Details

sample141.0ms

Algorithm

intervals

Results

53.0ms	251×	body	80	valid
32.0ms	51×	body	640	valid
17.0ms	21×	body	1280	valid
8.0ms	18×	body	320	valid
4.0ms	14×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1878
4	761
3	231
2	72
1	34
0	17

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize38.0ms

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)))
3.9b	(cos (/ (+ phi2 phi1) 2))

rewrite65.0ms

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))
12.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
41.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
11.0ms	(cos (/ (+ phi2 phi1) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

499.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
611.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
131.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
28.0ms	(cos (/ (+ phi2 phi1) 2))

simplify2.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4185
2	1076
1	360
0	144

prune665.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))
0.1b	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
3.9b	(cos (/ (+ phi1 phi2) 2))

rewrite81.0ms

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 (/ (+ phi1 phi2) 2))) (- phi1 phi2))
15.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
45.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
13.0ms	(cos (/ (+ phi1 phi2) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

531.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2))
622.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (- phi1 phi2)) R)
115.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))
35.0ms	(cos (/ (+ phi1 phi2) 2))

simplify2.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4260
2	1075
1	363
0	144

prune655.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.9b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2)))))
0.2b	(expm1 (log1p (cos (/ (+ phi1 phi2) 2))))
0.3b	(log1p (cos (/ (+ phi1 phi2) 2)))
3.9b	(cos (/ (+ phi1 phi2) 2))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

21.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2)))))
0.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2))))
0.0ms	(log1p (cos (/ (+ phi1 phi2) 2)))
13.0ms	(cos (/ (+ phi1 phi2) 2))

series324.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2)))))
50.0ms	(expm1 (log1p (cos (/ (+ phi1 phi2) 2))))
87.0ms	(log1p (cos (/ (+ phi1 phi2) 2)))
33.0ms	(cos (/ (+ phi1 phi2) 2))

simplify2.2s

Counts

71 → 71

Iterations

Iter	Nodes
done	5003
3	1612
2	481
1	205
0	100

prune573.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.9b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
0.3b	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
3.9b	(cos (/ (+ phi2 phi1) 2))
3.9b	(cos (/ (+ phi2 phi1) 2))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

22.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
49.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
21.0ms	(cos (/ (+ phi2 phi1) 2))
20.0ms	(cos (/ (+ phi2 phi1) 2))

series1.6s

Counts

4 → 12

Calls

4 calls:

862.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)
665.0ms	(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R))
23.0ms	(cos (/ (+ phi2 phi1) 2))
23.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5002
2	1160
1	334
0	127

prune618.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.9b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.4b and baseline of 3.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	8406×	body	80	valid
1.3s	1235×	body	640	valid
868.0ms	745×	body	1280	valid
404.0ms	658×	body	320	valid
117.0ms	403×	body	160	valid