Details

sample548.0ms

Algorithm

intervals

Results

439.0ms	159×	body	1280	valid
57.0ms	46×	body	640	valid
19.0ms	21×	body	320	valid
6.0ms	26×	body	80	valid
2.0ms	4×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.6b	(sin (- lambda1 lambda2))
3.7b	(cos (- lambda1 lambda2))

rewrite88.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

15.0ms	(* (sin phi1) (cos phi2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

series262.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin phi1) (cos phi2))
120.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(sin (- lambda1 lambda2))
29.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5008
3	3253
2	962
1	427
0	208

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b	(cos (- lambda1 lambda2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

10.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
9.0ms	(* (sin phi1) (cos phi2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))

series388.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
51.0ms	(* (sin phi1) (cos phi2))
129.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
3	4966
2	1267
1	462
0	206

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize103.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

10.0ms	(* (sin phi1) (cos phi2))
14.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
57.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin phi1) (cos phi2))
62.0ms	(* (sin lambda1) (sin lambda2))
185.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
130.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	1537
1	421
0	159

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize179.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
0.7b	(cbrt (sin lambda1))
0.7b	(cbrt (sin lambda1))
0.7b	(cbrt (sin lambda1))

rewrite31.0ms

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:

21.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
2.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))

series527.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (cbrt (sin lambda1)) (cbrt (sin lambda1)))
120.0ms	(cbrt (sin lambda1))
130.0ms	(cbrt (sin lambda1))
128.0ms	(cbrt (sin lambda1))

simplify1.9s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	1442
2	466
1	179
0	79

prune928.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes777.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample18.3s

Algorithm

intervals

Results

13.8s	4641×	body	1280	valid
2.9s	1929×	body	640	valid
801.0ms	554×	body	320	valid
241.0ms	661×	body	80	valid
102.0ms	215×	body	160	valid