Details

Time bar (total: 15.9s)

sample251.0ms

Algorithm
intervals
Results
162.0ms101×body1280valid
42.0ms49×body640valid
14.0ms25×body320valid
11.0ms70×body80valid
4.0ms11×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (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)))))))

rewrite13.0ms

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:
4.0ms
(* (sin theta) (sin delta))
4.0ms
(* (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))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin theta) (sin delta))
151.0ms
(* (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))))
179.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune373.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
1.0ms
(pow (cos delta) 3)
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series994.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
729.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
28.0ms
(pow (cos delta) 3)
230.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify90.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
04871389
124451288
250011284

prune544.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos delta) 3)
0.4b
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
6.4b
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
24×unpow-prod-down cube-prod
22×cbrt-prod
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×add-exp-log
9×pow-unpow pow-exp add-cbrt-cube
8×pow1 cube-mult unpow3 sqr-pow
5×cube-div
4×pow-to-exp pow-pow add-log-exp rem-cube-cbrt
3×sin-mult
2×prod-exp
1×cbrt-div pow1/3 pow-prod-down rem-cbrt-cube cbrt-unprod
Counts
4 → 115
Calls
4 calls:
1.0ms
(pow (cos delta) 3)
4.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
3.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
4.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

series1.4s

Counts
4 → 12
Calls
4 calls:
34.0ms
(pow (cos delta) 3)
927.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
238.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
220.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

simplify67.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
03912026
116761835
250021825

prune640.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
6.4b
(cbrt (pow (cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)) 3))
6.4b
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
122×cbrt-prod
66×unpow-prod-down cube-prod
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
14×cube-mult unpow3 sqr-pow
11×add-exp-log
8×cube-div pow-exp add-cbrt-cube
7×pow1
6×pow-unpow
4×sin-mult add-log-exp
3×pow-to-exp cbrt-div pow-pow rem-cube-cbrt
2×pow1/3 prod-exp rem-cbrt-cube
1×pow-prod-down cbrt-unprod
Counts
4 → 158
Calls
4 calls:
4.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
3.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
11.0ms
(cbrt (pow (cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)) 3))
4.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

series1.6s

Counts
4 → 12
Calls
4 calls:
939.0ms
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
235.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
229.0ms
(cbrt (pow (cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)) 3))
224.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

simplify75.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04693771
115433275
250013260

prune671.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes321.0ms

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
04158
14158

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.1s3155×body1280valid
1.7s1870×body640valid
556.0ms708×body320valid
325.0ms1976×body80valid
106.0ms291×body160valid