Details

sample1.2s

Algorithm

intervals

Results

802.0ms	164×	body	1280	valid
91.0ms	55×	body	640	valid
63.0ms	26×	body	320	valid
40.0ms	10×	body	160	valid
0.0ms	1×	body	80	valid

simplify30.0ms

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

prune59.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize42.0ms

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)
1.3b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.3b	(cos (- lambda1 lambda2))

rewrite111.0ms

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:

79.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(* (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)))))
17.0ms	(cos (- lambda1 lambda2))

series681.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
486.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
34.0ms	(cos (- lambda1 lambda2))

simplify7.5s

Counts

86 → 86

Iterations

Useful iterations: done (7.5s)

Iter	Nodes	Cost
0	196	1763
1	377	1589
2	962	1325
3	2320	1281
4	3808	1190
done	5001	1144

prune625.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.3b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite174.0ms

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` `sin-mult`
2×	`frac-times` `associate-r/` `associate-l/`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

13.0ms	(* (sin lambda1) (sin lambda2))
59.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
99.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin lambda1) (sin lambda2))
217.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
160.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
26.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify1.7s

Counts

97 → 97

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	158	1615
1	382	1509
2	1482	1193
done	5000	1192

prune723.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
0.4b	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
0.8b	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
1.3b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`acos-asin` `log-prod` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`exp-diff` `fma-udef`
1×	`distribute-rgt-in` `log-div` `distribute-lft-in` `rem-log-exp` `associate-l` `associate-l/` `cos-mult` `-commutative` `rem-exp-log`

Counts

4 → 65

Calls

4 calls:

49.0ms	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
17.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
7.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))
56.0ms	(exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
15.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))))
14.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))

simplify2.8s

Counts

77 → 77

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	127	2022
1	249	1969
2	753	1716
3	2956	1715
done	5001	1715

prune878.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.3b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)))))
28.6b	(cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`cbrt-prod`
6×	`cube-div` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `cos-mult` `sin-mult`
5×	`pow-pow` `pow-exp` `rem-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `pow1/3` `associate-r` `associate-l` `*-commutative` `rem-cbrt-cube`

Counts

4 → 95

Calls

4 calls:

51.0ms	(pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
62.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)))))
29.0ms	(cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

series714.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
170.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
46.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)))))
172.0ms	(cbrt (pow (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

simplify1.2s

Counts

107 → 107

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	171	2057
1	391	1714
2	1583	1499
done	5000	1484

prune948.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 4.4b

regimes1.7s

Accuracy

0% (0.3b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 4.1b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	34
1	32	34
done	32	34

end0.0ms

sample18.1s

Algorithm

intervals

Results

13.4s	4728×	body	1280	valid
3.2s	2153×	body	640	valid
792.0ms	718×	body	320	valid
184.0ms	269×	body	160	valid
33.0ms	127×	body	80	valid
31.0ms	7×	body	2560	valid