Details

Time bar (total: 41.6s)

sample841.0ms

Algorithm
intervals
Results
503.0ms154×body1280valid
212.0ms63×body640valid
27.0ms23×body320valid
9.0ms11×body160valid
2.0ms5×body80valid

simplify29.0ms

Counts
1 → 1
Iterations
IterNodes
done39
339
238
127
017

prune61.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.3b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
4.2b
(cos (- lambda1 lambda2))

rewrite34.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×acos-asin cos-diff sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 65
Calls
4 calls:
0.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
12.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
18.0ms
(cos (- lambda1 lambda2))

series331.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
29.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
17.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
56.0ms
(cos (- lambda1 lambda2))

simplify1.2s

Counts
77 → 77
Iterations
IterNodes
done2002
42002
31385
2530
1300
0172

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.3b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite38.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin fma-udef sin-mult
Counts
4 → 65
Calls
4 calls:
23.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
12.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series566.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (sin lambda1) (sin lambda2))
403.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
53.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
30.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify1.4s

Counts
77 → 77
Iterations
IterNodes
done2002
42002
31888
2635
1264
0131

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.5b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
1.3b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))
3.6b
(log (exp (* (sin lambda1) (sin lambda2))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod associate-*r* associate-*l* log-pow
1×acos-asin exp-prod exp-to-pow rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 60
Calls
4 calls:
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))
11.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))
9.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

series515.0ms

Counts
4 → 12
Calls
4 calls:
387.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))
42.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1)))))
17.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))) (* (sin phi2) (sin phi1))))
69.0ms
(log (exp (* (sin lambda1) (sin lambda2))))

simplify1.4s

Counts
72 → 72
Iterations
IterNodes
done2000
42000
31437
2512
1222
0118

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.5b

localize109.0ms

Local error

Found 4 expressions with local error:

0.3b
(* R (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))))
0.4b
(exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
0.8b
(log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
1.3b
(acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-in acos-asin distribute-lft-in associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 76
Calls
4 calls:
13.0ms
(* R (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))))
4.0ms
(exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
6.0ms
(log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
2.0ms
(acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

series82.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* R (log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))))
30.0ms
(exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
14.0ms
(log (exp (acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
10.0ms
(acos (fma (* (cos phi2) (cos phi1)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

simplify1.3s

Counts
88 → 88
Iterations
IterNodes
done2000
42000
3934
2356
1178
0115

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.5b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done29
129
023

end0.0ms

sample24.7s

Algorithm
intervals
Results
17.9s4854×body1280valid
5.0s2076×body640valid
902.0ms641×body320valid
277.0ms281×body160valid
106.0ms140×body80valid
71.0ms11×body2560valid