Details

Time bar (total: 17.4s)

sample272.0ms

Algorithm
intervals
Results
170.0ms104×body1280valid
59.0ms69×body640valid
10.0ms18×body320valid
9.0ms55×body80valid
4.0ms10×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: 0.1b

Counts
2 → 1

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)))))))

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

series392.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin theta) (sin delta))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
158.0ms
(* (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)))))))

simplify110.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune480.0ms

Filtered
84 candidates to 66 candidates (78.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New75984
Fresh000
Picked101
Done000
Total76985

Merged error: 0.1b

Counts
85 → 9

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (cos delta) (cos delta) (* (sin phi1) (* (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) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
0.3b
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
96×prod-diff
57×add-sqr-sqrt
49×*-un-lft-identity
47×add-cube-cbrt
45×unpow-prod-down cube-prod
29×sqr-pow
23×cube-mult unpow3
12×fma-neg
8×pow1 add-exp-log add-cbrt-cube difference-of-squares
6×pow-unpow add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-pow pow-exp rem-cube-cbrt
2×pow-to-exp
1×difference-cubes cube-div sub-neg flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod fma-udef sin-mult distribute-lft-out--
Counts
4 → 192
Calls
4 calls:
1.0ms
(fma (cos delta) (cos delta) (* (sin phi1) (* (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)))))
15.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
3.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.5s

Counts
4 → 12
Calls
4 calls:
498.0ms
(fma (cos delta) (cos delta) (* (sin phi1) (* (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)))))
744.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
33.0ms
(pow (cos delta) 3)
240.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify203.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (145.0ms)

IterNodesCost
08326759
141015079
250015078

prune760.0ms

Filtered
204 candidates to 79 candidates (38.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2013204
Fresh268
Picked101
Done000
Total2049213

Merged error: 0.0b

Counts
213 → 9

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (cos delta) (cos delta) (* (sin phi1) (* (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
(- (expm1 (log1p (pow (cos delta) 3))) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
0.3b
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×prod-diff
23×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
8×pow1 add-exp-log add-cbrt-cube
7×unpow-prod-down cube-prod
6×pow-unpow add-log-exp sqr-pow
5×cube-mult unpow3
4×expm1-log1p-u log1p-expm1-u
3×pow-pow fma-neg pow-exp rem-cube-cbrt
2×pow-to-exp difference-of-squares
1×cube-div associate--l- sub-neg flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod fma-udef sin-mult distribute-lft-out-- expm1-udef
Counts
4 → 105
Calls
4 calls:
1.0ms
(fma (cos delta) (cos delta) (* (sin phi1) (* (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)))))
5.0ms
(- (expm1 (log1p (pow (cos delta) 3))) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
3.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.5s

Counts
4 → 12
Calls
4 calls:
496.0ms
(fma (cos delta) (cos delta) (* (sin phi1) (* (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)))))
785.0ms
(- (expm1 (log1p (pow (cos delta) 3))) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
28.0ms
(pow (cos delta) 3)
237.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify154.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (131.0ms)

IterNodesCost
07232893
138462261
250012260

prune718.0ms

Filtered
117 candidates to 70 candidates (59.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1161117
Fresh088
Picked101
Done000
Total1179126

Merged error: 0.0b

Counts
126 → 9

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (cos delta) (cos delta) (* (sin phi1) (* (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) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
0.3b
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
96×prod-diff
57×add-sqr-sqrt
49×*-un-lft-identity
47×add-cube-cbrt
45×unpow-prod-down cube-prod
29×sqr-pow
23×cube-mult unpow3
12×fma-neg
8×pow1 add-exp-log add-cbrt-cube difference-of-squares
6×pow-unpow add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-pow pow-exp rem-cube-cbrt
2×pow-to-exp
1×difference-cubes cube-div sub-neg flip3-- diff-log pow-prod-down prod-exp flip-- cbrt-unprod fma-udef sin-mult distribute-lft-out--
Counts
4 → 192
Calls
4 calls:
1.0ms
(fma (cos delta) (cos delta) (* (sin phi1) (* (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)))))
12.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
3.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.5s

Counts
4 → 12
Calls
4 calls:
496.0ms
(fma (cos delta) (cos delta) (* (sin phi1) (* (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)))))
752.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
28.0ms
(pow (cos delta) 3)
245.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify198.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (139.0ms)

IterNodesCost
08326759
141015079
250015078

prune745.0ms

Filtered
204 candidates to 79 candidates (38.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2040204
Fresh088
Picked011
Done000
Total2049213

Merged error: 0.0b

Counts
213 → 9

regimes409.0ms

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
04258
14258

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.2s3149×body1280valid
1.7s1851×body640valid
411.0ms685×body320valid
321.0ms1984×body80valid
123.0ms331×body160valid