Details

Time bar (total: 12.2s)

sample274.0ms

Algorithm
intervals
Results
168.0ms104×body1280valid
63.0ms69×body640valid
10.0ms18×body320valid
9.0ms55×body80valid
4.0ms10×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 0.1b

Counts
2 → 1

localize32.0ms

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))))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite17.0ms

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))
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)))))))

series375.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin theta) (sin delta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
148.0ms
(* (sin phi1) (sin (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)))))))

simplify93.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune384.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New601070
Fresh000
Picked101
Done000
Total611071

Merged error: 0.1b

Counts
71 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.5b
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
2.3b
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite28.0ms

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:
1.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms
(* (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))))))))
8.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
145.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
182.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
38.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify129.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
03111574
19101391
236611325
350021306

prune438.0ms

Filtered
79 candidates to 57 candidates (72.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New76379
Fresh279
Picked101
Done000
Total791089

Merged error: 0.0b

Counts
89 → 10

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b
(sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b
(- (cos delta) (* (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
11.7b
(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
58.2b
(cos (/ PI 2))

rewrite11.0ms

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
1×neg-sub0 acos-asin cos-diff sub-neg flip3-- cos-PI/2 diff-log sin-neg sin-diff cos-acos flip--
Counts
4 → 38
Calls
4 calls:
2.0ms
(sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
3.0ms
(- (cos delta) (* (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
2.0ms
(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
2.0ms
(cos (/ PI 2))

series366.0ms

Counts
4 → 10
Calls
4 calls:
73.0ms
(sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
174.0ms
(- (cos delta) (* (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
119.0ms
(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.0ms
(cos (/ PI 2))

simplify192.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0218750
1550649
22392633
35002633

prune370.0ms

Filtered
48 candidates to 40 candidates (83.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New47148
Fresh279
Picked011
Done000
Total49958

Merged error: 0.0b

Counts
58 → 9

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos (/ PI 2)) (sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.4b
(sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
58.2b
(cos (/ PI 2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-log-exp
8×*-un-lft-identity
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l*
2×diff-log sin-neg
1×neg-sub0 sub-neg flip3-- cos-PI/2 pow-prod-down prod-exp sum-log sin-diff *-commutative distribute-rgt-neg-out flip-- cbrt-unprod associate--r+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 52
Calls
4 calls:
5.0ms
(* (cos (/ PI 2)) (sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
2.0ms
(sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
3.0ms
(cos (/ PI 2))

series269.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(* (cos (/ PI 2)) (sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
73.0ms
(sin (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
194.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin phi1) (* (cos phi1) (* (cos theta) (sin delta))))))
0.0ms
(cos (/ PI 2))

simplify45.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0256997
1870653
25001607

prune399.0ms

Filtered
62 candidates to 50 candidates (80.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New60262
Fresh167
Picked101
Done011
Total62971

Merged error: 0.0b

Counts
71 → 9

regimes415.0ms

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
04140
14140

end0.0ms

sample7.8s

Algorithm
intervals
Results
5.0s3149×body1280valid
1.7s1851×body640valid
406.0ms685×body320valid
322.0ms1984×body80valid
129.0ms331×body160valid