Details

sample108.0ms

Algorithm

intervals

Results

37.0ms	44×	body	640	valid
22.0ms	244×	body	80	valid
13.0ms	23×	body	1280	valid
8.0ms	28×	body	320	valid
2.0ms	11×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	17	32
1	34	16
2	76	16
3	257	16
4	826	16
5	2355	16
done	5000	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.6b	(cos (/ (+ phi1 phi2) 2.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `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 → 63

Calls

4 calls:

0.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
7.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
35.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms	(cos (/ (+ phi1 phi2) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

543.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
715.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
143.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
42.0ms	(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts

75 → 75

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	139	1279
1	327	1271
2	960	1077
3	3194	1060
done	5000	1059

prune437.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2)) R)
0.1b	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1))))
4.6b	(cos (* 0.5 (+ phi2 phi1)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `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` `flip3--` `distribute-lft-in` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 65

Calls

4 calls:

1.0ms	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2))
15.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2)) R)
60.0ms	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1))))
11.0ms	(cos (* 0.5 (+ phi2 phi1)))

series1.6s

Counts

4 → 12

Calls

4 calls:

610.0ms	(hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2))
818.0ms	(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2)) R)
123.0ms	(* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1))))
41.0ms	(cos (* 0.5 (+ phi2 phi1)))

simplify2.4s

Counts

77 → 77

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	150	1315
1	334	1307
2	960	1113
3	3138	1096
done	5000	1095

prune428.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
0.1b	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.1b	(* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))
0.2b	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

rewrite524.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`associate-l`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
9×	`flip3--` `associate-r` `flip--` `sin-mult`
8×	`frac-times` `cos-mult`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `frac-sub` `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 → 101

Calls

4 calls:

15.0ms	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
105.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
343.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))
54.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

series28.3s

Counts

4 → 12

Calls

4 calls:

27.6s	(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
188.0ms	(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
363.0ms	(* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))))
93.0ms	(* (sin (* phi2 0.5)) (sin (* phi1 0.5)))

simplify2.4s

Counts

113 → 113

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	353	4639
1	957	4328
2	3856	3884
done	5000	3878

prune955.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
0.3b	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
0.4b	(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
0.6b	(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `pow-pow` `pow-plus` `pow-exp` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`

Counts

4 → 128

Calls

4 calls:

161.0ms	(* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
37.0ms	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
155.0ms	(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
18.0ms	(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

series550.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))
169.0ms	(pow (* (sin (* phi2 0.5)) (sin (* phi1 0.5))) 3)
120.0ms	(* (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (cos (* phi2 0.5)) (cos (* phi1 0.5))))
148.0ms	(pow (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) 3)

simplify1.5s

Counts

140 → 140

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	195	2474
1	479	1522
2	1870	1435
done	5001	1424

prune912.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes429.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	57
1	42	57
done	42	57

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.4s	8470×	body	80	valid
1.0s	1295×	body	640	valid
732.0ms	776×	body	1280	valid
315.0ms	693×	body	320	valid
87.0ms	336×	body	160	valid