Details

sample598.0ms

Algorithm

intervals

Results

405.0ms	142×	body	1280	valid
117.0ms	66×	body	640	valid
22.0ms	21×	body	320	valid
7.0ms	23×	body	80	valid
3.0ms	4×	body	160	valid

simplify98.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	79
4	79
3	71
2	46
1	27
0	17

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize72.0ms

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))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `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:

29.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
37.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series254.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
111.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify756.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1355
1	272
0	116

prune794.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize101.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

17.0ms	(* (sin lambda2) (cos lambda1))
17.0ms	(* (sin lambda1) (cos lambda2))
45.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))

series274.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin lambda2) (cos lambda1))
64.0ms	(* (sin lambda1) (cos lambda2))
122.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify767.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1750
1	362
0	152

prune720.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

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`
7×	`sin-cos-mult`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-mult`
4×	`frac-times` `associate-r/` `cos-mult` `-commutative` `distribute-neg-frac` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
2×	`neg-sub0` `sub-neg` `flip3--` `frac-sub` `flip--` `sub-div` `associate--r-`
1×	`associate-*l/`

Counts

4 → 90

Calls

4 calls:

9.0ms	(* (sin lambda2) (cos lambda1))
9.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin lambda1) (sin lambda2))
65.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (- (* (sin lambda1) (sin lambda2)))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin lambda2) (cos lambda1))
49.0ms	(* (sin lambda1) (cos lambda2))
60.0ms	(* (sin lambda1) (sin lambda2))
276.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (- (* (sin lambda1) (sin lambda2)))))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	3017
1	548
0	202

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (- (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
30.1b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`cbrt-prod`
6×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`cube-div` `associate-l` `sin-cos-mult` `add-log-exp`
3×	`distribute-rgt-in` `frac-times` `pow-unpow` `cbrt-div` `distribute-lft-in` `associate-*r/`
2×	`neg-sub0` `cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `flip3--` `unpow3` `cube-prod` `pow-exp` `cos-mult` `*-commutative` `frac-sub` `flip--` `distribute-neg-frac` `associate--r-` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `associate-*l/` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
135.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (- (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))
13.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
6.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series466.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sin lambda1) (sin lambda2))
262.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (- (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))
74.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
50.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify1.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	3113
1	540
0	185

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes963.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	36
1	36
0	28

end0.0ms

sample20.5s

Algorithm

intervals

Results

15.0s	4571×	body	1280	valid
3.1s	1963×	body	640	valid
934.0ms	535×	body	320	valid
505.0ms	234×	body	160	valid
260.0ms	697×	body	80	valid