Details

Time bar (total: 17.0s)

sample249.0ms

Algorithm
intervals
Results
154.0ms100×body1280valid
50.0ms55×body640valid
12.0ms22×body320valid
11.0ms70×body80valid
3.0ms9×body160valid

simplify26.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02233
13632
25932
36832
done6832

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
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))
0.6b
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

rewrite9.0ms

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 flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 60
Calls
4 calls:
0.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
3.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (* (sin theta) (sin delta)) (cos phi1)) (- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
153.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
174.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify1.3s

Counts
72 → 72
Iterations

Useful iterations: 3 (279.0ms)

IterNodesCost
01392029
12831962
27111737
325681724
done50011724

prune425.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
11×pow1
9×times-frac
8×add-exp-log add-cbrt-cube
6×add-log-exp
5×sin-mult
4×expm1-log1p-u associate-*l/ cos-mult log1p-expm1-u associate-/l/
3×swap-sqr associate-*r* associate-*l* associate-/r* associate-/l*
2×flip3-- frac-sub flip-- sub-div
1×cbrt-undiv pow2 sub-neg asin-acos sqr-cos frac-2neg pow-plus fma-neg diff-log div-sub div-exp prod-diff pow-prod-down prod-exp associate--l+ clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin div-inv unswap-sqr
Counts
4 → 92
Calls
4 calls:
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms
(* (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))))))
14.0ms
(/ (- (* (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)))
9.0ms
(- (* (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
149.0ms
(* (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))))))
623.0ms
(/ (- (* (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)))
346.0ms
(- (* (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)))

simplify824.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (179.0ms)

IterNodesCost
02236043
15475595
223914962
done50014962

prune771.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin delta) (* (cos phi1) (sin theta)))
0.2b
(* (sin delta) (* (cos phi1) (cos theta)))
0.3b
(* (sin phi1) (fma (sin phi1) (cos delta) (* (sin delta) (* (cos phi1) (cos theta)))))
0.6b
(- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (sin delta) (* (cos phi1) (cos theta))))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
7×pow-prod-down prod-exp cbrt-unprod
6×add-log-exp
5×associate-*r*
4×expm1-log1p-u fma-udef log1p-expm1-u
3×fma-neg prod-diff *-commutative
2×distribute-rgt-in distribute-lft-in associate--r+
1×sub-neg flip3-- diff-log associate-*r/ cos-mult flip-- unswap-sqr
Counts
4 → 85
Calls
4 calls:
8.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
8.0ms
(* (sin delta) (* (cos phi1) (cos theta)))
4.0ms
(* (sin phi1) (fma (sin phi1) (cos delta) (* (sin delta) (* (cos phi1) (cos theta)))))
3.0ms
(- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (sin delta) (* (cos phi1) (cos theta))))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin delta) (* (cos phi1) (sin theta)))
75.0ms
(* (sin delta) (* (cos phi1) (cos theta)))
156.0ms
(* (sin phi1) (fma (sin phi1) (cos delta) (* (sin delta) (* (cos phi1) (cos theta)))))
175.0ms
(- (cos delta) (* (sin phi1) (fma (sin phi1) (cos delta) (* (sin delta) (* (cos phi1) (cos theta))))))

simplify534.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
01691743
13991668
214401453
done50001453

prune443.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* (cos delta) (cos delta)) (* (* (* (cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (cbrt (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)))
0.6b
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.6b
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.6b
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
1×sub-neg sqr-cos flip3-- fma-neg diff-log prod-diff associate--l+ flip--
Counts
4 → 56
Calls
4 calls:
18.0ms
(- (* (cos delta) (cos delta)) (* (* (* (cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (cbrt (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)))
1.0ms
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
358.0ms
(- (* (cos delta) (cos delta)) (* (* (* (cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (cbrt (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)))
232.0ms
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
230.0ms
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
232.0ms
(cbrt (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify485.0ms

Counts
68 → 68
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
01213293
13263169
214302097
done50002097

prune558.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes369.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01930
12530
done2530

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.9s3079×body1280valid
1.7s1890×body640valid
439.0ms709×body320valid
303.0ms1980×body80valid
127.0ms342×body160valid