Details

sample844.0ms

Algorithm

intervals

Results

362.0ms	154×	body	1280	valid
305.0ms	71×	body	640	valid
15.0ms	20×	body	320	valid
4.0ms	7×	body	160	valid
3.0ms	1×	body	2560	valid
1.0ms	3×	body	80	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	43	18
done	43	18

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.7b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.4b	(cos (- lambda1 lambda2))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
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:

14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
25.0ms	(* (sin phi1) (sin phi2))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

series283.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
89.0ms	(* (sin phi1) (sin phi2))
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
64.0ms	(cos (- lambda1 lambda2))

simplify5.0s

Counts

84 → 84

Iterations

Useful iterations: 5 (1.7s)

Iter	Nodes	Cost
0	187	1607
1	316	1393
2	593	1170
3	954	1127
4	1259	1054
5	1919	990
6	3862	990
done	5000	990

prune529.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 80

Calls

4 calls:

98.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
22.0ms	(* (sin phi1) (sin phi2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
105.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
56.0ms	(* (sin phi1) (sin phi2))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.8s

Counts

92 → 92

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	188	2166
1	503	2021
2	1957	1726
done	5000	1725

prune922.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.3b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2)))
0.2b	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2))))))) R)
0.6b	(log (acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2))))))
0.7b	(acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`log-prod`
4×	`expm1-log1p-u` `associate-r` `exp-sum` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`acos-asin` `associate-*r/` `rem-log-exp` `log-pow` `cos-mult`

Counts

4 → 69

Calls

4 calls:

36.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2)))
27.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2))))))) R)
1.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2)))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2)))
90.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2))))))) R)
41.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2))))))
26.0ms	(acos (fma (sin phi1) (sin phi2) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (cos phi2)))))

simplify2.8s

Counts

81 → 81

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	136	2276
1	261	2207
2	766	1888
3	3064	1881
done	5002	1878

prune887.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2))
0.2b	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2)))))) R)
0.6b	(log (acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2)))))
0.7b	(acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`log-prod` `associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `exp-sum` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`acos-asin` `rem-log-exp` `log-pow`

Counts

4 → 68

Calls

4 calls:

38.0ms	(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2))
36.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2)))))) R)
1.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2)))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2))
76.0ms	(* (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2)))))) R)
58.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2)))))
21.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2))))

simplify2.8s

Counts

80 → 80

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	132	2251
1	252	2180
2	754	1855
3	3169	1854
done	5002	1851

prune684.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

regimes817.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	28
1	28	28
done	28	28

end0.0ms

sample18.9s

Algorithm

intervals

Results

13.0s	4713×	body	1280	valid
4.2s	2154×	body	640	valid
605.0ms	695×	body	320	valid
159.0ms	290×	body	160	valid
85.0ms	136×	body	80	valid
80.0ms	13×	body	2560	valid