Details

Time bar (total: 12.8s)

sample274.0ms

Algorithm
intervals
Results
159.0ms102×body1280valid
68.0ms74×body640valid
16.0ms56×body80valid
8.0ms15×body320valid
3.0ms9×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03622
16122
27122
37222
47222

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (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))))))
0.3b
(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)))))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg associate-*r* associate-*l* prod-diff
1×sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 60
Calls
4 calls:
1.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
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)))))))

series373.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
163.0ms
(* (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))))
188.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify95.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
02771411
18191248
233641243
350021188

prune433.0ms

Filtered
72 candidates to 58 candidates (80.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New611172
Fresh000
Picked101
Done000
Total621173

Merged error: 0.0b

Counts
73 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (- (cos delta) (* (sin phi1) (sin (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))))))
0.3b
(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)))))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube add-log-exp
5×expm1-log1p-u
4×log1p-expm1-u
3×fma-neg associate-*r* associate-*l* prod-diff
1×sub-neg asin-acos log1p-udef flip3-- diff-log log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 62
Calls
4 calls:
1.0ms
(log1p (- (cos delta) (* (sin phi1) (sin (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))))))
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)))))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(log1p (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
159.0ms
(* (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))))
183.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify107.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
03011344
19151191
237021184
350011179

prune459.0ms

Filtered
74 candidates to 60 candidates (81.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New73174
Fresh01010
Picked011
Done000
Total731285

Merged error: 0.0b

Counts
85 → 12

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1)))))))
0.2b
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
0.3b
(pow (sin phi1) 2)
0.4b
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×pow1 add-exp-log add-cube-cbrt
13×add-cbrt-cube
9×prod-diff add-log-exp
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u
3×unpow-prod-down pow-unpow fma-neg associate-*l*
2×diff-log
1×pow-to-exp sub-neg flip3-- pow-pow associate-*r* pow-exp sum-log *-commutative flip-- associate--r+ distribute-lft-out-- unpow2 difference-of-squares sqr-pow
Counts
4 → 82
Calls
4 calls:
1.0ms
(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1)))))))
9.0ms
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
3.0ms
(pow (sin phi1) 2)
8.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1)))))))
111.0ms
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
19.0ms
(pow (sin phi1) 2)
185.0ms
(- (cos delta) (+ (* (pow (sin phi1) 2) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))

simplify70.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04191750
116121199
250011178

prune437.0ms

Filtered
94 candidates to 62 candidates (66.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New92294
Fresh2810
Picked101
Done011
Total9511106

Merged error: 0.0b

Counts
106 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
0.4b
(- (cos delta) (+ (* (cbrt (pow (sin phi1) 6)) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))
0.6b
(pow (sin phi1) 6)
11.1b
(cbrt (pow (sin phi1) 6))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt
14×pow1 add-exp-log
13×add-cbrt-cube
9×prod-diff add-log-exp
7×cbrt-prod
6×unpow-prod-down pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-neg associate-*l*
2×diff-log sqr-pow
1×pow-to-exp sub-neg flip3-- pow-pow pow1/3 associate-*r* pow-exp sum-log *-commutative flip-- associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 89
Calls
4 calls:
9.0ms
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
9.0ms
(- (cos delta) (+ (* (cbrt (pow (sin phi1) 6)) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))
3.0ms
(pow (sin phi1) 6)
3.0ms
(cbrt (pow (sin phi1) 6))

series528.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))
336.0ms
(- (cos delta) (+ (* (cbrt (pow (sin phi1) 6)) (cos delta)) (* (sin delta) (* (cos phi1) (* (cos theta) (sin phi1))))))
48.0ms
(pow (sin phi1) 6)
19.0ms
(cbrt (pow (sin phi1) 6))

simplify62.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04461629
116951097
250021056

prune395.0ms

Filtered
101 candidates to 68 candidates (67.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1001101
Fresh189
Picked011
Done011
Total10111112

Merged error: 0.0b

Counts
112 → 11

regimes585.0ms

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
03122
13122

end0.0ms

sample7.8s

Algorithm
intervals
Results
4.9s3060×body1280valid
1.7s1858×body640valid
447.0ms738×body320valid
337.0ms2004×body80valid
144.0ms340×body160valid