Details

sample617.0ms

Algorithm

intervals

Results

475.0ms	155×	body	1280	valid
80.0ms	54×	body	640	valid
19.0ms	21×	body	320	valid
5.0ms	9×	body	160	valid
4.0ms	17×	body	80	valid

simplify50.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite143.0ms

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:

46.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
48.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
35.0ms	(cos (- lambda1 lambda2))
12.0ms	(sin (- lambda1 lambda2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
138.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
28.0ms	(sin (- lambda1 lambda2))

simplify1.6s

Counts: 72 → 72

prune416.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(cos (- lambda1 lambda2))

rewrite203.0ms

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:

24.0ms	(* (cos lambda1) (sin lambda2))
121.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
33.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

series438.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos lambda1) (sin lambda2))
179.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
149.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify743.0ms

Counts: 81 → 81

prune510.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

62.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
65.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
58.0ms	(* (sin lambda1) (sin lambda2))
120.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
177.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify788.0ms

Counts: 101 → 101

prune565.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
0.5b	(cbrt (sin lambda2))
0.5b	(cbrt (sin lambda2))
0.5b	(cbrt (sin lambda2))

rewrite22.0ms

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 lambda2)) (cbrt (sin lambda2)))
1.0ms	(cbrt (sin lambda2))
1.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))

series437.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
100.0ms	(cbrt (sin lambda2))
104.0ms	(cbrt (sin lambda2))
106.0ms	(cbrt (sin lambda2))

simplify904.0ms

Counts: 85 → 85

prune596.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes443.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.1s

end0.0ms

sample17.6s

Algorithm

intervals

Results

12.2s	4634×	body	1280	valid
4.1s	1945×	body	640	valid
511.0ms	562×	body	320	valid
147.0ms	666×	body	80	valid
94.0ms	193×	body	160	valid