Details

sample260.0ms

Algorithm

intervals

Results

187.0ms	152×	body	1280	valid
40.0ms	53×	body	640	valid
10.0ms	23×	body	320	valid
3.0ms	24×	body	80	valid
1.0ms	4×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	46	24
3	71	24
4	72	24
done	72	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
29.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos phi1) (sin phi2))
100.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify4.5s

Counts

71 → 71

Iterations

Useful iterations: 3 (692.0ms)

Iter	Nodes	Cost
0	128	709
1	284	697
2	873	607
3	2286	599
4	3911	599
done	5000	599

prune298.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite65.0ms

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`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 68

Calls

4 calls:

11.0ms	(* (cos lambda1) (sin lambda2))
11.0ms	(* (sin lambda1) (cos lambda2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))

series212.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos lambda1) (sin lambda2))
46.0ms	(* (sin lambda1) (cos lambda2))
100.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify4.4s

Counts

80 → 80

Iterations

Useful iterations: 3 (772.0ms)

Iter	Nodes	Cost
0	147	782
1	332	769
2	1028	661
3	2572	659
4	4479	659
done	5001	659

prune389.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
5×	`sin-mult`
4×	`frac-times` `associate-r/` `cos-mult` `-commutative` `add-log-exp`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div`
1×	`associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 88

Calls

4 calls:

11.0ms	(* (cos lambda1) (sin lambda2))
12.0ms	(* (sin lambda1) (cos lambda2))
14.0ms	(* (sin lambda1) (sin (- lambda2)))
83.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos lambda1) (sin lambda2))
45.0ms	(* (sin lambda1) (cos lambda2))
53.0ms	(* (sin lambda1) (sin (- lambda2)))
188.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify856.0ms

Counts

100 → 100

Iterations

Useful iterations: done (854.0ms)

Iter	Nodes	Cost
0	202	1445
1	495	1398
2	1773	1196
done	5000	1163

prune571.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
0.5b	(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.5b	(cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))
0.5b	(cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-div`
25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cos-mult` `sin-mult`
11×	`pow1`
10×	`flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `flip3--` `pow-plus` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `sub-div`

Counts

4 → 98

Calls

4 calls:

77.0ms	(* (cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
15.0ms	(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
9.0ms	(cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))
9.0ms	(cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))
161.0ms	(cbrt (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
155.0ms	(cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))
143.0ms	(cbrt (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))

simplify1.5s

Counts

110 → 110

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	168	3338
1	352	3101
2	984	2705
3	2563	2527
done	5000	2453

prune666.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes427.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	136
1	55	136
done	55	136

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.3s	4646×	body	1280	valid
1.4s	1855×	body	640	valid
275.0ms	592×	body	320	valid
99.0ms	699×	body	80	valid
58.0ms	208×	body	160	valid