Details

Time bar (total: 39.4s)

sample628.0ms

Algorithm
intervals
Results
427.0ms101×body1280valid
103.0ms54×body640valid
27.0ms76×body80valid
21.0ms17×body320valid
6.0ms8×body160valid

simplify111.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
02233
13632
26032
37032
done7032

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

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:
13.0ms
(* (sin theta) (sin delta))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
44.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
13.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series992.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (sin theta) (sin delta))
15.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
591.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
302.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify2.7s

Counts
84 → 84
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01581747
13221677
27611520
319231479
done50001418

prune862.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
0.3b
(* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))
0.4b
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
0.5b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×add-exp-log
18×add-cube-cbrt *-un-lft-identity
13×add-cbrt-cube
11×pow1 associate-*r*
10×prod-exp
9×times-frac
6×sin-mult add-log-exp
5×associate-*l/ unswap-sqr
4×expm1-log1p-u unpow-prod-down associate-*l* cos-mult cbrt-unprod log1p-expm1-u associate-/l/
3×swap-sqr associate-/r* associate-/l*
2×pow2 pow-to-exp flip3-- pow-prod-down pow-exp *-commutative frac-sub flip-- unpow2 sub-div sqr-pow
1×cbrt-undiv sub-neg sqr-cos frac-2neg pow-plus fma-neg diff-log div-sub div-exp prod-diff associate--l+ clear-num pow-sqr pow-prod-up sqr-sin div-inv
Counts
4 → 115
Calls
4 calls:
68.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
81.0ms
(* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))
68.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
41.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
1.1s
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
265.0ms
(* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))
539.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
230.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify1.6s

Counts
127 → 127
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02597326
16446634
221165873
done50004745

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* (cos delta) (cos delta)) (cbrt (* (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6) (pow (sin phi1) 6))))
0.6b
(pow (sin phi1) 6)
0.9b
(pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)
7.4b
(cbrt (* (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6) (pow (sin phi1) 6)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log unpow-prod-down pow-unpow add-log-exp
4×expm1-log1p-u prod-diff add-cbrt-cube log1p-expm1-u
2×cbrt-prod pow-to-exp pow-pow pow-exp sqr-pow
1×sub-neg sqr-cos flip3-- fma-neg pow1/3 diff-log associate--l+ flip-- difference-of-squares
Counts
4 → 70
Calls
4 calls:
34.0ms
(- (* (cos delta) (cos delta)) (cbrt (* (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6) (pow (sin phi1) 6))))
4.0ms
(pow (sin phi1) 6)
4.0ms
(pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)
9.0ms
(cbrt (* (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6) (pow (sin phi1) 6)))

series1.5s

Counts
4 → 12
Calls
4 calls:
576.0ms
(- (* (cos delta) (cos delta)) (cbrt (* (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6) (pow (sin phi1) 6))))
55.0ms
(pow (sin phi1) 6)
500.0ms
(pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6)
339.0ms
(cbrt (* (pow (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) 6) (pow (sin phi1) 6)))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01962464
14702085
213731888
done50011734

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize165.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos phi1) 2)
0.4b
(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* 2 (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta))))) (* (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))) (sin delta))))))
0.4b
(pow (sin phi1) 3)
0.5b
(pow (sin phi1) 4)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
27×add-cube-cbrt
24×prod-diff
22×unpow-prod-down
9×pow-unpow
8×fma-neg sqr-pow
7×pow1 add-exp-log
6×unpow2 add-log-exp
5×add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×pow-to-exp pow-pow cube-prod pow-exp
1×cube-mult sub-neg flip3-- diff-log unpow3 flip-- fma-udef associate--r+ distribute-lft-out-- rem-cube-cbrt
Counts
4 → 116
Calls
4 calls:
4.0ms
(pow (cos phi1) 2)
35.0ms
(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* 2 (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta))))) (* (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))) (sin delta))))))
22.0ms
(pow (sin phi1) 3)
7.0ms
(pow (sin phi1) 4)

series812.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(pow (cos phi1) 2)
680.0ms
(- (pow (cos delta) 2) (fma (pow (sin phi1) 4) (pow (cos delta) 2) (* (sin delta) (+ (* 2 (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta))))) (* (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2))) (sin delta))))))
66.0ms
(pow (sin phi1) 3)
41.0ms
(pow (sin phi1) 4)

simplify1.3s

Counts
128 → 128
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02349599
15455917
215384583
done50023411

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04283
15783
done5783

end0.0ms

sample19.3s

Algorithm
intervals
Results
11.5s3220×body1280valid
4.6s1788×body640valid
1.4s1929×body80valid
1.0s740×body320valid
225.0ms323×body160valid