Details

Time bar (total: 15.3s)

sample288.0ms

Algorithm
intervals
Results
177.0ms108×body1280valid
63.0ms55×body640valid
11.0ms18×body320valid
10.0ms60×body80valid
6.0ms15×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03522
15622
25922
35922

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

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

series395.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
158.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(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)))))))

simplify99.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune409.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(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 (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube difference-of-squares sqr-pow
6×unpow-prod-down pow-unpow cube-prod add-log-exp
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp unpow3
1×difference-cubes cube-div sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod sin-mult distribute-lft-out--
Counts
4 → 76
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
3.0ms
(pow (cos delta) 3)
9.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.0s

Counts
4 → 12
Calls
4 calls:
12.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
740.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
35.0ms
(pow (cos delta) 3)
234.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify88.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
04871373
124471276
250011264

prune617.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (sin phi1) 4)
0.5b
(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (pow (sin phi1) 6) (pow (cos delta) 3)))
0.5b
(pow (sin phi1) 5)
0.6b
(pow (sin phi1) 6)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down pow-unpow add-log-exp
7×pow1 add-exp-log
4×add-cbrt-cube
3×pow-to-exp pow-pow diff-log pow-exp sqr-pow
2×sub-neg associate--l+
1×associate--l- flip3-- flip--
Counts
4 → 67
Calls
4 calls:
3.0ms
(pow (sin phi1) 4)
16.0ms
(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (pow (sin phi1) 6) (pow (cos delta) 3)))
3.0ms
(pow (sin phi1) 5)
3.0ms
(pow (sin phi1) 6)

series379.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(pow (sin phi1) 4)
256.0ms
(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (pow (sin phi1) 6) (pow (cos delta) 3)))
44.0ms
(pow (sin phi1) 5)
48.0ms
(pow (sin phi1) 6)

simplify60.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0375720
11511654
25001635

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 3)
0.5b
(pow (sin phi1) 4)
0.5b
(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (* (pow (sin phi1) 3) (pow (sin phi1) 3)) (pow (cos delta) 3)))
0.5b
(pow (sin phi1) 5)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down pow-unpow add-log-exp
7×pow1 add-exp-log
5×add-cbrt-cube
3×pow-to-exp pow-pow diff-log cube-prod pow-exp sqr-pow
2×sub-neg associate--l+
1×associate--l- cube-mult flip3-- unpow3 flip-- rem-cube-cbrt
Counts
4 → 73
Calls
4 calls:
3.0ms
(pow (sin phi1) 3)
3.0ms
(pow (sin phi1) 4)
19.0ms
(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (* (pow (sin phi1) 3) (pow (sin phi1) 3)) (pow (cos delta) 3)))
3.0ms
(pow (sin phi1) 5)

series366.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(pow (sin phi1) 3)
30.0ms
(pow (sin phi1) 4)
256.0ms
(- (- (pow (cos delta) 3) (* (pow (sin delta) 3) (* (pow (cos phi1) 3) (* (pow (cos theta) 3) (pow (sin phi1) 3))))) (* (* (pow (sin phi1) 3) (pow (sin phi1) 3)) (pow (cos delta) 3)))
43.0ms
(pow (sin phi1) 5)

simplify67.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0401777
11745691
25002684

prune933.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes718.0ms

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
08696
18696

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.4s3177×body1280valid
1.7s1796×body640valid
465.0ms734×body320valid
364.0ms1979×body80valid
142.0ms314×body160valid