Details

Time bar (total: 30.7s)

sample525.0ms

Algorithm
intervals
Results
345.0ms155×body1280valid
67.0ms64×body640valid
17.0ms27×body320valid
4.0ms9×body160valid
0.0ms1×body80valid

simplify100.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01719
12718
23818
34418
44618
done4618

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.1b
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.1b
(cos (- lambda1 lambda2))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×pow1 add-exp-log cos-sum add-cbrt-cube
9×prod-diff
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×cos-diff
2×*-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 74
Calls
4 calls:
68.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
23.0ms
(cos (- lambda1 lambda2))

series282.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
78.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
14.0ms
(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
48.0ms
(cos (- lambda1 lambda2))

simplify1.1s

Counts
86 → 86
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01961763
14001595
215971331
done50001299

prune654.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.2b
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b
(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.2b
(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1 add-exp-log add-cbrt-cube
17×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity cos-mult
5×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative
2×frac-times associate-*r/ associate-*l/ sin-mult
1×acos-asin unswap-sqr
Counts
4 → 84
Calls
4 calls:
88.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
64.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
8.0ms
(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series537.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
197.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
98.0ms
(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
22.0ms
(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify1.4s

Counts
96 → 96
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01662336
14212267
218251680
done50011641

prune833.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.2b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
0.4b
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
0.9b
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
1.2b
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 66
Calls
4 calls:
26.0ms
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
5.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
7.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
2.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

series197.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
50.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
18.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
41.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

simplify2.2s

Counts
78 → 78
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
0932330
11492225
24091971
323761971
done50001971

prune692.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.2b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
0.3b
(* (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
0.5b
(expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
1.2b
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*r* associate-*l*
1×acos-asin expm1-log1p pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef expm1-udef unswap-sqr
Counts
4 → 51
Calls
4 calls:
1.0ms
(fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
16.0ms
(* (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
1.0ms
(expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
2.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
431.0ms
(fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
528.0ms
(* (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
107.0ms
(expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
27.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

simplify1.4s

Counts
63 → 63
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0991851
11821785
24801547
320631544
done50001543

prune597.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.2b

regimes1.4s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02428
12828
done2828

end0.0ms

sample17.2s

Algorithm
intervals
Results
11.3s4708×body1280valid
4.4s2171×body640valid
623.0ms674×body320valid
149.0ms308×body160valid
47.0ms10×body2560valid
30.0ms131×body80valid