Details

Time bar (total: 33.8s)

sample585.0ms

Algorithm
intervals
Results
376.0ms157×body1280valid
71.0ms63×body640valid
43.0ms7×body80valid
13.0ms18×body320valid
8.0ms11×body160valid

simplify29.0ms

Counts
1 → 1
Iterations
IterNodes
done46
446
344
238
127
017

prune81.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi2) (sin phi1))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.4b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.4b
(cos (- lambda1 lambda2))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
8×pow1 add-cbrt-cube add-exp-log
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×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 72
Calls
4 calls:
28.0ms
(* (sin phi2) (sin phi1))
7.0ms
(* 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))))
13.0ms
(cos (- lambda1 lambda2))

series162.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (sin phi2) (sin phi1))
30.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
11.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
42.0ms
(cos (- lambda1 lambda2))

simplify3.9s

Counts
84 → 84
Iterations
IterNodes
done5001
34440
2844
1327
0184

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.4b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (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)))))
1.4b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 72
Calls
4 calls:
10.0ms
(* (sin lambda1) (sin lambda2))
10.0ms
(* (sin phi2) (sin phi1))
7.0ms
(* 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))))

series219.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (sin lambda1) (sin lambda2))
56.0ms
(* (sin phi2) (sin phi1))
57.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
22.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify1.1s

Counts
84 → 84
Iterations
IterNodes
done5000
2861
1258
0135

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize126.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (sin phi2) (sin phi1)))))
1.4b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (sin phi2) (sin phi1))))
24.1b
(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
45×pow1
18×add-cbrt-cube pow-prod-down add-exp-log
16×sin-mult
9×prod-exp cbrt-unprod
8×add-sqr-sqrt
7×cbrt-div
6×frac-times *-un-lft-identity associate-*r/ add-cube-cbrt
4×expm1-log1p-u associate-*r* associate-*l* associate-*l/ pow-sqr pow-prod-up log1p-expm1-u add-log-exp
2×pow-plus *-commutative
1×cbrt-prod pow2 acos-asin pow1/3 cube-unmult swap-sqr rem-cbrt-cube unswap-sqr
Counts
4 → 88
Calls
4 calls:
57.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
5.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (sin phi2) (sin phi1))))
125.0ms
(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

series233.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
46.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (sin phi2) (sin phi1)))))
28.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))) (* (sin phi2) (sin phi1))))
64.0ms
(cbrt (* (* (sin lambda1) (sin lambda2)) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.7s

Counts
100 → 100
Iterations
IterNodes
done5001
21512
1347
0156

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))
0.2b
(* (sin phi1) (sin phi2))
0.3b
(* R (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (* (sin phi1) (sin phi2)))))
1.4b
(acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (* (sin phi1) (sin phi2))))

rewrite17.0ms

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×acos-asin fma-udef sin-mult
Counts
4 → 61
Calls
4 calls:
0.0ms
(fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))
10.0ms
(* (sin phi1) (sin phi2))
6.0ms
(* R (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (* (sin phi1) (sin phi2)))))
1.0ms
(acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (* (sin phi1) (sin phi2))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))
57.0ms
(* (sin phi1) (sin phi2))
72.0ms
(* R (acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (* (sin phi1) (sin phi2)))))
23.0ms
(acos (fma (cos phi1) (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (* (sin phi1) (sin phi2))))

simplify2.6s

Counts
73 → 73
Iterations
IterNodes
done5000
33490
2617
1207
0115

prune790.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.3b

regimes1.3s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done31
131
024

end0.0ms

sample17.1s

Algorithm
intervals
Results
12.2s4746×body1280valid
3.7s2148×body640valid
504.0ms705×body320valid
130.0ms272×body160valid
87.0ms117×body80valid
54.0ms13×body2560valid