Details

Time bar (total: 1.0m)

sample850.0ms

Algorithm
intervals
Results
453.0ms93×body1280valid
181.0ms68×body640valid
131.0ms26×body320valid
24.0ms59×body80valid
9.0ms10×body160valid

simplify79.0ms

Counts
1 → 1
Iterations
IterNodes
done56
356
254
135
022

prune76.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize127.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1))
0.3b
(* (sin theta) (* (sin delta) (cos phi1)))
0.4b
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
0.6b
(- (cos delta) (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×sub-neg asin-acos flip3-- diff-log associate-*r/ sin-cos-mult flip-- sin-mult unswap-sqr
Counts
4 → 58
Calls
4 calls:
34.0ms
(* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1))
77.0ms
(* (sin theta) (* (sin delta) (cos phi1)))
5.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
15.0ms
(- (cos delta) (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1)))

series996.0ms

Counts
4 → 12
Calls
4 calls:
447.0ms
(* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1))
154.0ms
(* (sin theta) (* (sin delta) (cos phi1)))
16.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
379.0ms
(- (cos delta) (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1)))

simplify4.9s

Counts
70 → 70
Iterations
IterNodes
done5001
32696
2895
1333
0148

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize315.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
8×difference-of-squares
7×pow1 add-exp-log *-un-lft-identity add-cbrt-cube sqr-pow
6×add-log-exp
5×add-cube-cbrt
3×unpow-prod-down pow-unpow cube-prod
2×asin-acos pow-pow pow-exp rem-cube-cbrt
1×difference-cubes cube-div cube-mult pow-to-exp sub-neg flip3-- diff-log unpow3 pow-prod-down prod-exp flip-- cbrt-unprod sin-mult distribute-lft-out--
Counts
4 → 61
Calls
4 calls:
5.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
5.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
45.0ms
(- (pow (cos delta) 3) (pow (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1)) 3))
22.0ms
(pow (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1)) 3)

series2.2s

Counts
4 → 12
Calls
4 calls:
16.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
16.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
1.7s
(- (pow (cos delta) 3) (pow (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1)) 3))
546.0ms
(pow (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1)) 3)

simplify3.7s

Counts
73 → 73
Iterations
IterNodes
done5008
21705
1470
0164

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize463.0ms

Local error

Found 4 expressions with local error:

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

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube add-log-exp
3×swap-sqr associate-*r* associate-*l*
2×asin-acos pow3 pow-prod-down
1×difference-cubes pow2 sub-neg flip3-- pow-plus diff-log prod-exp pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod sqr-sin sin-mult unswap-sqr
Counts
4 → 56
Calls
4 calls:
5.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
7.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
225.0ms
(- (pow (cos delta) 3) (* (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1)))))) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1)))))) (* (* (sin phi1) (sin phi1)) (sin phi1))))
43.0ms
(* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
16.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
16.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
1.7s
(- (pow (cos delta) 3) (* (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1)))))) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1)))))) (* (* (sin phi1) (sin phi1)) (sin phi1))))
326.0ms
(* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))))

simplify4.1s

Counts
68 → 68
Iterations
IterNodes
done5000
21696
1451
0159

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize372.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
0.4b
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
0.4b
(- (pow (cos delta) 3) (* (pow (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) 3) (* (sin phi1) (* (sin phi1) (sin phi1)))))
0.6b
(pow (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) 3)

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×pow1 add-exp-log add-cbrt-cube
3×unpow-prod-down pow-unpow cube-prod
2×asin-acos
1×difference-cubes cube-mult pow-to-exp sub-neg flip3-- pow-pow cube-unmult diff-log unpow3 pow-prod-down pow-exp flip-- rem-cube-cbrt sqr-pow
Counts
4 → 52
Calls
4 calls:
4.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
3.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
104.0ms
(- (pow (cos delta) 3) (* (pow (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) 3) (* (sin phi1) (* (sin phi1) (sin phi1)))))
12.0ms
(pow (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) 3)

series2.1s

Counts
4 → 12
Calls
4 calls:
22.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
17.0ms
(asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))
1.7s
(- (pow (cos delta) 3) (* (pow (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) 3) (* (sin phi1) (* (sin phi1) (sin phi1)))))
409.0ms
(pow (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) 3)

simplify4.1s

Counts
64 → 64
Iterations
IterNodes
done5003
21713
1442
0148

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes1.3s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify28.0ms

Iterations
IterNodes
done47
147
034

end0.0ms

sample27.9s

Algorithm
intervals
Results
17.7s3110×body1280valid
5.3s1886×body640valid
2.7s691×body320valid
1.0s1990×body80valid
397.0ms323×body160valid