Details

sample181.0ms

Algorithm

intervals

Results

52.0ms	275×	body	80	valid
38.0ms	30×	body	1280	valid
31.0ms	37×	body	640	valid
24.0ms	11×	body	160	valid
13.0ms	22×	body	320	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2013
6	2013
5	1878
4	761
3	231
2	72
1	34
0	17

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
4.0b	(cos (/ (+ phi2 phi1) 2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`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×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
24.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
15.0ms	(cos (/ (+ phi2 phi1) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

450.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
705.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
134.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
35.0ms	(cos (/ (+ phi2 phi1) 2))

simplify846.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2005
3	2005
2	1076
1	360
0	144

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
4.0b	(cos (* 1/2 (+ phi1 phi2)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `hypot-udef` `distribute-lft-in` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 69

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
6.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
29.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
17.0ms	(cos (* 1/2 (+ phi1 phi2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

468.0ms	(hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2))
575.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)
109.0ms	(* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2))))
23.0ms	(cos (* 1/2 (+ phi1 phi2)))

simplify1.1s

Counts

81 → 81

Iterations

Iter	Nodes
done	2002
3	2002
2	1076
1	377
0	158

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite581.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))) (- phi1 phi2)) R)
101.0ms	(- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))
53.0ms	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))
418.0ms	(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))

series22.7s

Counts

4 → 12

Calls

4 calls:

22.1s	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))) (- phi1 phi2)) R)
128.0ms	(- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))
71.0ms	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))
378.0ms	(* (- lambda1 lambda2) (- (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))) (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))

simplify2.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	2000
2	2000
1	879
0	311

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (- lambda1 lambda2) (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))) (* (- lambda1 lambda2) (- (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))))
0.2b	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))
0.2b	(* (- lambda1 lambda2) (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))))
4.2b	(* (- lambda1 lambda2) (- (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))

rewrite489.0ms

Algorithm

rewrite-expression-head

Rules

25×	`frac-add`
24×	`frac-times` `flip3--` `associate-*l/` `flip--`
19×	`sin-mult`
18×	`cos-mult` `distribute-neg-frac`
17×	`add-sqr-sqrt`
13×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-l*` `add-exp-log`
12×	`associate-*r/`
10×	`associate-r`
9×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative` `distribute-rgt-neg-out`
2×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`distribute-lft-neg-in` `+-commutative` `neg-mul-1` `sum-log` `fma-def` `distribute-rgt-neg-in` `flip3-+` `unsub-neg` `flip-+` `distribute-lft-out`

Counts

4 → 125

Calls

4 calls:

194.0ms	(+ (* (- lambda1 lambda2) (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))) (* (- lambda1 lambda2) (- (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))))
37.0ms	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))
122.0ms	(* (- lambda1 lambda2) (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))))
133.0ms	(* (- lambda1 lambda2) (- (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

554.0ms	(+ (* (- lambda1 lambda2) (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2)))) (* (- lambda1 lambda2) (- (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2))))))
101.0ms	(* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))
662.0ms	(* (- lambda1 lambda2) (* (cos (* 1/2 phi1)) (cos (* 1/2 phi2))))
143.0ms	(* (- lambda1 lambda2) (- (* (sin (* 1/2 phi1)) (sin (* 1/2 phi2)))))

simplify1.4s

Counts

137 → 137

Iterations

Iter	Nodes
done	2002
2	2002
1	960
0	287

prune2.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes802.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	43
3	43
2	42
1	36
0	22

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.2s	1315×	body	640	valid
2.2s	8237×	body	80	valid
1.2s	775×	body	1280	valid
584.0ms	713×	body	320	valid
177.0ms	358×	body	160	valid