Details

Time bar (total: 21.4s)

sample403.0ms

Algorithm
intervals
Results
233.0ms101×body1280valid
107.0ms54×body640valid
19.0ms76×body80valid
13.0ms17×body320valid
4.0ms8×body160valid

simplify3.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize74.0ms

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
12.0ms
(* (sin theta) (sin delta))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin theta) (sin delta))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
168.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
212.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify85.0ms

Counts
70 → 70

prune415.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
15.9b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×cbrt-prod *-un-lft-identity
9×pow1 add-exp-log add-cbrt-cube
8×add-cube-cbrt
6×add-log-exp
3×pow-unpow associate-*r* associate-*l* sin-mult difference-of-squares sqr-pow
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod rem-cube-cbrt
1×pow-to-exp sub-neg cbrt-div flip3-- pow1/3 diff-log *-commutative flip-- rem-cbrt-cube distribute-lft-out-- unswap-sqr
Counts
4 → 76
Calls
4 calls:
14.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
10.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
10.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
5.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
173.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
472.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
259.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
174.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify48.0ms

Counts
88 → 88

prune547.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 3)
0.4b
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3))))
0.5b
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
15.9b
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
6×pow1 add-exp-log unpow-prod-down pow-unpow cube-prod add-cbrt-cube add-log-exp
2×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
1×cbrt-prod sub-neg flip3-- pow1/3 diff-log pow-prod-down flip-- rem-cbrt-cube distribute-lft-out-- difference-of-squares
Counts
4 → 70
Calls
4 calls:
4.0ms
(pow (sin phi1) 3)
7.0ms
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3))))
5.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
10.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))

series625.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(pow (sin phi1) 3)
207.0ms
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3))))
212.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
175.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))

simplify46.0ms

Counts
82 → 82

prune485.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
0.5b
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
15.9b
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))
15.9b
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log unpow-prod-down pow-unpow cube-prod add-cbrt-cube
4×add-log-exp
2×cbrt-prod cube-mult pow-to-exp pow-pow pow1/3 unpow3 pow-prod-down pow-exp rem-cbrt-cube rem-cube-cbrt sqr-pow
Counts
4 → 66
Calls
4 calls:
5.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
5.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
15.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))
9.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))

series762.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
211.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
174.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))
170.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))

simplify172.0ms

Counts
78 → 78

prune530.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes403.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample14.9s

Algorithm
intervals
Results
8.9s3220×body1280valid
3.9s1788×body640valid
857.0ms1929×body80valid
618.0ms740×body320valid
204.0ms323×body160valid