Details

Time bar (total: 21.4s)

sample287.0ms

Algorithm
intervals
Results
181.0ms107×body1280valid
63.0ms70×body640valid
10.0ms56×body80valid
9.0ms16×body320valid
3.0ms7×body160valid

simplify24.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02233
13632
25932
36732
done6732

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.2b
(* (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))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite15.0ms

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))
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)))))))

series386.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin theta) (sin delta))
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))))
180.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.0s

Counts
84 → 84
Iterations

Useful iterations: 3 (526.0ms)

IterNodesCost
01571824
13181677
27961492
322611479
done50011479

prune497.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.4b
(pow (cos delta) 3)
0.5b
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3)

rewrite7.0ms

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×expm1-log1p-u unpow-prod-down cube-prod log1p-expm1-u 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 → 70
Calls
4 calls:
0.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
2.0ms
(pow (cos delta) 3)
3.0ms
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3)

series254.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
6.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
28.0ms
(pow (cos delta) 3)
214.0ms
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3)

simplify2.3s

Counts
82 → 82
Iterations

Useful iterations: 3 (656.0ms)

IterNodesCost
01131327
12641239
28191105
345261103
done50001103

prune525.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.4b
(pow (cos delta) 3)
0.5b
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3)

rewrite7.0ms

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×expm1-log1p-u unpow-prod-down cube-prod log1p-expm1-u 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 → 70
Calls
4 calls:
0.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
2.0ms
(pow (cos delta) 3)
3.0ms
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3)

series263.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
6.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
32.0ms
(pow (cos delta) 3)
219.0ms
(pow (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)) 3)

simplify2.3s

Counts
82 → 82
Iterations

Useful iterations: 3 (655.0ms)

IterNodesCost
01131327
12641239
28191105
345261103
done50001103

prune586.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
0.3b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.3b
(log1p (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))))
0.5b
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))

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
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:
4.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
0.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.0ms
(log1p (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))))
3.0ms
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))

series597.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))
6.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
243.0ms
(log1p (- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1))))
180.0ms
(- (cos delta) (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1)))

simplify2.3s

Counts
74 → 74
Iterations

Useful iterations: 3 (595.0ms)

IterNodesCost
01391936
12901864
26861651
319911632
done50001632

prune430.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes283.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03083
13683
done3683

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.1s3108×body1280valid
1.7s1806×body640valid
447.0ms694×body320valid
363.0ms2077×body80valid
133.0ms315×body160valid