Details

sample1.3s

Algorithm

intervals

Results

697.0ms	145×	body	1280	valid
440.0ms	68×	body	640	valid
44.0ms	31×	body	320	valid
7.0ms	7×	body	160	valid
2.0ms	5×	body	80	valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
3	34
2	33
1	26
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize83.0ms

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)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.8b	(cos (- lambda1 lambda2))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
2×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 59

Calls

4 calls:

11.0ms	(* (sin phi1) (sin phi2))
5.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
15.0ms	(cos (- lambda1 lambda2))

series184.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin phi1) (sin phi2))
72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
26.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
30.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

71 → 71

Iterations

Iter	Nodes
done	5008
4	2710
3	1060
2	432
1	211
0	115

prune705.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite528.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `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 → 76

Calls

4 calls:

460.0ms	(* (sin lambda1) (sin lambda2))
52.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
12.0ms	(* (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))))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin lambda1) (sin lambda2))
300.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
125.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
28.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1842
1	506
0	185

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.9b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
4.5b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`log-prod` `log-pow` `cos-mult`
2×	`frac-times` `flip3-+` `associate-r/` `-commutative` `flip-+`
1×	`distribute-rgt-in` `acos-asin` `exp-prod` `distribute-lft-in` `exp-to-pow` `rem-log-exp` `associate-*l/` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

74.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
4.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series482.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))
92.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
31.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
56.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify2.3s

Counts

81 → 81

Iterations

Iter	Nodes
done	5031
2	1595
1	422
0	164

prune878.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.9b

localize106.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.1b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 62

Calls

4 calls:

11.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
3.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
5.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series218.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
63.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
21.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
26.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.6s

Counts

74 → 74

Iterations

Iter	Nodes
done	5006
6	4531
5	1614
4	998
3	703
2	383
1	190
0	107

prune716.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 5.9b

regimes2.3s

Accuracy

0% (0.5b remaining)

Error of 4.1b against oracle of 3.6b and baseline of 4.1b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample22.0s

Algorithm

intervals

Results

15.8s	4716×	body	1280	valid
4.4s	2166×	body	640	valid
1.0s	695×	body	320	valid
197.0ms	271×	body	160	valid
93.0ms	144×	body	80	valid
56.0ms	11×	body	2560	valid