Details

sample1.1s

Algorithm

intervals

Results

579.0ms	158×	body	1280	valid
137.0ms	64×	body	640	valid
107.0ms	14×	body	320	valid
13.0ms	15×	body	160	valid
7.0ms	1×	body	2560	valid
2.0ms	5×	body	80	valid

simplify70.0ms

Counts: 1 → 1

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize73.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (- lambda1 lambda2))
1.4b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))

rewrite47.0ms

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:

Slowest

19.0ms	(cos (- lambda1 lambda2))
18.0ms	(* (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)))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
62.0ms	(* (sin phi1) (sin phi2))
28.0ms	(cos (- lambda1 lambda2))
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.5s

Counts: 71 → 71

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize103.0ms

Local error

Found 4 expressions with local error:

1.4b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))

rewrite44.0ms

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×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 68

Calls

4 calls:

Slowest

21.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (sin phi1) (sin phi2))
5.0ms	(* (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))))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
79.0ms	(* (sin phi1) (sin phi2))
56.0ms	(* (sin lambda1) (sin lambda2))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.4s

Counts: 80 → 80

prune2.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

localize87.0ms

Local error

Found 4 expressions with local error:

1.4b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.8b	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.4b	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.2b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)

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:

Slowest

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

series176.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

74.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
49.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
30.0ms	(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify4.1s

Counts: 74 → 74

prune2.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.6b

localize119.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
0.7b	(asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))
0.2b	(* (- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))) R)
0.2b	(* (sin phi2) (sin phi1))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`associate-l`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `add-log-exp`
4×	`insert-posit16` `difference-of-squares`
2×	`asin-acos` `times-frac` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`sub-neg` `diff-log` `sin-mult` `associate--r-`

Counts

4 → 70

Calls

4 calls:

Slowest

55.0ms	(* (- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))) R)
20.0ms	(* (sin phi2) (sin phi1))
16.0ms	(- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
6.0ms	(asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

429.0ms	(asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))
222.0ms	(* (- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))) R)
80.0ms	(- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
60.0ms	(* (sin phi2) (sin phi1))

simplify1.3s

Counts: 82 → 82

prune2.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.5b

regimes2.4s

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch7.0ms

end0.0ms

sample22.5s

Algorithm

intervals

Results

15.2s	4747×	body	1280	valid
5.6s	2117×	body	640	valid
920.0ms	698×	body	320	valid
250.0ms	292×	body	160	valid
87.0ms	8×	body	2560	valid
51.0ms	139×	body	80	valid