Details

Time bar (total: 16.8s)

sample268.0ms

Algorithm
intervals
Results
170.0ms104×body1280valid
53.0ms59×body640valid
12.0ms67×body80valid
8.0ms14×body320valid
5.0ms12×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03622
16122
27122
37222
47222

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg prod-diff
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 72
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))))))
5.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
160.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
192.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify106.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune509.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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)
0.4b
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
18.3b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
34×cbrt-prod
33×add-sqr-sqrt prod-diff
28×*-un-lft-identity
26×add-cube-cbrt
9×pow1 add-exp-log add-cbrt-cube
6×add-log-exp sqr-pow
5×cube-mult unpow-prod-down unpow3 cube-prod
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-neg associate-*r* associate-*l* sin-mult difference-of-squares
2×cube-div pow-pow 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 → 120
Calls
4 calls:
6.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
8.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
3.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series751.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
243.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
187.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
161.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify83.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04914889
117883708
250013688

prune663.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

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

rewrite44.0ms

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
6×pow-unpow
4×difference-cubes expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
3×pow-pow associate-*r* associate-*l* pow-exp associate-/r* rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 pow-prod-down prod-exp cbrt-unprod associate-/l/ sin-mult
1×cbrt-undiv cube-div flip3-- frac-2neg div-sub div-exp clear-num *-commutative flip-- div-inv unswap-sqr
Counts
4 → 143
Calls
4 calls:
6.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
20.0ms
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (fma (cos delta) (cos delta) (* (sin phi1) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta))))))
3.0ms
(pow (cos delta) 3)
9.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series2.1s

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.6s
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)) (fma (cos delta) (cos delta) (* (sin phi1) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta))))))
35.0ms
(pow (cos delta) 3)
243.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify193.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
08796989
148896676
250016676

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 4)
0.4b
(pow (cos theta) 3)
0.4b
(pow (sin phi1) 5)
0.5b
(pow (sin phi1) 6)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down pow-unpow
8×pow1 add-exp-log
5×add-cbrt-cube
4×expm1-log1p-u pow-to-exp pow-pow pow-exp log1p-expm1-u add-log-exp sqr-pow
3×cube-prod
1×cube-mult unpow3 rem-cube-cbrt
Counts
4 → 82
Calls
4 calls:
3.0ms
(pow (sin phi1) 4)
3.0ms
(pow (cos theta) 3)
3.0ms
(pow (sin phi1) 5)
3.0ms
(pow (sin phi1) 6)

series154.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(pow (sin phi1) 4)
28.0ms
(pow (cos theta) 3)
48.0ms
(pow (sin phi1) 5)
42.0ms
(pow (sin phi1) 6)

simplify44.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0316325
11209297
25001288

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes441.0ms

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
0107104
1107104

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.2s3132×body1280valid
1.9s1801×body640valid
480.0ms743×body320valid
368.0ms2010×body80valid
124.0ms314×body160valid