Details

Time bar (total: 42.9s)

sample471.0ms

Algorithm
intervals
Results
265.0ms93×body1280valid
129.0ms60×body640valid
20.0ms21×body320valid
19.0ms71×body80valid
7.0ms11×body160valid

simplify22.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25633
36233
done6233

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.2b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
18.0ms
(* (sin theta) (sin delta))
22.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
10.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series569.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin theta) (sin delta))
236.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
254.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify722.0ms

Counts
70 → 70
Iterations

Useful iterations: done (719.0ms)

IterNodesCost
01441435
13121369
211201233
done50011229

prune739.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize140.0ms

Local error

Found 4 expressions with local error:

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

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
11×pow1
9×times-frac
8×add-cbrt-cube add-exp-log
6×add-log-exp
5×sin-mult
4×associate-*r/ cos-mult associate-/l/
3×associate-/r* swap-sqr associate-*r* associate-*l* associate-/l*
2×flip3-- associate-/r/ frac-sub flip-- sub-div
1×pow2 cbrt-undiv asin-acos sqr-cos clear-num sub-neg frac-2neg flip3-+ pow-plus diff-log div-sub div-exp pow-prod-down prod-exp associate--l+ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ sqr-sin div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
64.0ms
(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
46.0ms
(- (* (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))))))))
32.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series2.4s

Counts
4 → 12
Calls
4 calls:
15.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.4s
(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
861.0ms
(- (* (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))))))))
193.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify2.1s

Counts
96 → 96
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02396070
16875604
234584959
done50014082

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize188.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.6b
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.6b
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.6b
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
19.0ms
(* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
1.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series430.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
82.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
124.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
91.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify1.3s

Counts
85 → 85
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0772628
11702423
27541939
done50011873

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize137.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×pow1 add-exp-log
14×add-cbrt-cube
13×add-log-exp
12×*-un-lft-identity
10×add-cube-cbrt
7×unpow-prod-down
6×pow-unpow pow-prod-down prod-exp cbrt-unprod
4×difference-of-squares
3×sum-log diff-log cube-prod associate-*l* sqr-pow
2×pow-to-exp pow-pow pow-exp associate-*r/
1×cube-mult sub-neg flip3-- unpow3 associate-*r* cos-mult *-commutative flip-- associate--r+ distribute-lft-out-- unpow2 rem-cube-cbrt
Counts
4 → 82
Calls
4 calls:
3.9s
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (sin phi1) 2) (* (pow (cos theta) 2) (pow (cos phi1) 2)))) (+ (* 2 (* (pow (sin phi1) 3) (* (sin delta) (* (cos phi1) (* (cos theta) (cos delta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
54.0ms
(* (sin delta) (* (cos phi1) (* (cos theta) (cos delta))))
3.0ms
(pow (sin phi1) 3)
3.0ms
(pow (sin phi1) 4)

series896.0ms

Counts
4 → 12
Calls
4 calls:
634.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (sin phi1) 2) (* (pow (cos theta) 2) (pow (cos phi1) 2)))) (+ (* 2 (* (pow (sin phi1) 3) (* (sin delta) (* (cos phi1) (* (cos theta) (cos delta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
175.0ms
(* (sin delta) (* (cos phi1) (* (cos theta) (cos delta))))
51.0ms
(pow (sin phi1) 3)
36.0ms
(pow (sin phi1) 4)

simplify1.9s

Counts
94 → 94
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02152519
16242370
233162177
done50022171

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
033113
144113
done44113

end0.0ms

sample21.4s

Algorithm
intervals
Results
13.4s3157×body1280valid
4.2s1870×body640valid
1.4s1966×body80valid
1.3s695×body320valid
304.0ms312×body160valid