Details

Time bar (total: 15.9s)

sample274.0ms

Algorithm
intervals
Results
187.0ms113×body1280valid
39.0ms42×body640valid
13.0ms22×body320valid
12.0ms68×body80valid
4.0ms11×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03522
15622
25922
35922

prune6.0ms

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

localize34.0ms

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)))))))

series389.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
157.0ms
(* (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))))
180.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify97.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune425.0ms

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

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
18×add-exp-log add-cbrt-cube
17×pow-prod-down
16×sin-mult
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×times-frac
10×cos-mult
8×prod-exp cbrt-unprod
7×associate-/l/
6×frac-sub add-log-exp
5×associate-*r/ associate-*l/ difference-of-squares
4×pow-sqr pow-prod-up associate-/l* sub-div
3×frac-times associate-/r*
2×flip3-- pow-plus associate-/r/ flip--
1×cbrt-undiv pow2 sub-neg asin-acos sqr-cos frac-2neg flip3-+ diff-log div-sub swap-sqr div-exp associate-*r* associate-*l* associate--l+ clear-num *-commutative flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (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) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
11.0ms
(* (* (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)))))))
8.0ms
(- (* (cos delta) (cos delta)) (* (* (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))))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
802.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (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) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
180.0ms
(* (* (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)))))))
497.0ms
(- (* (cos delta) (cos delta)) (* (* (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))))))))

simplify108.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06354481
131043982
250023958

prune739.0ms

Filtered
117 candidates to 84 candidates (71.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1107117
Fresh6410
Picked101
Done000
Total11711128

Merged error: 0.0b

Counts
128 → 11

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
0.4b
(pow (sin phi1) 3)
0.5b
(pow (sin phi1) 4)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
32×*-un-lft-identity
24×times-frac
22×add-cube-cbrt
20×difference-of-squares
13×add-log-exp
11×unpow-prod-down
8×add-exp-log associate-/l*
7×add-cbrt-cube sqr-pow
6×pow1 pow-unpow
5×distribute-lft-out-- unpow2
3×diff-log cube-prod associate-/r* sum-log
2×pow-to-exp flip3-- pow-pow pow-exp associate-/r/ flip-- associate-/l/
1×cbrt-undiv cube-mult sub-neg frac-2neg flip3-+ unpow3 div-sub div-exp clear-num flip-+ div-inv associate--r+ rem-cube-cbrt
Counts
4 → 112
Calls
4 calls:
28.0ms
(/ (- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
27.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
3.0ms
(pow (sin phi1) 3)
3.0ms
(pow (sin phi1) 4)

series1.2s

Counts
4 → 12
Calls
4 calls:
717.0ms
(/ (- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
417.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
37.0ms
(pow (sin phi1) 3)
33.0ms
(pow (sin phi1) 4)

simplify106.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06715261
129454957
250034946

prune1.0s

Filtered
124 candidates to 78 candidates (62.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1213124
Fresh2810
Picked101
Done000
Total12411135

Merged error: 0.0b

Counts
135 → 11

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

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 flip3-- diff-log flip--
Counts
4 → 36
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(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)))))))

series207.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
186.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify147.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0158786
1383692
21284692
34127692
45001692

prune281.0ms

Filtered
48 candidates to 39 candidates (81.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New47148
Fresh01010
Picked011
Done000
Total471259

Merged error: 0.0b

Counts
59 → 12

regimes638.0ms

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
03454
13454

end0.0ms

sample8.5s

Algorithm
intervals
Results
5.4s3117×body1280valid
1.7s1830×body640valid
466.0ms735×body320valid
382.0ms2002×body80valid
134.0ms316×body160valid

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