Details

Time bar (total: 16.8s)

sample285.0ms

Algorithm
intervals
Results
176.0ms104×body1280valid
58.0ms61×body640valid
13.0ms20×body320valid
12.0ms64×body80valid
3.0ms7×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03522
15622
25922
35922

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

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)))))))

rewrite35.0ms

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:
12.0ms
(* (sin theta) (sin delta))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series552.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (sin theta) (sin delta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
140.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
365.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify91.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune388.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.5b
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
15.9b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×cbrt-prod *-un-lft-identity
9×pow1 add-exp-log add-cbrt-cube
8×add-cube-cbrt
6×add-log-exp
3×pow-unpow associate-*r* associate-*l* sin-mult difference-of-squares sqr-pow
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod rem-cube-cbrt
1×pow-to-exp sub-neg cbrt-div flip3-- pow1/3 diff-log *-commutative flip-- rem-cbrt-cube distribute-lft-out-- unswap-sqr
Counts
4 → 76
Calls
4 calls:
15.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
10.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
10.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
5.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series658.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
215.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
164.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
138.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify51.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03341587
113101468
250021463

prune509.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
39×times-frac
36×*-un-lft-identity
32×difference-of-squares
28×add-cube-cbrt
26×sqr-pow
13×associate-/l*
12×add-exp-log unpow-prod-down cube-prod add-cbrt-cube
10×pow1
7×associate-/r/
6×pow-unpow
5×frac-add cos-mult sin-mult
4×difference-cubes distribute-lft-out-- add-log-exp
3×pow-pow flip3-+ associate-*r* associate-*l* pow-exp associate-/r* flip-+ rem-cube-cbrt
2×cube-mult frac-times pow-to-exp unpow3 associate-*r/ pow-prod-down prod-exp cbrt-unprod associate-/l/
1×cbrt-undiv cube-div flip3-- frac-2neg div-sub div-exp associate-*l/ clear-num *-commutative flip-- div-inv unswap-sqr
Counts
4 → 142
Calls
4 calls:
13.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
102.0ms
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (+ (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta))) (* (cos delta) (cos delta))))
3.0ms
(pow (cos delta) 3)
10.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series2.1s

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.7s
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (+ (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (+ (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cos delta))) (* (cos delta) (cos delta))))
29.0ms
(pow (cos delta) 3)
219.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify78.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010607668
150017400

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize102.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (sin phi1) 4)
0.5b
(pow (sin phi1) 4)
0.6b
(pow (sin phi1) 5)
0.7b
(pow (sin phi1) 6)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down pow-unpow *-un-lft-identity
8×pow1 add-exp-log
4×pow-to-exp pow-pow pow-exp add-cbrt-cube add-log-exp sqr-pow
Counts
4 → 68
Calls
4 calls:
3.0ms
(pow (sin phi1) 4)
3.0ms
(pow (sin phi1) 4)
3.0ms
(pow (sin phi1) 5)
4.0ms
(pow (sin phi1) 6)

series135.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (sin phi1) 4)
27.0ms
(pow (sin phi1) 4)
42.0ms
(pow (sin phi1) 5)
38.0ms
(pow (sin phi1) 6)

simplify85.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
0214303
1680287
22715266
35002260

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes592.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03324
13324

end0.0ms

sample8.7s

Algorithm
intervals
Results
5.3s3047×body1280valid
1.9s1852×body640valid
476.0ms726×body320valid
407.0ms2042×body80valid
151.0ms333×body160valid