Details

Time bar (total: 15.9s)

sample270.0ms

Algorithm
intervals
Results
176.0ms108×body1280valid
49.0ms55×body640valid
11.0ms18×body320valid
10.0ms60×body80valid
6.0ms15×body160valid

simplify10.0ms

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: 0.2b

localize41.0ms

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)))))))

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))
6.0ms
(* (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)))))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin theta) (sin delta))
148.0ms
(* (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))))
180.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify105.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune506.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

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)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
96×prod-diff
57×add-sqr-sqrt
49×*-un-lft-identity
47×add-cube-cbrt
45×unpow-prod-down cube-prod
29×sqr-pow
23×cube-mult unpow3
12×fma-neg
8×pow1 add-exp-log add-cbrt-cube difference-of-squares
6×pow-unpow add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-pow pow-exp rem-cube-cbrt
2×pow-to-exp
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 → 192
Calls
4 calls:
2.0ms
(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))
3.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series998.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
728.0ms
(- (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)
236.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify172.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
07046457
132624820
250014818

prune797.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×unpow-prod-down cube-prod
12×fma-neg prod-diff
9×pow-unpow
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
5×cube-mult unpow3 sqr-pow
4×expm1-log1p-u log1p-expm1-u
3×cube-div pow-to-exp pow-pow pow-exp rem-cube-cbrt
1×difference-cubes sub-neg flip3-- flip3-+ diff-log associate-*r/ pow-prod-down frac-add cos-mult sin-cos-mult flip-- flip-+
Counts
4 → 117
Calls
4 calls:
15.0ms
(- (pow (cos delta) 3) (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))
3.0ms
(pow (cos delta) 3)
3.0ms
(pow (sin phi1) 3)
9.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

series969.0ms

Counts
4 → 12
Calls
4 calls:
738.0ms
(- (pow (cos delta) 3) (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))
29.0ms
(pow (cos delta) 3)
34.0ms
(pow (sin phi1) 3)
168.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)

simplify150.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (136.0ms)

IterNodesCost
07091815
139441514
250011496

prune895.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down pow-unpow cube-prod
7×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
1×fma-udef
Counts
4 → 85
Calls
4 calls:
3.0ms
(pow (sin phi1) 3)
1.0ms
(fma (pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 3) (- (pow (sin phi1) 3)) (pow (cos delta) 3))
2.0ms
(pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 3)
2.0ms
(pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 3)

series886.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(pow (sin phi1) 3)
502.0ms
(fma (pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 3) (- (pow (sin phi1) 3)) (pow (cos delta) 3))
174.0ms
(pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 3)
174.0ms
(pow (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) 3)

simplify76.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
04131065
12086927
25002914

prune665.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes474.0ms

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
05380
15380

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.3s3177×body1280valid
1.7s1796×body640valid
439.0ms734×body320valid
354.0ms1979×body80valid
124.0ms314×body160valid