Details

sample120.0ms

Algorithm

intervals

Results

46.0ms	49×	body	640	valid
24.0ms	258×	body	80	valid
15.0ms	25×	body	1280	valid
9.0ms	31×	body	320	valid
2.0ms	10×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
5	1878
4	761
3	231
2	72
1	34
0	17

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
3.6b	(cos (/ (+ phi2 phi1) 2.0))

rewrite74.0ms

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` `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 (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
11.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
41.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
19.0ms	(cos (/ (+ phi2 phi1) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

556.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
702.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
153.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
53.0ms	(cos (/ (+ phi2 phi1) 2.0))

simplify2.3s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	4293
2	1093
1	359
0	142

prune808.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
3.6b	(cos (* 0.5 (+ phi1 phi2)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
12×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum` `sub-neg` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`hypot-udef` `flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
5.0ms	(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
37.0ms	(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
10.0ms	(cos (* 0.5 (+ phi1 phi2)))

series1.8s

Counts

4 → 12

Calls

4 calls:

876.0ms	(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
650.0ms	(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
205.0ms	(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
46.0ms	(cos (* 0.5 (+ phi1 phi2)))

simplify2.9s

Counts

99 → 99

Iterations

Iter	Nodes
done	5006
3	4019
2	1067
1	425
0	195

prune927.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

5.0ms	(* (hypot (* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
66.0ms	(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
19.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
173.0ms	(* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2))

series2.6s

Counts

4 → 12

Calls

4 calls:

1.8s	(* (hypot (* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2)) (- phi1 phi2)) R)
171.0ms	(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
127.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
504.0ms	(* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2))

simplify2.6s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	3050
1	825
0	308

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
0.2b	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
0.2b	(* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (- lambda1 lambda2))
4.1b	(log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`prod-diff`
23×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1`
8×	`add-cbrt-cube` `associate-r` `add-exp-log`
7×	`flip3--` `flip--` `add-log-exp`
6×	`log-prod` `associate-l` `log-pow`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`sub-neg` `associate--r+`
2×	`exp-prod` `exp-to-pow` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log` `rem-log-exp` `sin-mult` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

53.0ms	(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
30.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
109.0ms	(* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (- lambda1 lambda2))
7.0ms	(log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))

series812.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))))
122.0ms	(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
443.0ms	(* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))) (- lambda1 lambda2))
103.0ms	(log (exp (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))))

simplify2.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	1657
1	537
0	240

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.9s	8314×	body	80	valid
1.3s	770×	body	1280	valid
799.0ms	1272×	body	640	valid
302.0ms	740×	body	320	valid
163.0ms	346×	body	160	valid