Details

Time bar (total: 32.5s)

sample329.0ms

Algorithm
intervals
Results
177.0ms125×body1280valid
101.0ms68×body640valid
13.0ms25×body320valid
6.0ms17×body160valid
4.0ms21×body80valid

simplify19.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01420
12020
22319
done2319

prune51.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

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))
2.9b
(cos (- lambda1 lambda2))
3.0b
(sin (- lambda1 lambda2))

rewrite45.0ms

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)))
1.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
26.0ms
(cos (- lambda1 lambda2))
14.0ms
(sin (- lambda1 lambda2))

series282.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
193.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
19.0ms
(cos (- lambda1 lambda2))
51.0ms
(sin (- lambda1 lambda2))

simplify3.6s

Counts
73 → 73
Iterations

Useful iterations: 5 (2.2s)

IterNodesCost
01721599
12731267
24141016
3735930
41400785
53319658
done5000658

prune416.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.6b
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
2.9b
(cos (- lambda1 lambda2))

rewrite89.0ms

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*
2×associate-*r/
1×distribute-rgt-in cos-diff sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ fma-udef unswap-sqr
Counts
4 → 64
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
70.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
17.0ms
(cos (- lambda1 lambda2))

series491.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1)))
248.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
201.0ms
(fma (cos phi2) (cos (- lambda1 lambda2)) (cos phi1))
20.0ms
(cos (- lambda1 lambda2))

simplify2.8s

Counts
76 → 76
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01831652
13671436
210431195
337401102
done50001102

prune572.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

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-+ flip-+ fma-udef sin-mult
Counts
4 → 64
Calls
4 calls:
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)))
83.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
12.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

series583.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1)))
227.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
54.0ms
(* (sin lambda1) (sin lambda2))
282.0ms
(fma (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi1))

simplify3.5s

Counts
76 → 76
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01421455
13341370
211101196
340321194
done50001194

prune849.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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×associate-*r/ exp-sum
1×distribute-rgt-in distribute-lft-in flip3-+ rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ rem-exp-log unswap-sqr
Counts
4 → 66
Calls
4 calls:
50.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
4.0ms
(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
1.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
6.0ms
(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

series1.3s

Counts
4 → 12
Calls
4 calls:
201.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
414.0ms
(exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1)))
336.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
373.0ms
(log (exp (fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))))

simplify3.2s

Counts
78 → 78
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01351581
13161488
210491300
340921296
done50001296

prune712.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes989.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02436
13236
23436
done3436

end0.0ms

sample12.4s

Algorithm
intervals
Results
7.6s3522×body1280valid
3.1s2401×body640valid
713.0ms915×body320valid
210.0ms428×body160valid
133.0ms734×body80valid