Details

Time bar (total: 6.8s)

sample262.0ms

Algorithm
intervals
Results
160.0ms100×body1280valid
52.0ms55×body640valid
13.0ms22×body320valid
11.0ms70×body80valid
4.0ms9×body160valid

simplify20.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25433
35733
done5733

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (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))))
0.3b
(* (sin phi1) (sin (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)))))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
1×sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 46
Calls
4 calls:
0.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (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))))
145.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
176.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.1s

Counts
58 → 58
Iterations

Useful iterations: 3 (230.0ms)

IterNodesCost
01191686
12451622
26221437
317521435
done50001435

prune333.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
13×pow1
10×add-exp-log add-cbrt-cube
9×times-frac
6×associate-*r* associate-*l* sin-mult add-log-exp
4×associate-*r/ cos-mult associate-/l/
3×swap-sqr associate-/r* associate-/l*
2×flip3-- pow-prod-down prod-exp associate-/r/ *-commutative frac-sub flip-- cbrt-unprod sub-div unswap-sqr
1×cbrt-undiv pow2 sub-neg sqr-cos frac-2neg flip3-+ pow-plus diff-log div-sub div-exp associate--l+ clear-num pow-sqr pow-prod-up flip-+ sqr-sin div-inv
Counts
4 → 95
Calls
4 calls:
4.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
5.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
15.0ms
(/ (- (* (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))))))))
8.0ms
(- (* (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))))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
152.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
787.0ms
(/ (- (* (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))))))))
499.0ms
(- (* (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))))))))

simplify831.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (197.0ms)

IterNodesCost
02326372
16075870
224375234
done50015234

prune785.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite504.0ms

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:
2.0ms
(pow (sin phi1) 3)
2.0ms
(pow (sin phi1) 3)
497.0ms
(- (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)))))))))
2.0ms
(pow (sin phi1) 4)

series698.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (sin phi1) 3)
32.0ms
(pow (sin phi1) 3)
603.0ms
(- (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)))))))))
34.0ms
(pow (sin phi1) 4)

simplify122.0ms

Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
01662878
14292684