Details

Time bar (total: 44.0s)

sample994.0ms

Algorithm
intervals
Results
615.0ms166×body1280valid
164.0ms59×body640valid
29.0ms20×body320valid
7.0ms8×body160valid
1.0ms3×body80valid

simplify47.0ms

Counts
1 → 1
Iterations
IterNodes
439
339
238
127
017

prune48.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.7b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.2b
(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))))
5.2b
(cos (- lambda1 lambda2))

rewrite30.0ms

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:
7.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.0ms
(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))))
19.0ms
(cos (- lambda1 lambda2))

series297.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
224.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
9.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
38.0ms
(cos (- lambda1 lambda2))

simplify1.8s

Counts
77 → 77
Iterations
IterNodes
43406
31169
2486
1287
0172

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi2) (sin phi1))
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)))))
1.1b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite23.0ms

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:
11.0ms
(* (sin phi2) (sin phi1))
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
9.0ms
(* 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))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (sin phi2) (sin phi1))
352.0ms
(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)))))
11.0ms
(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
44440
31360
2546
1251
0130

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.8b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))))
1.1b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1))))))
2.6b
(log (exp (* (sin phi2) (sin phi1))))

rewrite26.0ms

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)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))
6.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1))))))
18.0ms
(log (exp (* (sin phi2) (sin phi1))))

series519.0ms

Counts
4 → 12
Calls
4 calls:
392.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))
35.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1)))))))
19.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (log (exp (* (sin phi2) (sin phi1))))))
73.0ms
(log (exp (* (sin phi2) (sin phi1))))

simplify2.4s

Counts
72 → 72
Iterations
IterNodes
43985
31071
2414
1208
0117

prune1.8s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 2.8b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
0.4b
(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
0.7b
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
1.1b
(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

rewrite16.0ms

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:
10.0ms
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
2.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
3.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
1.0ms
(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

series108.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))))
37.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
15.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
16.0ms
(acos (fma (* (cos phi2) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

simplify2.1s

Counts
88 → 88
Iterations
IterNodes
52155
41007
3485
2259
1161
0109

prune1.9s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 2.7b

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
229
129
023

end0.0ms

sample24.4s

Algorithm
intervals
Results
17.1s4811×body1280valid
5.6s2047×body640valid
919.0ms685×body320valid
244.0ms323×body160valid
80.0ms123×body80valid
74.0ms11×body2560valid