Details

sample1.2s

Algorithm

intervals

Results

730.0ms	139×	body	1280	valid
243.0ms	75×	body	640	valid
37.0ms	28×	body	320	valid
9.0ms	11×	body	160	valid
1.0ms	3×	body	80	valid

simplify63.0ms

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize61.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (- lambda1 lambda2))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))

rewrite63.0ms

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

22.0ms	(* (sin phi1) (sin phi2))
19.0ms	(cos (- lambda1 lambda2))
12.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(* (sin phi1) (sin phi2))
134.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
48.0ms	(cos (- lambda1 lambda2))
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify473.0ms

Counts: 75 → 71

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize115.0ms

Local error

Found 4 expressions with local error:

1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (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)
0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))

rewrite29.0ms

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

10.0ms	(* (sin phi1) (sin phi2))
10.0ms	(* (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))))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
83.0ms	(* (sin phi1) (sin phi2))
61.0ms	(* (sin lambda1) (sin lambda2))
23.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.1s

Counts: 81 → 80

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.7b

localize109.0ms

Local error

Found 4 expressions with local error:

1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.7b	(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)))))))
0.3b	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)

rewrite36.0ms

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

22.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
7.0ms	(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))))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

94.0ms	(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
51.0ms	(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
26.0ms	(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))))))

simplify1.4s

Counts: 78 → 74

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize103.0ms

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)))))
0.5b	(asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))
0.3b	(* (- (/ 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))

rewrite111.0ms

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

61.0ms	(* (- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))) R)
21.0ms	(* (sin phi2) (sin phi1))
21.0ms	(- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
7.0ms	(asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

184.0ms	(* (- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))) R)
75.0ms	(- (/ PI 2) (asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1)))))
61.0ms	(* (sin phi2) (sin phi1))
29.0ms	(asin (+ (* (* (cos phi2) (cos phi1)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (* (sin phi2) (sin phi1))))

simplify645.0ms

Counts: 87 → 82

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.5b

regimes998.0ms

Accuracy

0% (0.6b remaining)

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

bsearch8.0ms

end0.0ms

sample22.6s

Algorithm

intervals

Results

16.1s	4782×	body	1280	valid
4.8s	2151×	body	640	valid
1.0s	660×	body	320	valid
184.0ms	270×	body	160	valid
48.0ms	135×	body	80	valid
45.0ms	9×	body	2560	valid