Details

Time bar (total: 30.1s)

sample426.0ms

Algorithm
intervals
Results
307.0ms135×body1280valid
60.0ms54×body640valid
22.0ms29×body320valid
6.0ms12×body160valid
6.0ms26×body80valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.6b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.6b
(sin (- lambda1 lambda2))
3.7b
(cos (- lambda1 lambda2))

rewrite446.0ms

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 log1p-expm1-u add-log-exp
2×sub-neg
1×cos-diff sin-diff fma-udef
Counts
4 → 61
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))
18.0ms
(sin (- lambda1 lambda2))
426.0ms
(cos (- lambda1 lambda2))

series236.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
168.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
29.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify2.8s

Counts
73 → 73
Iterations
IterNodes
done5001
42049
3897
2441
1290
0172

prune915.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize105.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.6b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
3.7b
(cos (- lambda1 lambda2))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×cos-diff sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 60
Calls
4 calls:
18.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
22.0ms
(cos (- lambda1 lambda2))

series327.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (cos lambda1) (sin lambda2))
21.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
206.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
33.0ms
(cos (- lambda1 lambda2))

simplify3.2s

Counts
72 → 72
Iterations
IterNodes
done5000
43828
31553
2605
1321
0175

prune932.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize97.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (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))
0.6b
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

rewrite30.0ms

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 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×fma-udef sin-mult
Counts
4 → 60
Calls
4 calls:
18.0ms
(* (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)))
10.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series516.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (cos lambda1) (sin lambda2))
34.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
66.0ms
(* (sin lambda1) (sin lambda2))
329.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify2.0s

Counts
72 → 72
Iterations
IterNodes
done5001
31776
2630
1275
0128

prune835.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.6b
(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
0.8b
(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×exp-prod
5×pow1 add-log-exp
4×expm1-log1p-u log-prod add-cbrt-cube add-exp-log log-pow log1p-expm1-u
3×fma-udef
2×exp-sum
1×rem-log-exp rem-exp-log
Counts
4 → 51
Calls
4 calls:
3.0ms
(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
0.0ms
(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
4.0ms
(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

series1.1s

Counts
4 → 12
Calls
4 calls:
420.0ms
(exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
25.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
324.0ms
(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
330.0ms
(log (exp (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))))

simplify3.4s

Counts
63 → 63
Iterations
IterNodes
done5000
44524
31212
2383
1189
0100

prune645.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes996.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done26
126
021

end0.0ms

sample10.8s

Algorithm
intervals
Results
6.2s3573×body1280valid
2.6s2327×body640valid
1.3s944×body320valid
156.0ms710×body80valid
153.0ms446×body160valid