Details

Time bar (total: 11.3s)

sample295.0ms

Algorithm
intervals
Results
188.0ms106×body1280valid
52.0ms53×body640valid
15.0ms23×body320valid
13.0ms69×body80valid
4.0ms5×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05333
15333

prune23.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 2

localize32.0ms

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)))))))

rewrite16.0ms

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))
5.0ms
(* (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))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series98.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
34.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
45.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify45.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
049691229
149691229

prune156.0ms

Filtered
55 candidates to 70 candidates (-27.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New63770
Fresh101
Picked101
Done000
Total65772

Merged error: 0.0b

Counts
72 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.4b
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
0.6b
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3)

rewrite17.0ms

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 (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
4.0ms
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
6.0ms
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3)

series178.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
46.0ms
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3))
45.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
81.0ms
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))) 3)

simplify59.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049662299
149662299

prune145.0ms

Filtered
49 candidates to 80 candidates (-63.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New79180
Fresh066
Picked011
Done000
Total79887

Merged error: 0.0b

Counts
87 → 8

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×asin-acos
1×sub-neg sqr-cos flip3-- diff-log associate--l+ flip--
Counts
4 → 37
Calls
4 calls:
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
6.0ms
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (pow (sin phi1) 2))))

series162.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
146.0ms
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (pow (sin phi1) 2))))

simplify44.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
059001436

prune130.0ms

Filtered
37 candidates to 49 candidates (-32.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New48149
Fresh066
Picked011
Done011
Total48957

Merged error: 0.0b

Counts
57 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)
0.5b
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)))
20.0b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×cbrt-prod
8×*-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×add-cube-cbrt add-log-exp
3×pow-unpow difference-of-squares sqr-pow
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-exp sin-mult rem-cube-cbrt
1×pow-to-exp sub-neg asin-acos cbrt-div flip3-- pow1/3 diff-log pow-prod-down prod-exp flip-- rem-cbrt-cube cbrt-unprod distribute-lft-out--
Counts
4 → 65
Calls
4 calls:
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)
8.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)))
3.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3))

series150.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
66.0ms
(pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)
44.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)))
35.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3))

simplify49.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049661806
149661806

prune109.0ms

Filtered
57 candidates to 77 candidates (-35.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New75277
Fresh246
Picked101
Done022
Total78886

Merged error: 0.0b

Counts
86 → 8

regimes523.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03437
13437

end0.0ms

sample8.9s

Algorithm
intervals
Results
5.5s3045×body1280valid
1.9s1874×body640valid
467.0ms722×body320valid
401.0ms2030×body80valid
140.0ms329×body160valid

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