Details

Time bar (total: 27.1s)

sample422.0ms

Algorithm
intervals
Results
286.0ms126×body1280valid
83.0ms67×body640valid
22.0ms27×body320valid
7.0ms13×body160valid
6.0ms23×body80valid

simplify41.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.5b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
2.3b
(sin (- lambda1 lambda2))
2.4b
(cos (- lambda1 lambda2))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cos-sum sin-sum
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×sub-neg
1×cos-diff sin-diff fma-udef
Counts
4 → 65
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
30.0ms
(sin (- lambda1 lambda2))
12.0ms
(cos (- lambda1 lambda2))

series215.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
143.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
30.0ms
(sin (- lambda1 lambda2))
30.0ms
(cos (- lambda1 lambda2))

simplify890.0ms

Counts
77 → 77
Iterations
IterNodes
done2000
3918
2445
1294
0176

prune833.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
2.3b
(sin (- lambda1 lambda2))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×sin-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×sub-neg pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 65
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
11.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
9.0ms
(sin (- lambda1 lambda2))

series382.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
65.0ms
(* (sin lambda1) (sin lambda2))
272.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))
35.0ms
(sin (- lambda1 lambda2))

simplify838.0ms

Counts
77 → 77
Iterations
IterNodes
done2000
31701
2654
1342
0188

prune913.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×sub-neg prod-diff pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×flip3-- fma-udef flip-- sin-mult
Counts
4 → 72
Calls
4 calls:
72.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
29.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series664.0ms

Counts
4 → 12
Calls
4 calls:
259.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
31.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
63.0ms
(* (sin lambda1) (sin lambda2))
310.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify771.0ms

Counts
84 → 84
Iterations
IterNodes
done2006
21100
1352
0152

prune835.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
0.5b
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
0.5b
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
0.6b
(cbrt (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)) (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
1×cbrt-prod pow1/3 cube-unmult rem-cbrt-cube
Counts
4 → 46
Calls
4 calls:
0.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
0.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
0.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
9.0ms
(cbrt (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)) (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
250.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
261.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
264.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
231.0ms
(cbrt (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)) (* (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)) (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)))))

simplify673.0ms

Counts
58 → 58
Iterations
IterNodes
done2004
3815
2200
193
053

prune708.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes982.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done28
128
022

end0.0ms

sample16.5s

Algorithm
intervals
Results
8.7s3562×body1280valid
4.4s2321×body640valid
2.3s958×body320valid
368.0ms451×body160valid
263.0ms708×body80valid