ms
(- (pow (cos delta) 2) (+ (* (sin delta) (+ (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))
8.0ms
(pow (pow (sin phi1) 3) 3)
4.0ms
(pow (sin phi1) 4)
8.0ms
(cbrt (pow (pow (sin phi1) 3) 3))

series863.0ms

Counts
4 → 12
Calls
4 calls:
684.0ms
(- (pow (cos delta) 2) (+ (* (sin delta) (+ (* (sin delta) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (* (* (cos phi1) (* (cbrt (pow (pow (sin phi1) 3) 3)) (* (cos delta) (cos theta)))) 2))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))
85.0ms
(pow (pow (sin phi1) 3) 3)
59.0ms
(pow (sin phi1) 4)
35.0ms
(cbrt (pow (pow (sin phi1) 3) 3))

simplify1.4s

Counts
130 → 130
Iterations

Useful iterations: 2 (350.0ms)

IterNodesCost
02133044
15242410
216612278
done50012278

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes840.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
04688
16688
done6688

end0.0ms

sample19.7s

Algorithm
intervals
Results
11.6s3122×body1280valid
4.4s1847×body640valid
1.6s749×body320valid
1.1s1973×body80valid
208.0ms309×body160valid