Details

sample657.0ms

Algorithm

intervals

Results

382.0ms	156×	body	1280	valid
83.0ms	64×	body	640	valid
19.0ms	23×	body	320	valid
6.0ms	10×	body	160	valid
1.0ms	3×	body	80	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	34
3	34
2	33
1	26
0	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize53.0ms

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)
0.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.8b	(cos (- lambda1 lambda2))

rewrite37.0ms

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))
6.0ms	(* (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)))))
16.0ms	(cos (- lambda1 lambda2))

series167.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin phi1) (sin phi2))
58.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
41.0ms	(cos (- lambda1 lambda2))

simplify1.9s

Counts

71 → 71

Iterations

Iter	Nodes
5	2416
4	1509
3	872
2	439
1	209
0	115

prune670.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
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)
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite118.0ms

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:

22.0ms	(* (sin phi1) (sin phi2))
86.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
6.0ms	(* (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))))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin phi1) (sin phi2))
316.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
82.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
31.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify7.5s

Counts

88 → 88

Iterations

Iter	Nodes
3	8945
2	1876
1	516
0	187

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize522.0ms

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)
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.4b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite44.0ms

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:

23.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
6.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
10.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
61.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
15.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify5.0s

Counts

74 → 74

Iterations

Iter	Nodes
6	4942
5	1438
4	813
3	613
2	383
1	189
0	107

prune920.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.2b

localize138.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b	(/ (sqrt (exp PI)) (exp (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.4b	(log (/ (sqrt (exp PI)) (exp (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
1.0b	(exp PI)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
36×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`log-prod`
21×	`sqrt-prod`
7×	`exp-prod` `add-exp-log`
6×	`add-cbrt-cube` `associate-/l*`
5×	`pow1` `add-log-exp`
4×	`insert-posit16`
3×	`asin-acos` `associate-/r*`
2×	`sqrt-pow1` `exp-diff` `div-exp` `rem-log-exp` `associate-/r/` `log-pow` `div-inv` `pow-div`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `rem-exp-log`

Counts

4 → 99

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
17.0ms	(/ (sqrt (exp PI)) (exp (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
11.0ms	(log (/ (sqrt (exp PI)) (exp (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
3.0ms	(exp PI)

series553.0ms

Counts

4 → 10

Calls

4 calls:

20.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
223.0ms	(/ (sqrt (exp PI)) (exp (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
309.0ms	(log (/ (sqrt (exp PI)) (exp (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
0.0ms	(exp PI)

simplify11.0s

Counts

109 → 109

Iterations

Iter	Nodes
4	11651
3	1966
2	711
1	333
0	176

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

regimes1.3s

Accuracy

0% (0.6b remaining)

Error of 3.8b against oracle of 3.2b and baseline of 3.8b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
2	36
1	36
0	28

end0.0ms

sample25.2s

Algorithm

intervals

Results

17.6s	4745×	body	1280	valid
4.6s	2109×	body	640	valid
1.2s	722×	body	320	valid
727.0ms	278×	body	160	valid
561.0ms	144×	body	80	valid
40.0ms	7×	body	2560	valid