Details

Time bar (total: 14.0s)

sample275.0ms

Algorithm
intervals
Results
176.0ms106×body1280valid
51.0ms57×body640valid
12.0ms19×body320valid
11.0ms60×body80valid
5.0ms14×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

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))))
0.5b
(- (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:
5.0ms
(* (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)))))))

series368.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin theta) (sin delta))
146.0ms
(* (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))))
173.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify92.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune375.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New591170
Fresh000
Picked101
Done000
Total601171

Merged error: 0.1b

Counts
71 → 11

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1
15×add-exp-log add-sqr-sqrt add-cbrt-cube
13×add-cube-cbrt *-un-lft-identity
6×pow-unpow associate-*r*
5×pow-prod-down prod-exp cbrt-unprod
4×unpow-prod-down cube-prod associate-*l* sin-mult add-log-exp
3×pow-pow swap-sqr pow-exp rem-cube-cbrt
2×cube-mult frac-times pow-to-exp flip3-+ unpow3 associate-*r/ *-commutative flip-+ sqr-pow
1×cube-div pow2 distribute-rgt-in sqr-cos distribute-lft-in pow-plus associate-*l/ pow-sqr cos-mult pow-prod-up unswap-sqr
Counts
4 → 98
Calls
4 calls:
4.0ms
(* (cos delta) (cos delta))
12.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta)))
2.0ms
(pow (cos delta) 3)
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series610.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (cos delta) (cos delta))
340.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta)))
27.0ms
(pow (cos delta) 3)
226.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify125.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
05271619
133401396
250011387

prune584.0ms

Filtered
110 candidates to 66 candidates (60.0%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1073110
Fresh01010
Picked101
Done000
Total10813121

Merged error: 0.0b

Counts
121 → 13

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×pow1 add-exp-log add-cbrt-cube
9×unpow-prod-down pow-unpow cube-prod
4×add-log-exp
3×cube-div cube-mult pow-to-exp pow-pow flip3-+ unpow3 associate-*r/ associate-*r* pow-prod-down pow-exp prod-exp cbrt-unprod flip-+ sin-mult rem-cube-cbrt sqr-pow
2×frac-times
1×distribute-rgt-in distribute-lft-in associate-*l* associate-*l/ frac-add cos-mult *-commutative sin-cos-mult
Counts
4 → 97
Calls
4 calls:
12.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta)))
3.0ms
(pow (sin phi1) 3)
3.0ms
(pow (cos delta) 3)
9.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

series579.0ms

Counts
4 → 12
Calls
4 calls:
357.0ms
(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta)))
29.0ms
(pow (sin phi1) 3)
30.0ms
(pow (cos delta) 3)
163.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

simplify139.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (126.0ms)

IterNodesCost
06591696
139961478
250011465

prune627.0ms

Filtered
109 candidates to 61 candidates (56.0%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1063109
Fresh11112
Picked101
Done000
Total10814122

Merged error: 0.0b

Counts
122 → 14

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
10×add-exp-log add-cbrt-cube
6×pow-unpow add-log-exp
4×unpow-prod-down cube-prod
3×pow-pow swap-sqr associate-*r* associate-*l* pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 pow-prod-down prod-exp cbrt-unprod sin-mult sqr-pow
1×cube-div pow2 sub-neg flip3-- pow-plus diff-log pow-sqr *-commutative pow-prod-up flip-- sqr-sin unswap-sqr
Counts
4 → 85
Calls
4 calls:
6.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(pow (cos delta) 3)
7.0ms
(- (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta))
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series557.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
27.0ms
(pow (cos delta) 3)
163.0ms
(- (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta))
222.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify66.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
03951377
117901169
250011102

prune580.0ms

Filtered
97 candidates to 61 candidates (62.9%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New95297
Fresh21113
Picked011
Done000
Total9714111

Merged error: 0.0b

Counts
111 → 14

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
05680
15680

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.1s3101×body1280valid
1.8s1844×body640valid
427.0ms701×body320valid
357.0ms2018×body80valid
133.0ms336×body160valid

Profiling

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