Details

Time bar (total: 15.5s)

sample273.0ms

Algorithm
intervals
Results
160.0ms97×body1280valid
57.0ms56×body640valid
20.0ms75×body80valid
14.0ms21×body320valid
3.0ms7×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: 0.2b

localize36.0ms

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)))))))

rewrite14.0ms

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))
5.0ms
(* (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)))))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin theta) (sin delta))
153.0ms
(* (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))))
182.0ms
(- (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

prune376.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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)))))))
0.8b
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
5×log-prod
4×log-pow
3×exp-prod associate-*r* associate-*l*
2×sub-neg exp-sum
1×log-div asin-acos flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
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)))))))
5.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

series525.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* (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))))
181.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
184.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))

simplify87.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02531234
17641106
229491102
350011102

prune404.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
43×pow1
17×pow-prod-down
16×add-exp-log add-cbrt-cube
10×sin-mult
8×prod-exp cbrt-unprod
6×add-log-exp
5×cos-mult
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow-sqr pow-prod-up
3×associate-*r/ associate-*l/ frac-sub
2×frac-times asin-acos pow-plus sub-div
1×pow2 sub-neg sqr-cos flip3-- diff-log swap-sqr associate-*r* associate-*l* associate--l+ *-commutative flip-- difference-of-squares
Counts
4 → 72
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
15.0ms
(* (* (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)))))))
12.0ms
(- (* (cos delta) (cos delta)) (* (* (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))))))))

series696.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
183.0ms
(* (* (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)))))))
499.0ms
(- (* (cos delta) (cos delta)) (* (* (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))))))))

simplify73.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04272117
119801743
250011711

prune461.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(pow (sin phi1) 3)
0.4b
(pow (sin phi1) 4)
0.4b
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-log-exp
11×*-un-lft-identity
9×add-cube-cbrt
7×unpow-prod-down
6×pow1 add-exp-log pow-unpow
5×add-cbrt-cube
4×difference-of-squares
3×diff-log cube-prod sum-log sqr-pow
2×pow-to-exp pow-pow pow-exp
1×cube-mult sub-neg asin-acos flip3-- unpow3 flip-- associate--r+ distribute-lft-out-- unpow2 rem-cube-cbrt
Counts
4 → 68
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(pow (sin phi1) 3)
1.0ms
(pow (sin phi1) 4)
1.5s
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
37.0ms
(pow (sin phi1) 3)
31.0ms
(pow (sin phi1) 4)
416.0ms
(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04241360
118221261
250011254

prune623.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes440.0ms

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
06980
16980

end0.0ms

sample8.8s

Algorithm
intervals
Results
5.5s3145×body1280valid
1.9s1827×body640valid
504.0ms2022×body80valid
468.0ms698×body320valid
146.0ms308×body160valid