Details

Time bar (total: 12.5s)

sample274.0ms

Algorithm
intervals
Results
165.0ms102×body1280valid
67.0ms74×body640valid
9.0ms56×body80valid
8.0ms15×body320valid
3.0ms9×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

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

localize39.0ms

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)))))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
1×sub-neg asin-acos flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 46
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))))))))
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)))))))

series367.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
154.0ms
(* (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))))
184.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify82.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02441107
1692985
22754983
35001983

prune357.0ms

Filtered
58 candidates to 44 candidates (75.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New471158
Fresh000
Picked101
Done000
Total481159

Merged error: 0.0b

Counts
59 → 11

localize49.0ms

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×pow-unpow
4×unpow-prod-down cube-prod add-log-exp
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp asin-acos unpow3 sqr-pow
1×cube-div pow-prod-down prod-exp cbrt-unprod sin-mult
Counts
4 → 62
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))))
2.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series292.0ms

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))))
34.0ms
(pow (cos delta) 3)
244.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify42.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0250777
11023671
25001666

prune464.0ms

Filtered
74 candidates to 48 candidates (64.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New72274
Fresh01010
Picked101
Done000
Total731285

Merged error: 0.0b

Counts
85 → 12

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(pow (cos delta) 3)
0.4b
(pow (sin phi1) 3)
0.6b
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)

rewrite14.0ms

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×add-log-exp
3×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
1×asin-acos
Counts
4 → 77
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(pow (cos delta) 3)
3.0ms
(pow (sin phi1) 3)
4.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)

series249.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
28.0ms
(pow (cos delta) 3)
35.0ms
(pow (sin phi1) 3)
178.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)

simplify46.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0290731
11214628
25002616

prune478.0ms

Filtered
89 candidates to 49 candidates (55.1%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New89089
Fresh01111
Picked011
Done000
Total8912101

Merged error: 0.0b

Counts
101 → 12

localize39.0ms

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
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.8b
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×*-un-lft-identity
8×pow1 add-cube-cbrt
6×add-exp-log log-prod add-cbrt-cube add-log-exp
4×log-pow
3×associate-*r* associate-*l* associate--r+
2×distribute-lft-out--
1×sub-neg asin-acos exp-prod flip3-- exp-to-pow diff-log rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult difference-of-squares unswap-sqr
Counts
4 → 59
Calls
4 calls:
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))))
6.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
3.0ms
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series504.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
12.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
179.0ms
(- (cos delta) (log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
158.0ms
(log (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify78.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02501229
16861110
225901106
350021106

prune341.0ms

Filtered
71 candidates to 52 candidates (73.2%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New70171
Fresh1910
Picked011
Done011
Total711283

Merged error: 0.0b

Counts
83 → 12

regimes683.0ms

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
04459
14459

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.0s3060×body1280valid
1.7s1858×body640valid
441.0ms738×body320valid
341.0ms2004×body80valid
127.0ms340×body160valid