Details

Time bar (total: 44.6s)

sample1.5s

Algorithm
intervals
Results
587.0ms161×body1280valid
124.0ms69×body640valid
21.0ms16×body320valid
7.0ms8×body160valid
1.0ms2×body80valid

simplify44.0ms

Counts
1 → 1
Iterations
IterNodes
done43
343
238
127
017

prune61.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.4b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.1b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
2.7b
(cos (- lambda1 lambda2))

rewrite40.0ms

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))))
22.0ms
(cos (- lambda1 lambda2))

series328.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
25.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
15.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
60.0ms
(cos (- lambda1 lambda2))

simplify3.3s

Counts
77 → 77
Iterations
IterNodes
done5000
44021
31402
2556
1300
0172

prune947.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.2b
(* (sin lambda1) (sin lambda2))
1.0b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite37.0ms

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:
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
11.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
23.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series542.0ms

Counts
4 → 12
Calls
4 calls:
405.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
47.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
63.0ms
(* (sin lambda1) (sin lambda2))
26.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.4s

Counts
77 → 77
Iterations
IterNodes
done5000
31999
2643
1262
0131

prune877.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.6b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi2) (sin phi1))
0.2b
(* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
0.2b
(* R (acos (+ (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
1.0b
(acos (+ (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×fma-udef unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/ cos-mult sin-mult
Counts
4 → 78
Calls
4 calls:
20.0ms
(* (sin phi2) (sin phi1))
25.0ms
(* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
6.0ms
(* R (acos (+ (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
2.0ms
(acos (+ (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

series386.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sin phi2) (sin phi1))
278.0ms
(* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
36.0ms
(* R (acos (+ (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
11.0ms
(acos (+ (* (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

simplify1.8s

Counts
90 → 90
Iterations
IterNodes
done5002
21114
1367
0164

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b
(* R (log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))))
0.4b
(exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
0.9b
(log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
1.0b
(acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))

rewrite32.0ms

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:
19.0ms
(* R (log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))))
4.0ms
(exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
5.0ms
(log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
1.0ms
(acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* R (log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))))
49.0ms
(exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
18.0ms
(log (exp (acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
29.0ms
(acos (fma (cos phi2) (* (cos phi1) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))

simplify3.7s

Counts
88 → 88
Iterations
IterNodes
done5041
53825
42043
3749
2293
1161
0105

prune826.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.5b

regimes1.5s

Accuracy

0% (0.5b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done26
126
022

end0.0ms

sample24.6s

Algorithm
intervals
Results
16.9s4788×body1280valid
5.2s2070×body640valid
1.6s730×body320valid
267.0ms272×body160valid
94.0ms16×body2560valid
47.0ms126×body80valid