Details

sample393.0ms

Algorithm

intervals

Results

302.0ms	153×	body	1280	valid
53.0ms	58×	body	640	valid
12.0ms	22×	body	320	valid
3.0ms	18×	body	80	valid
2.0ms	5×	body	160	valid

simplify4.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0b	(sin (- lambda1 lambda2))
3.1b	(cos (- lambda1 lambda2))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

31.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(sin (- lambda1 lambda2))
11.0ms	(cos (- lambda1 lambda2))

series213.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
103.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(sin (- lambda1 lambda2))
19.0ms	(cos (- lambda1 lambda2))

simplify98.0ms

Counts: 72 → 72

prune352.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
58.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))

series317.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos phi1) (sin phi2))
139.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
101.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify39.0ms

Counts: 81 → 81

prune467.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult` `sin-mult`
4×	`frac-times` `associate-r/` `cos-mult` `-commutative` `add-log-exp`
3×	`flip3--` `associate-*l/` `flip--` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `frac-sub` `sub-div`
1×	`sin-neg` `distribute-rgt-neg-out`

Counts

4 → 89

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
58.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
16.0ms	(* (sin lambda1) (sin (- lambda2)))
99.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos phi1) (sin phi2))
141.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
62.0ms	(* (sin lambda1) (sin (- lambda2)))
207.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify60.0ms

Counts: 101 → 101

prune661.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin phi2)) (cbrt (sin phi2)))
0.6b	(cbrt (sin phi2))
0.6b	(cbrt (sin phi2))
0.6b	(cbrt (sin phi2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

15.0ms	(* (cbrt (sin phi2)) (cbrt (sin phi2)))
1.0ms	(cbrt (sin phi2))
1.0ms	(cbrt (sin phi2))
1.0ms	(cbrt (sin phi2))

series452.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (cbrt (sin phi2)) (cbrt (sin phi2)))
106.0ms	(cbrt (sin phi2))
106.0ms	(cbrt (sin phi2))
119.0ms	(cbrt (sin phi2))

simplify86.0ms

Counts: 85 → 85

prune543.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes575.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample14.5s

Algorithm

intervals

Results

10.1s	4656×	body	1280	valid
2.9s	1930×	body	640	valid
795.0ms	568×	body	320	valid
130.0ms	236×	body	160	valid
105.0ms	610×	body	80	valid