Details

Time bar (total: 37.8s)

sample13.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 14.941406%

Results
158.0ms86×body1280valid
77.0ms69×body640valid
15.0ms23×body320valid
15.0ms71×body80valid
3.0ms7×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 1

localize33.0ms

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

series101.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
36.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
50.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify91.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune157.0ms

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New63770
Fresh000
Picked101
Done000
Total64771

Merged error: 0.0b

Counts
71 → 7

localize41.0ms

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)))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
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:
5.0ms
(* (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)))))

series131.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
28.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
32.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
29.0ms
(cbrt (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify87.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
01101704
13801481
225841395
350011379

prune148.0ms

Filtered
56 candidates to 85 candidates (-51.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New85085
Fresh066
Picked011
Done000
Total85792

Merged error: 0.0b

Counts
92 → 7

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.4b
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.4b
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.8b
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×sin-sum
8×*-un-lft-identity add-log-exp
6×pow1 add-exp-log distribute-rgt-in acos-asin add-cube-cbrt sub-neg distribute-lft-in add-cbrt-cube associate--r+
5×associate--r-
3×associate-*r* associate-*l*
2×flip3-- diff-log flip-- difference-of-squares
1×times-frac pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult distribute-lft-out-- unswap-sqr
Counts
4 → 67
Calls
4 calls:
13.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
5.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
1.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series107.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
49.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
6.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify132.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (120.0ms)

IterNodesCost
03111574
19101389
236541325
350011306

prune152.0ms

Filtered
57 candidates to 79 candidates (-38.6%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New79079
Fresh055
Picked011
Done011
Total79786

Merged error: 0.0b

Counts
86 → 7

localize39.0ms

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
(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)))))))
0.7b
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
5×log-prod
4×log-pow
3×exp-prod associate-*r* associate-*l*
2×sub-neg exp-sum
1×log-div asin-acos flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
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))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
3.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series136.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
48.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
46.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify85.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02531234
17641106
229491102
350011102

prune101.0ms

Filtered
51 candidates to 69 candidates (-35.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New68169
Fresh044
Picked011
Done022
Total68876

Merged error: 0.0b

Counts
76 → 8

regimes573.0ms

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
03447
13447

end0.0ms

sample22.4s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 14.941406%

Results
5.9s3205×body1280valid
1.9s1818×body640valid
473.0ms675×body320valid
404.0ms1982×body80valid
146.0ms320×body160valid

Profiling

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