Details

Time bar (total: 19.4s)

analyze3.9s

Algorithm
search

sample292.0ms

Algorithm
intervals
Results
171.0ms91×body1280valid
69.0ms63×body640valid
14.0ms71×body80valid
12.0ms17×body320valid
6.0ms14×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
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))))))
0.4b
(- (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))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series99.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
34.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
49.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify94.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune165.0ms

Filtered
51 candidates to 70 candidates (-37.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New62870
Fresh000
Picked101
Done000
Total63871

Merged error: 0.0b

Counts
71 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))
0.4b
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
0.6b
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
6.5b
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-mult unpow3 sqr-pow
1×pow-to-exp sub-neg flip3-- pow-pow pow1/3 diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- rem-cbrt-cube cbrt-unprod sin-mult rem-cube-cbrt unswap-sqr
Counts
4 → 75
Calls
4 calls:
6.0ms
(* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
3.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
2.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

series105.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))))
45.0ms
(- (cos delta) (* (sin phi1) (sin (cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)))))
20.0ms
(pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3)
6.0ms
(cbrt (pow (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) 3))

simplify46.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
02861560
110221431
250011423

prune185.0ms

Filtered
50 candidates to 87 candidates (-74.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New85287
Fresh077
Picked101
Done000
Total86995

Merged error: 0.0b

Counts
95 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod add-log-exp
4×cube-div
3×pow-unpow flip3-- associate-*r* associate-*l* flip--
2×cube-mult cbrt-div unpow3 sqr-pow
1×pow-to-exp sub-neg pow-pow pow1/3 diff-log pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod sin-mult rem-cube-cbrt unswap-sqr
Counts
4 → 79
Calls
4 calls:
5.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
4.0ms
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
4.0ms
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

series201.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
43.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
45.0ms
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3))
80.0ms
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) 3)

simplify54.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03401992
112631858
250021846

prune177.0ms

Filtered
56 candidates to 91 candidates (-62.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New90191
Fresh088
Picked011
Done000
Total9010100

Merged error: 0.0b

Counts
100 → 10

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (cos delta) (* (sin phi1) (sin (* (cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))) (cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))
0.4b
(* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
0.6b
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
4.0b
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube add-log-exp
4×cbrt-prod
3×swap-sqr associate-*r* associate-*l*
2×pow1/3
1×pow2 sub-neg flip3-- pow-plus diff-log pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod unswap-sqr
Counts
4 → 57
Calls
4 calls:
3.0ms
(- (cos delta) (* (sin phi1) (sin (* (cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))) (cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))
5.0ms
(* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
1.0ms
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
2.0ms
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))

series124.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (cos delta) (* (sin phi1) (sin (* (cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))) (cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))))))
13.0ms
(* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
25.0ms
(cbrt (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))
40.0ms
(cbrt (* (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))) (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))

simplify91.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
02211783
17191439
229611397
350021385

prune97.0ms

Filtered
46 candidates to 69 candidates (-50.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New69069
Fresh088
Picked011
Done011
Total691079

Merged error: 0.0b

Counts
79 → 10

regimes603.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03324
13324

end0.0ms

analyze3.7s

Algorithm
search

sample9.3s

Algorithm
intervals
Results
5.6s3113×body1280valid
2.2s1884×body640valid
469.0ms667×body320valid
412.0ms2024×body80valid
142.0ms312×body160valid

Profiling

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