Details

Time bar (total: 16.7s)

sample285.0ms

Algorithm
intervals
Results
164.0ms96×body1280valid
56.0ms56×body640valid
22.0ms29×body320valid
16.0ms57×body80valid
8.0ms18×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03622
16122
27122
37222
47222

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

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))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite14.0ms

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

series392.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin theta) (sin delta))
156.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
185.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify113.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
03221198
110211064
241241059
350011054

prune505.0ms

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
(expm1 (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))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite10.0ms

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 expm1-log1p flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult expm1-udef unswap-sqr
Counts
4 → 62
Calls
4 calls:
0.0ms
(expm1 (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))))
3.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series602.0ms

Counts
4 → 12
Calls
4 calls:
255.0ms
(expm1 (log1p (- (cos delta) (* (sin phi1) (sin (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))))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
182.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify93.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
02651329
18041178
233461169
350021114

prune676.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
96×prod-diff
61×add-sqr-sqrt
51×*-un-lft-identity
49×add-cube-cbrt
45×unpow-prod-down cube-prod
29×sqr-pow
23×cube-mult unpow3
12×fma-neg
10×pow1 add-exp-log add-cbrt-cube
8×difference-of-squares
6×pow-unpow add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-pow associate-*r* associate-*l* pow-exp rem-cube-cbrt
2×pow-to-exp pow-prod-down prod-exp cbrt-unprod fma-udef
1×difference-cubes cube-div distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log *-commutative flip-- sin-mult distribute-lft-out-- unswap-sqr
Counts
4 → 204
Calls
4 calls:
4.0ms
(* (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)))
18.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
1.0ms
(pow (cos delta) 3)
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.3s

Counts
4 → 12
Calls
4 calls:
312.0ms
(* (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)))
743.0ms
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
27.0ms
(pow (cos delta) 3)
231.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify183.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (129.0ms)

IterNodesCost
07997052
138845356
250015355

prune923.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

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)))
0.4b
(- (pow (cos delta) 3) (log1p (expm1 (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))))
0.4b
(pow (cos delta) 3)
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
36×*-un-lft-identity prod-diff
34×add-cube-cbrt
17×unpow-prod-down cube-prod
12×fma-neg
10×pow1 add-exp-log add-cbrt-cube
7×add-log-exp sqr-pow
6×cube-mult pow-unpow unpow3
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×pow-pow associate-*r* associate-*l* pow-exp rem-cube-cbrt
2×pow-to-exp diff-log pow-prod-down prod-exp cbrt-unprod fma-udef
1×cube-div distribute-rgt-in sub-neg log1p-udef flip3-- distribute-lft-in *-commutative flip-- sin-mult distribute-lft-out-- unswap-sqr
Counts
4 → 140
Calls
4 calls:
4.0ms
(* (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)))
13.0ms
(- (pow (cos delta) 3) (log1p (expm1 (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))))
4.0ms
(pow (cos delta) 3)
4.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.1s

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)))
528.0ms
(- (pow (cos delta) 3) (log1p (expm1 (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))))
33.0ms
(pow (cos delta) 3)
235.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify136.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
06734166
133883187
250013183

prune879.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes425.0ms

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
04561
14561

end0.0ms

sample8.8s

Algorithm
intervals
Results
5.6s3222×body1280valid
1.8s1779×body640valid
465.0ms671×body320valid
402.0ms1995×body80valid
146.0ms333×body160valid