Details

Time bar (total: 25.7s)

sample350.0ms

Algorithm
intervals
Results
173.0ms113×body1280valid
62.0ms16×body160valid
61.0ms71×body640valid
22.0ms35×body320valid
4.0ms21×body80valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
01420
12020
22319
done2319

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize47.0ms

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))
3.4b
(cos (- lambda1 lambda2))
3.5b
(sin (- lambda1 lambda2))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube 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))
17.0ms
(cos (- lambda1 lambda2))
44.0ms
(sin (- lambda1 lambda2))

series254.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
182.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
19.0ms
(cos (- lambda1 lambda2))
41.0ms
(sin (- lambda1 lambda2))

simplify1.4s

Counts
73 → 73
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01721599
12901279
26101016
31583930
done5000821

prune432.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.2b

localize46.0ms

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))
3.5b
(sin (- lambda1 lambda2))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×sin-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×sub-neg pow-prod-down prod-exp sin-neg sin-diff *-commutative distribute-rgt-neg-out cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 62
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
30.0ms
(* (sin lambda1) (sin (- lambda2)))
1.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))
37.0ms
(sin (- lambda1 lambda2))

series458.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
61.0ms
(* (sin lambda1) (sin (- lambda2)))
348.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))
35.0ms
(sin (- lambda1 lambda2))

simplify2.9s

Counts
74 → 74
Iterations

Useful iterations: 3 (905.0ms)

IterNodesCost
01901471
13571301
29901088
34646985
done5000985

prune692.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-+ sin-neg distribute-rgt-neg-out flip-+ fma-udef sin-mult
Counts
4 → 65
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
76.0ms
(* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2)))))
25.0ms
(* (sin lambda1) (sin (- lambda2)))
0.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

series704.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
245.0ms
(* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2)))))
72.0ms
(* (sin lambda1) (sin (- lambda2)))
350.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify1.3s

Counts
77 → 77
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01501524
13851464
219561287
done50001223

prune769.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2)))))
0.5b
(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
0.5b
(cbrt (pow (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) 3))
0.7b
(pow (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) 3)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-mult unpow3 associate-*r/ sqr-pow
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod flip-+ fma-udef rem-cube-cbrt unswap-sqr
Counts
4 → 82
Calls
4 calls:
53.0ms
(* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2)))))
1.0ms
(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
5.0ms
(cbrt (pow (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) 3))
6.0ms
(pow (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) 3)

series1.3s

Counts
4 → 12
Calls
4 calls:
198.0ms
(* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2)))))
308.0ms
(fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1))
283.0ms
(cbrt (pow (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) 3))
529.0ms
(pow (fma (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) 3)

simplify2.1s

Counts
94 → 94
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01462223
14341967
226701705
done50021701

prune686.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes679.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02956
13656
done3656

end0.0ms

sample11.2s

Algorithm
intervals
Results
6.4s3498×body1280valid
2.9s2340×body640valid
997.0ms974×body320valid
271.0ms454×body160valid
121.0ms734×body80valid