Details

sample909.0ms

Algorithm

intervals

Results

757.0ms	149×	body	1280	valid
88.0ms	52×	body	640	valid
25.0ms	23×	body	320	valid
13.0ms	13×	body	160	valid
7.0ms	19×	body	80	valid

simplify70.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	73
4	73
3	69
2	45
1	27
0	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.3b	(sin (- lambda1 lambda2))
2.4b	(cos (- lambda1 lambda2))

rewrite89.0ms

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` `insert-posit16` `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 → 64

Calls

4 calls:

21.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
30.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(sin (- lambda1 lambda2))
23.0ms	(cos (- lambda1 lambda2))

series223.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
99.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(sin (- lambda1 lambda2))
31.0ms	(cos (- lambda1 lambda2))

simplify449.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2000
2	793
1	276
0	120

prune617.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.9b

localize82.0ms

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)))
2.4b	(cos (- lambda1 lambda2))

rewrite162.0ms

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×	`insert-posit16` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `sin-cos-mult` `flip--`

Counts

4 → 73

Calls

4 calls:

14.0ms	(* (cos lambda1) (sin lambda2))
83.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
42.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

series376.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cos lambda1) (sin lambda2))
191.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
104.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify730.0ms

Counts

85 → 85

Iterations

Iter	Nodes
done	2001
2	1188
1	369
0	149

prune768.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize92.0ms

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

rewrite189.0ms

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`
4×	`*-commutative` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-l/` `associate-r/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 88

Calls

4 calls:

10.0ms	(* (cos lambda1) (sin lambda2))
79.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
16.0ms	(* (sin lambda1) (sin lambda2))
83.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos lambda1) (sin lambda2))
167.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
64.0ms	(* (sin lambda1) (sin lambda2))
196.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify441.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2003
1	557
0	192

prune990.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize100.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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×	`add-cbrt-cube` `insert-posit16` `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 → 77

Calls

4 calls:

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

series625.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(* (cbrt (cos phi2)) (cbrt (cos phi2)))
121.0ms	(cbrt (cos phi2))
148.0ms	(cbrt (cos phi2))
122.0ms	(cbrt (cos phi2))

simplify826.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	2003
3	1190
2	353
1	145
0	66

prune683.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes509.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample21.9s

Algorithm

intervals

Results

16.1s	4567×	body	1280	valid
4.3s	1965×	body	640	valid
695.0ms	569×	body	320	valid
274.0ms	672×	body	80	valid
188.0ms	227×	body	160	valid