Details

Time bar (total: 13.6s)

sample284.0ms

Algorithm
intervals
Results
170.0ms107×body1280valid
61.0ms61×body640valid
16.0ms19×body320valid
9.0ms51×body80valid
7.0ms18×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03622
16122
27122
37222
47222

prune6.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

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)))))))

rewrite15.0ms

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:
4.0ms
(* (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))))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series393.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin theta) (sin delta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
156.0ms
(* (sin phi1) (sin (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)))))))

simplify104.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune521.0ms

Filtered
84 candidates to 66 candidates (78.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.3b
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×*-un-lft-identity
18×add-cube-cbrt prod-diff
13×log-pow
11×pow1
9×add-log-exp
6×add-exp-log log-prod add-cbrt-cube
4×expm1-log1p-u exp-prod exp-to-pow log1p-expm1-u
3×fma-neg associate-*r* associate-*l* associate--r+
2×distribute-lft-out--
1×sub-neg asin-acos flip3-- diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult difference-of-squares unswap-sqr
Counts
4 → 88
Calls
4 calls:
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))))))
10.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
2.0ms
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
157.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
182.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
153.0ms
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify145.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
03282628
19571860
249451838
350011808

prune557.0ms

Filtered
100 candidates to 66 candidates (66.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.5b
(- (cos delta) (log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
2.3b
(log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
2.8b
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
39×log-prod
30×add-sqr-sqrt
29×*-un-lft-identity
26×add-cube-cbrt
18×sin-sum prod-diff
17×log-pow
12×pow1 exp-sum
9×distribute-rgt-in distribute-lft-in associate--r+ add-log-exp
7×exp-prod
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u exp-to-pow log1p-expm1-u
3×fma-neg associate-*r* associate-*l*
2×rem-log-exp distribute-lft-out--
1×sub-neg log-div asin-acos flip3-- exp-diff diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult difference-of-squares unswap-sqr
Counts
4 → 114
Calls
4 calls:
12.0ms
(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
8.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
5.0ms
(log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
2.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series506.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
186.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
155.0ms
(log (exp (* (sin phi1) (sin (log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))
7.0ms
(log (exp (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04693996
113593127
250023079

prune775.0ms

Filtered
126 candidates to 84 candidates (66.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
0.2b
(* (sin theta) (sin delta))
0.3b
(* (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) (sin phi1))
0.5b
(- (cos delta) (* (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) (sin phi1)))

rewrite16.0ms

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 unswap-sqr
1×sub-neg flip3-- diff-log flip-- fma-udef sin-mult
Counts
4 → 71
Calls
4 calls:
0.0ms
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
4.0ms
(* (sin theta) (sin delta))
7.0ms
(* (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) (sin phi1))
3.0ms
(- (cos delta) (* (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) (sin phi1)))

series521.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
54.0ms
(* (sin theta) (sin delta))
165.0ms
(* (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) (sin phi1))
180.0ms
(- (cos delta) (* (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))) (sin phi1)))

simplify40.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0295962
11056849
25001845

prune415.0ms

Filtered
83 candidates to 62 candidates (74.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes313.0ms

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
02519
12519

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.3s3169×body1280valid
1.7s1784×body640valid
430.0ms690×body320valid
349.0ms2037×body80valid
128.0ms320×body160valid