Details

Time bar (total: 13.9s)

sample262.0ms

Algorithm
intervals
Results
168.0ms100×body1280valid
45.0ms50×body640valid
14.0ms23×body320valid
12.0ms72×body80valid
4.0ms11×body160valid

simplify9.0ms

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

localize31.0ms

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

rewrite22.0ms

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))
10.0ms
(* (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)))))))

series385.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin theta) (sin delta))
147.0ms
(* (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
84 → 84
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune466.0ms

Filtered
84 candidates to 66 candidates (78.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New741084
Fresh000
Picked101
Done000
Total751085

Merged error: 0.1b

Counts
85 → 10

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×pow-unpow
4×expm1-log1p-u unpow-prod-down cube-prod log1p-expm1-u add-log-exp
3×pow-pow associate-*r* associate-*l* pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 pow-prod-down prod-exp cbrt-unprod fma-udef sqr-pow
1×cube-div distribute-rgt-in asin-acos distribute-lft-in *-commutative sin-mult unswap-sqr
Counts
4 → 82
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
2.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series570.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
299.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
33.0ms
(pow (cos delta) 3)
231.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify59.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
03701448
117101285
250031281

prune598.0ms

Filtered
94 candidates to 63 candidates (67.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New91394
Fresh099
Picked101
Done000
Total9212104

Merged error: 0.0b

Counts
104 → 12

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×pow-unpow
4×expm1-log1p-u unpow-prod-down cube-prod log1p-expm1-u add-log-exp
3×pow-pow associate-*r* associate-*l* pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 pow-prod-down prod-exp cbrt-unprod fma-udef sqr-pow
1×cube-div distribute-rgt-in asin-acos distribute-lft-in *-commutative sin-mult unswap-sqr
Counts
4 → 82
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
3.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series569.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
299.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
32.0ms
(pow (cos delta) 3)
231.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify58.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
03701448
117101285
250031281

prune644.0ms

Filtered
94 candidates to 63 candidates (67.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New93194
Fresh11011
Picked101
Done000
Total9511106

Merged error: 0.0b

Counts
106 → 11

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
0.3b
(pow (cos delta) 3)
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.6b
(expm1 (pow (cos delta) 3))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×pow-unpow
5×log1p-expm1-u
4×expm1-log1p-u unpow-prod-down cube-prod add-log-exp
3×pow-pow associate-*r* associate-*l* pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 pow-prod-down prod-exp cbrt-unprod fma-udef sqr-pow
1×cube-div distribute-rgt-in expm1-log1p distribute-lft-in *-commutative sin-mult expm1-udef unswap-sqr
Counts
4 → 83
Calls
4 calls:
5.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
3.0ms
(pow (cos delta) 3)
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
1.0ms
(expm1 (pow (cos delta) 3))

series649.0ms

Counts
4 → 12
Calls
4 calls:
311.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (fma (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
28.0ms
(pow (cos delta) 3)
237.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
72.0ms
(expm1 (pow (cos delta) 3))

simplify61.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
03931343
118341189
250031184

prune554.0ms

Filtered
95 candidates to 62 candidates (65.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New94195
Fresh01010
Picked101
Done000
Total9511106

Merged error: 0.0b

Counts
106 → 11

regimes453.0ms

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
03224
13224

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.2s3111×body1280valid
1.7s1785×body640valid
435.0ms718×body320valid
399.0ms2054×body80valid
132.0ms332×body160valid