Details

sample819.0ms

Algorithm

intervals

Results

535.0ms	144×	body	1280	valid
82.0ms	76×	body	640	valid
78.0ms	19×	body	320	valid
5.0ms	1×	body	2560	valid
4.0ms	12×	body	160	valid
1.0ms	4×	body	80	valid

simplify52.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	39
3	39
2	38
1	27
0	17

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize90.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.9b	(cos (- lambda1 lambda2))
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `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 → 78

Calls

4 calls:

107.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
20.0ms	(cos (- lambda1 lambda2))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series663.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
185.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
76.0ms	(cos (- lambda1 lambda2))
60.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify2.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5004
3	3442
2	964
1	406
0	201

prune953.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.0b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `cos-mult` `add-cube-cbrt`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-l/` `associate-r/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

62.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
95.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
162.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
111.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
30.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify2.3s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1594
1	462
0	180

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))))
0.3b	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)
0.7b	(log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
2.0b	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`log-prod` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
7×	`exp-sum`
6×	`add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`log-pow` `unswap-sqr`
1×	`acos-asin` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log`

Counts

4 → 69

Calls

4 calls:

4.0ms	(exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))))
46.0ms	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)
3.0ms	(log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
1.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

series162.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))))
88.0ms	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)
44.0ms	(log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
10.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

simplify3.7s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
5	2980
4	1312
3	711
2	327
1	171
0	107

prune1.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 5.8b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)))
0.2b	(* (sin lambda2) (sin lambda1))
0.3b	(* (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2))))) R)
2.0b	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
7×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`acos-asin` `sin-mult`

Counts

4 → 75

Calls

4 calls:

47.0ms	(* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)))
24.0ms	(* (sin lambda2) (sin lambda1))
14.0ms	(* (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2))))) R)
1.0ms	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)))
85.0ms	(* (sin lambda2) (sin lambda1))
67.0ms	(* (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2))))) R)
10.0ms	(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2)))))

simplify3.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
3	4624
2	981
1	314
0	148

prune878.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 5.8b

regimes2.0s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample18.4s

Algorithm

intervals

Results

13.0s	4823×	body	1280	valid
3.8s	2129×	body	640	valid
589.0ms	633×	body	320	valid
530.0ms	257×	body	160	valid
56.0ms	12×	body	2560	valid
38.0ms	147×	body	80	valid