Details

sample1.1s

Algorithm

intervals

Results

841.0ms	167×	body	1280	valid
128.0ms	57×	body	640	valid
20.0ms	22×	body	320	valid
3.0ms	6×	body	160	valid
2.0ms	4×	body	80	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	46
4	46
3	44
2	38
1	27
0	17

prune68.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.7b	(cos (- lambda1 lambda2))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

22.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
25.0ms	(cos (- lambda1 lambda2))

series179.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin phi1) (sin phi2))
69.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
40.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	932
1	335
0	187

prune941.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 72

Calls

4 calls:

9.0ms	(* (sin phi1) (sin phi2))
10.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin phi1) (sin phi2))
81.0ms	(* (sin lambda1) (sin lambda2))
127.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
35.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1042
1	291
0	142

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.4b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))))))
24.3b	(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
18×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
16×	`sin-mult`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`cbrt-div`
6×	`frac-times` `-un-lft-identity` `associate-l/` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-r` `associate-l` `associate-*r/` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
2×	`pow-plus` `*-commutative`
1×	`cbrt-prod` `pow2` `acos-asin` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

45.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))))))
126.0ms	(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
131.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2)))))))) R)
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))))))
55.0ms	(cbrt (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1555
1	370
0	162

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.4b

localize112.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.3b	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))))) R)
0.7b	(log (acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))))
0.9b	(acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

9.0ms	(* (sin lambda2) (sin lambda1))
14.0ms	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))))) R)
1.0ms	(log (acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))))
1.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin lambda2) (sin lambda1))
106.0ms	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))))) R)
73.0ms	(log (acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1)))))
23.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (cos phi2)) (cos phi1))))

simplify2.7s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
3	3605
2	629
1	226
0	127

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.3b

regimes1.9s

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample17.6s

Algorithm

intervals

Results

12.6s	4738×	body	1280	valid
3.5s	2174×	body	640	valid
769.0ms	676×	body	320	valid
123.0ms	262×	body	160	valid
47.0ms	12×	body	2560	valid
35.0ms	142×	body	80	valid