Details

Time bar (total: 14.7s)

sample272.0ms

Algorithm
intervals
Results
166.0ms105×body1280valid
52.0ms58×body640valid
13.0ms23×body320valid
10.0ms60×body80valid
9.0ms10×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03622
16122
27122
37222
47222

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

localize32.0ms

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
36×prod-diff
34×*-un-lft-identity
30×add-cube-cbrt
16×associate-*l*
15×associate-*r*
8×pow1 add-exp-log add-cbrt-cube
6×add-log-exp unswap-sqr
5×*-commutative
4×expm1-log1p-u log1p-expm1-u
3×fma-neg
2×pow-prod-down prod-exp cbrt-unprod sin-mult distribute-lft-out-- difference-of-squares
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 109
Calls
4 calls:
5.0ms
(* (sin theta) (sin delta))
7.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series393.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin theta) (sin delta))
153.0ms
(* (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))))
185.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04903725
114872512
250012414

prune450.0ms

Filtered
121 candidates to 70 candidates (57.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11110121
Fresh000
Picked101
Done000
Total11210122

Merged error: 0.0b

Counts
122 → 10

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×prod-diff
30×*-un-lft-identity
26×add-cube-cbrt
10×associate-*l*
9×associate-*r*
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u unswap-sqr
3×asin-acos fma-neg *-commutative
2×distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- diff-log flip--
Counts
4 → 87
Calls
4 calls:
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series204.0ms

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))))
183.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03763591
110822377
250012279

prune457.0ms

Filtered
99 candidates to 58 candidates (58.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New95499
Fresh459
Picked101
Done000
Total1009109

Merged error: 0.0b

Counts
109 → 9

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
176×unpow-prod-down
136×prod-diff
114×add-sqr-sqrt
86×*-un-lft-identity
76×add-cube-cbrt
34×sqr-pow
28×associate-*l*
27×unpow3 associate-*r*
12×difference-of-squares unswap-sqr
9×*-commutative
8×fma-neg
7×pow1 add-exp-log pow-unpow add-cbrt-cube
6×add-log-exp
4×difference-cubes expm1-log1p-u log1p-expm1-u
3×distribute-lft-out--
2×asin-acos pow-pow pow-exp rem-cube-cbrt
1×pow-to-exp sub-neg flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod
Counts
4 → 230
Calls
4 calls:
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
18.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
8.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.0s

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))))
762.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
241.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify200.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (123.0ms)

IterNodesCost
0100712093
139577899
250017893

prune860.0ms

Filtered
242 candidates to 88 candidates (36.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2402242
Fresh178
Picked101
Done000
Total2429251

Merged error: 0.0b

Counts
251 → 9

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.6b
(pow (cos delta) 6)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
24×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
14×pow1 add-exp-log
13×add-cbrt-cube
12×pow-unpow
9×associate-*r* associate-*l*
7×pow-pow pow-exp
6×rem-cube-cbrt
4×expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp sqr-pow
3×unpow3 pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 118
Calls
4 calls:
9.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
9.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
12.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
2.0ms
(pow (cos delta) 6)

series816.0ms

Counts
4 → 12
Calls
4 calls:
253.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
248.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
269.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
45.0ms
(pow (cos delta) 6)

simplify56.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03031939
112421756
250021710

prune854.0ms

Filtered
130 candidates to 83 candidates (63.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1282130
Fresh178
Picked101
Done000
Total1309139

Merged error: 0.0b

Counts
139 → 9

regimes463.0ms

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
04588
14588

end0.0ms

sample8.3s

Algorithm
intervals
Results
5.3s3049×body1280valid
1.7s1838×body640valid
434.0ms713×body320valid
363.0ms2061×body80valid
141.0ms339×body160valid