Details

Time bar (total: 11.9s)

sample306.0ms

Algorithm
intervals
Results
181.0ms103×body1280valid
72.0ms67×body640valid
17.0ms26×body320valid
10.0ms51×body80valid
4.0ms9×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05333
15333

prune24.0ms

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: 0.2b

Counts
2 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (* (sin delta) (cos phi1)))
0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.4b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×sub-neg asin-acos flip3-- diff-log associate-*r/ sin-cos-mult flip-- sin-mult unswap-sqr
Counts
4 → 58
Calls
4 calls:
6.0ms
(* (sin theta) (* (sin delta) (cos phi1)))
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series105.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (sin theta) (* (sin delta) (cos phi1)))
7.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
35.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
47.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
050311280

prune171.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New61970
Fresh011
Picked101
Done000
Total621072

Merged error: 0.1b

Counts
72 → 10

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (* (sin delta) (cos phi1)))
0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b
(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
3.1b
(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod
11×add-sqr-sqrt *-un-lft-identity
10×add-exp-log
9×pow1 add-cube-cbrt add-cbrt-cube
7×associate--r+
6×unpow-prod-down
5×add-log-exp
3×asin-acos rem-log-exp associate-*l* pow-prod-down prod-exp cbrt-unprod
2×log-div sin-diff pow-sub sqr-pow
1×pow-to-exp sub-neg flip3-- diff-log associate-*r/ associate-*r* pow-exp log-pow *-commutative sin-cos-mult flip-- distribute-lft-out-- associate--r- difference-of-squares
Counts
4 → 68
Calls
4 calls:
6.0ms
(* (sin theta) (* (sin delta) (cos phi1)))
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
8.0ms
(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
4.0ms
(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series137.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (sin theta) (* (sin delta) (cos phi1)))
5.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
58.0ms
(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
56.0ms
(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
048481525
148481525

prune166.0ms

Filtered
61 candidates to 80 candidates (-31.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New79180
Fresh099
Picked101
Done000
Total801090

Merged error: 0.0b

Counts
90 → 10

localize34.0ms

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)))))))

series94.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin theta) (sin delta))
5.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
37.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
42.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049691229
149691229

prune150.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New70070
Fresh099
Picked011
Done000
Total701080

Merged error: 0.0b

Counts
80 → 10

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

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

series199.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
42.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
44.0ms
(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3))
80.0ms
(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3)

simplify42.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
053432565

prune115.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New88391
Fresh178
Picked101
Done011
Total9011101

Merged error: 0.0b

Counts
101 → 11

regimes947.0ms

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
03438
13438

end0.0ms

sample9.1s

Algorithm
intervals
Results
5.7s3160×body1280valid
1.8s1837×body640valid
480.0ms692×body320valid
375.0ms1985×body80valid
140.0ms326×body160valid

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