Details

Time bar (total: 16.5s)

sample270.0ms

Algorithm
intervals
Results
162.0ms96×body1280valid
53.0ms56×body640valid
18.0ms29×body320valid
11.0ms57×body80valid
7.0ms18×body160valid

simplify13.0ms

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

localize30.0ms

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)))))))

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))))
2.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
155.0ms
(* (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)))))))

simplify90.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune404.0ms

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

rewrite20.0ms

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)
3.0ms
(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))))
738.0ms
(- (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)
235.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify91.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
04871389
124451288
250011284

prune577.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos delta) 3)
0.4b
(pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3)
0.4b
(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:
33.0ms
(pow (cos delta) 3)
924.0ms
(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)
225.0ms
(cbrt (pow (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3) 3))

simplify63.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03912049
116691841
250011841

prune685.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
18×pow-exp
15×cube-div
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×pow-to-exp pow-unpow associate-*r/ prod-exp add-cbrt-cube
8×cbrt-prod unpow-prod-down cube-prod
7×pow1
4×cube-mult pow-pow unpow3 add-log-exp rem-cube-cbrt sqr-pow
3×cbrt-div flip3-+ frac-add cos-mult sin-cos-mult flip-+
1×pow1/3 pow-prod-down rem-cbrt-cube cbrt-unprod
Counts
4 → 102
Calls
4 calls:
2.0ms
(pow (sin phi1) 3)
21.0ms
(pow (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)) 3)
19.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
16.0ms
(cbrt (pow (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)) 3))

series1.3s

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (sin phi1) 3)
910.0ms
(pow (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)) 3)
173.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
222.0ms
(cbrt (pow (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)) 3))

simplify99.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
05401593
126571445
250021436

prune750.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes346.0ms

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
05259
15259

end0.0ms

sample8.7s

Algorithm
intervals
Results
5.6s3222×body1280valid
1.8s1779×body640valid
434.0ms671×body320valid
382.0ms1995×body80valid
138.0ms333×body160valid