Details

Time bar (total: 17.7s)

sample175.0ms

Algorithm
intervals
Results
104.0ms119×body1280valid
35.0ms68×body640valid
10.0ms29×body320valid
6.0ms12×body160valid
3.0ms28×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01420
12020
22319
done2319

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

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))
3.6b
(sin (- lambda1 lambda2))

rewrite30.0ms

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))
13.0ms
(cos (- lambda1 lambda2))
14.0ms
(sin (- lambda1 lambda2))

series172.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
120.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
18.0ms
(cos (- lambda1 lambda2))
23.0ms
(sin (- lambda1 lambda2))

simplify2.4s

Counts
73 → 73
Iterations

Useful iterations: 5 (1.5s)

IterNodesCost
01721599
12731267
24141016
3735930
41400785
53319658
done5000658

prune261.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos 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))
3.4b
(cos (- lambda1 lambda2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×cos-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×cos-diff sub-neg pow-prod-down prod-exp *-commutative sin-cos-mult cbrt-unprod fma-udef unswap-sqr
Counts
4 → 61
Calls
4 calls:
12.0ms
(* (sin lambda1) (cos 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))
14.0ms
(cos (- lambda1 lambda2))

series189.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (cos lambda2))
14.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
110.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
20.0ms
(cos (- lambda1 lambda2))

simplify3.1s

Counts
73 → 73
Iterations

Useful iterations: 5 (2.1s)

IterNodesCost
01831321
13171133
2613947
31146849
42096766
54825765
done5000765

prune350.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos 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))

rewrite33.0ms

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×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-neg distribute-rgt-neg-out sin-cos-mult fma-udef sin-mult
Counts
4 → 62
Calls
4 calls:
15.0ms
(* (sin lambda1) (cos 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)))
16.0ms
(* (sin lambda1) (sin (- lambda2)))
0.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

series343.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (cos lambda2))
21.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1)))
53.0ms
(* (sin lambda1) (sin (- lambda2)))
225.0ms
(fma (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))) (cos phi1))

simplify2.3s

Counts
74 → 74
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
01401193
12811161
26971017
31504958
43569957
done5000957

prune405.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (cos lambda2))
0.2b
(exp (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)))
0.5b
(fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
0.7b
(log (exp (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×pow1
6×add-exp-log exp-prod add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log-prod log-pow log1p-expm1-u
3×associate-*r* associate-*l* fma-udef
2×exp-sum
1×rem-log-exp pow-prod-down prod-exp *-commutative sin-cos-mult cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 63
Calls
4 calls:
11.0ms
(* (sin lambda1) (cos lambda2))
2.0ms
(exp (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)))
0.0ms
(fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
3.0ms
(log (exp (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))))

series685.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin lambda1) (cos lambda2))
253.0ms
(exp (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1)))
197.0ms
(fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))
189.0ms
(log (exp (fma (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2) (cos phi1))))

simplify905.0ms

Counts
75 → 75
Iterations

Useful iterations: done (903.0ms)

IterNodesCost
01221244
12351185
25441037
313431031
done50001027

prune371.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes393.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02335
12935
done2935

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.3s3556×body1280valid
1.2s2302×body640valid
324.0ms943×body320valid
103.0ms460×body160valid
80.0ms739×body80valid