Details

sample706.0ms

Algorithm

intervals

Results

535.0ms	151×	body	1280	valid
120.0ms	65×	body	640	valid
15.0ms	15×	body	320	valid
7.0ms	18×	body	80	valid
5.0ms	7×	body	160	valid

simplify454.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	80
4	80
3	77
2	47
1	28
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

10.0ms	(* (cos phi1) (sin phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

series257.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (cos phi1) (sin phi2))
119.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
30.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

simplify2.1s

Counts

97 → 97

Iterations

Iter	Nodes
3	3161
2	1036
1	448
0	222

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.9b

localize109.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(cos (- lambda1 lambda2))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

18.0ms	(* (sin phi1) (cos phi2))
18.0ms	(* (cos phi1) (sin phi2))
47.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))

series288.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin phi1) (cos phi2))
64.0ms	(* (cos phi1) (sin phi2))
121.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify2.6s

Counts

97 → 97

Iterations

Iter	Nodes
3	3168
2	1071
1	436
0	210

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-*r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 91

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (sin phi1) (cos phi2))
9.0ms	(* (cos phi1) (sin phi2))
76.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(* (sin phi1) (cos phi2))
49.0ms	(* (cos phi1) (sin phi2))
266.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify673.0ms

Counts

103 → 103

Iterations

Iter	Nodes
2	2058
1	535
0	190

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize123.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (cos phi2)) (cbrt (cos phi2)))
0.3b	(cbrt (cos phi2))
0.3b	(cbrt (cos phi2))
0.3b	(cbrt (cos phi2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

15.0ms	(* (cbrt (cos phi2)) (cbrt (cos phi2)))
2.0ms	(cbrt (cos phi2))
2.0ms	(cbrt (cos phi2))
2.0ms	(cbrt (cos phi2))

series605.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(* (cbrt (cos phi2)) (cbrt (cos phi2)))
131.0ms	(cbrt (cos phi2))
116.0ms	(cbrt (cos phi2))
137.0ms	(cbrt (cos phi2))

simplify1.7s

Counts

93 → 93

Iterations

Iter	Nodes
4	4214
3	1014
2	348
1	143
0	68

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes667.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	37
1	37
0	27

end0.0ms

sample23.8s

Algorithm

intervals

Results

17.2s	4633×	body	1280	valid
4.8s	1985×	body	640	valid
878.0ms	545×	body	320	valid
290.0ms	634×	body	80	valid
256.0ms	203×	body	160	valid