Details

sample201.0ms

Algorithm

intervals

Results

74.0ms	295×	body	80	valid
59.0ms	39×	body	640	valid
23.0ms	16×	body	1280	valid
10.0ms	19×	body	160	valid
8.0ms	10×	body	320	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	5437
5	1878
4	761
3	231
2	72
1	34
0	17

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize47.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
3.7b	(cos (/ (+ phi2 phi1) 2))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`associate-l`
7×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
37.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
15.0ms	(cos (/ (+ phi2 phi1) 2))

series801.0ms

Counts

3 → 9

Calls

3 calls:

651.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
125.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
25.0ms	(cos (/ (+ phi2 phi1) 2))

simplify934.0ms

Counts

65 → 65

Iterations

Iter	Nodes
3	3356
2	915
1	307
0	128

prune961.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.0b

localize39.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (hypot (* (cos (* 1/2 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.1b	(* (cos (* 1/2 (+ phi1 phi2))) (- lambda1 lambda2))
3.7b	(cos (* 1/2 (+ phi1 phi2)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
12×	`distribute-rgt-in` `distribute-lft-in`
8×	`associate-r`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-l`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum` `sub-neg` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 80

Calls

3 calls:

12.0ms	(* (hypot (* (cos (* 1/2 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
39.0ms	(* (cos (* 1/2 (+ phi1 phi2))) (- lambda1 lambda2))
8.0ms	(cos (* 1/2 (+ phi1 phi2)))

series759.0ms

Counts

3 → 9

Calls

3 calls:

574.0ms	(* (hypot (* (cos (* 1/2 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
147.0ms	(* (cos (* 1/2 (+ phi1 phi2))) (- lambda1 lambda2))
37.0ms	(cos (* 1/2 (+ phi1 phi2)))

simplify1.3s

Counts

89 → 89

Iterations

Iter	Nodes
3	3492
2	1047
1	417
0	195

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (* (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.1b	(* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))
0.1b	(* (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))) (- lambda1 lambda2))
0.2b	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`prod-diff`
14×	`associate-r`
12×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`frac-times` `flip3--` `flip--`
7×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`frac-sub` `sub-div`
2×	`sub-neg` `associate-*r/`
1×	`distribute-lft-out--` `difference-of-squares`

Counts

4 → 124

Calls

4 calls:

12.0ms	(* (hypot (* (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
24.0ms	(* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))
187.0ms	(* (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))) (- lambda1 lambda2))
49.0ms	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.6s	(* (hypot (* (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
74.0ms	(* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))
431.0ms	(* (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))) (- lambda1 lambda2))
69.0ms	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))

simplify1.5s

Counts

136 → 136

Iterations

Iter	Nodes
2	3177
1	852
0	331

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.1b	(* lambda1 (cos (* 1/2 phi1)))
0.1b	(* (* (cos (* 1/2 phi1)) lambda2) (cos (* phi2 1/2)))
0.1b	(* (sin (* 1/2 phi1)) lambda2)
0.2b	(* (* (sin (* 1/2 phi1)) lambda2) (sin (* phi2 1/2)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
12×	`associate-r`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`unswap-sqr`

Counts

4 → 84

Calls

4 calls:

14.0ms	(* lambda1 (cos (* 1/2 phi1)))
40.0ms	(* (* (cos (* 1/2 phi1)) lambda2) (cos (* phi2 1/2)))
25.0ms	(* (sin (* 1/2 phi1)) lambda2)
53.0ms	(* (* (sin (* 1/2 phi1)) lambda2) (sin (* phi2 1/2)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* lambda1 (cos (* 1/2 phi1)))
136.0ms	(* (* (cos (* 1/2 phi1)) lambda2) (cos (* phi2 1/2)))
66.0ms	(* (sin (* 1/2 phi1)) lambda2)
96.0ms	(* (* (sin (* 1/2 phi1)) lambda2) (sin (* phi2 1/2)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
3	2989
2	883
1	303
0	138

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes648.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
2	33
1	33
0	24

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.9s	8387×	body	80	valid
1.4s	741×	body	1280	valid
1.3s	1309×	body	640	valid
594.0ms	732×	body	320	valid
221.0ms	400×	body	160	valid