Details

Time bar (total: 12.9s)

sample272.0ms

Algorithm
intervals
Results
163.0ms101×body1280valid
59.0ms64×body640valid
17.0ms29×body320valid
8.0ms51×body80valid
4.0ms11×body160valid

simplify14.0ms

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: 0.2b

Counts
2 → 1

localize31.0ms

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))))))
0.6b
(- (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))
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)))))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin theta) (sin delta))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
154.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
178.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify90.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune390.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New581270
Fresh000
Picked101
Done000
Total591271

Merged error: 0.1b

Counts
71 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.4b
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
2.2b
(- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite27.0ms

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:
11.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
1.0ms
(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)))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
7.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
186.0ms
(- (cos delta) (* (sin phi1) (sin (- (/ PI 2) (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
39.0ms
(- (/ 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 (118.0ms)

IterNodesCost
03111574
19101389
236541325
350011306

prune420.0ms

Filtered
79 candidates to 57 candidates (72.2%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New76379
Fresh3811
Picked011
Done000
Total791291

Merged error: 0.1b

Counts
91 → 12

localize40.0ms

Local error

Found 4 expressions with local error:

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))))))
0.6b
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.1b
(log (exp (* (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
11×*-un-lft-identity
8×pow1 add-cube-cbrt
6×add-exp-log log-prod add-cbrt-cube add-log-exp
4×log-pow
3×associate-*r* associate-*l* associate--r+
2×distribute-lft-out--
1×sub-neg asin-acos exp-prod flip3-- exp-to-pow diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult difference-of-squares unswap-sqr
Counts
4 → 59
Calls
4 calls:
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))))))
6.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.0ms
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
155.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
181.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
152.0ms
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify78.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02501229
16861110
225901106
350021106

prune408.0ms

Filtered
71 candidates to 53 candidates (74.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New68371
Fresh2810
Picked101
Done011
Total711283

Merged error: 0.1b

Counts
83 → 12

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1))))
2.1b
(log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1)))
14.3b
(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
16×log-prod
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt unpow-prod-down associate--r+
5×add-exp-log add-log-exp
4×pow1 acos-asin add-cbrt-cube
3×cos-diff rem-log-exp
2×exp-sum sqr-pow
1×pow-to-exp sub-neg flip3-- diff-log pow-exp log-pow cos-acos flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 58
Calls
4 calls:
1.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms
(- (cos delta) (log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1))))
4.0ms
(log (pow (exp (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)))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
235.0ms
(- (cos delta) (log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1))))
215.0ms
(log (pow (exp (cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1)))
126.0ms
(cos (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify72.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
02701305
15771138
218981115
350011102

prune377.0ms

Filtered
70 candidates to 55 candidates (78.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New68270
Fresh1910
Picked101
Done011
Total701282

Merged error: 0.1b

Counts
82 → 12

regimes483.0ms

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
03424
13424

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.2s3168×body1280valid
1.7s1792×body640valid
405.0ms651×body320valid
387.0ms2071×body80valid
129.0ms318×body160valid

Profiling

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