Details

Time bar (total: 20.9s)

sample293.0ms

Algorithm
intervals
Results
178.0ms107×body1280valid
70.0ms70×body640valid
14.0ms16×body320valid
9.0ms56×body80valid
3.0ms7×body160valid

simplify21.0ms

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: 0.1b

localize36.0ms

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))))))
0.3b
(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)))))))

rewrite12.0ms

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:
4.0ms
(* (sin theta) (sin delta))
4.0ms
(* (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))))
2.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series379.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
154.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
174.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.3s

Counts
70 → 70
Iterations

Useful iterations: 3 (445.0ms)

IterNodesCost
01391435
12851368
27161235
319121229
done50001229

prune397.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

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
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×pow-unpow
4×unpow-prod-down cube-prod add-log-exp
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp asin-acos unpow3 sqr-pow
1×cube-div pow-prod-down prod-exp cbrt-unprod sin-mult
Counts
4 → 62
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(pow (cos delta) 3)
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series281.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
29.0ms
(pow (cos delta) 3)
239.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify2.3s

Counts
74 → 74
Iterations

Useful iterations: 3 (610.0ms)

IterNodesCost
01091265
12521181
27471039
340681037
done50011037

prune482.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×cube-div
3×pow-unpow flip3-- flip--
2×cube-mult cbrt-div unpow3 sqr-pow
1×pow-to-exp sub-neg asin-acos pow-pow pow1/3 diff-log pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 68
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
2.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.0ms
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

series608.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
180.0ms
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
179.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
242.0ms
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

simplify2.2s

Counts
80 → 80
Iterations

Useful iterations: 3 (588.0ms)

IterNodesCost
01242938
12862627
27972322
341242304
done50002304

prune415.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
1×sub-neg flip3-- diff-log flip--
Counts
4 → 45
Calls
4 calls:
2.0ms
(- (cos delta) (* (* (sin phi1) (* (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series875.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(- (cos delta) (* (* (sin phi1) (* (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
226.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
236.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
229.0ms
(cbrt (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify1.2s

Counts
57 → 57
Iterations

Useful iterations: 3 (285.0ms)

IterNodesCost
0872288
12042212
25631353
319611327
done50001327

prune333.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes281.0ms

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 (1.0ms)

IterNodesCost
02570
13470
done3470

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.2s3108×body1280valid
1.9s1806×body640valid
443.0ms694×body320valid
360.0ms2077×body80valid
124.0ms315×body160valid