Details

Time bar (total: 25.4s)

sample359.0ms

Algorithm
intervals
Results
173.0ms117×body1280valid
90.0ms73×body640valid
15.0ms27×body320valid
7.0ms15×body160valid
4.0ms24×body80valid

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

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))
4.6b
(cos (- lambda1 lambda2))
4.6b
(sin (- lambda1 lambda2))

rewrite40.0ms

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)))
1.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
25.0ms
(cos (- lambda1 lambda2))
11.0ms
(sin (- lambda1 lambda2))

series226.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
158.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
19.0ms
(cos (- lambda1 lambda2))
31.0ms
(sin (- lambda1 lambda2))

simplify1.1s

Counts
73 → 73
Iterations
IterNodes
done5001
31578
2611
1290
0172

prune549.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1)))
0.2b
(* (sin lambda2) (sin lambda1))
0.6b
(fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1))
4.6b
(sin (- lambda1 lambda2))

rewrite22.0ms

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 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 → 61
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1)))
9.0ms
(* (sin lambda2) (sin lambda1))
0.0ms
(fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1))
11.0ms
(sin (- lambda1 lambda2))

series383.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1)))
64.0ms
(* (sin lambda2) (sin lambda1))
275.0ms
(fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1))
30.0ms
(sin (- lambda1 lambda2))

simplify2.4s

Counts
73 → 73
Iterations
IterNodes
done5000
34301
2928
1349
0186

prune664.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:
9.0ms
(* (cos lambda2) (sin lambda1))
0.0ms
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (sin lambda2) (cos lambda1))))) (fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1)))
12.0ms
(* (sin lambda2) (sin lambda1))
1.0ms
(fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1))

series482.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (cos lambda2) (sin lambda1))
23.0ms
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (sin lambda2) (cos lambda1))))) (fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1)))
76.0ms
(* (sin lambda2) (sin lambda1))
318.0ms
(fma (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))) (cos phi1))

simplify625.0ms

Counts
72 → 72
Iterations
IterNodes
done5001
21006
1290
0130

prune841.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (sin lambda2) (cos lambda1))))) (log (exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))))
0.2b
(exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))
0.6b
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
0.7b
(log (exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))

rewrite11.0ms

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:
0.0ms
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (sin lambda2) (cos lambda1))))) (log (exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))))
3.0ms
(exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))
1.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
5.0ms
(log (exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))

series977.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (- (* (sin lambda2) (cos lambda1))))) (log (exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))))
391.0ms
(exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1)))
273.0ms
(fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))
295.0ms
(log (exp (fma (fma (sin lambda2) (sin lambda1) (* (cos lambda2) (cos lambda1))) (cos phi2) (cos phi1))))

simplify2.2s

Counts
63 → 63
Iterations
IterNodes
done5001
33201
2569
1195
0102

prune586.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes848.0ms

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
done38
238
136
024

end0.0ms

sample12.9s

Algorithm
intervals
Results
7.7s3483×body1280valid
3.3s2411×body640valid
909.0ms973×body320valid
179.0ms424×body160valid
171.0ms709×body80valid