Details

sample216.0ms

Algorithm

intervals

Results

93.0ms	289×	body	80	valid
41.0ms	49×	body	640	valid
34.0ms	30×	body	1280	valid
10.0ms	17×	body	320	valid
5.0ms	14×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1037
3	259
2	76
1	34
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize27.0ms

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)))
3.0b	(cos (/ (+ phi2 phi1) 2))

rewrite33.0ms

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)
19.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
7.0ms	(cos (/ (+ phi2 phi1) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

532.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
690.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
145.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
40.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
2	1572
1	360
0	144

prune701.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2)) (- phi1 phi2))
0.1b	(* (hypot (* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b	(* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2))
3.0b	(cos (/ (+ phi2 phi1) 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`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 → 89

Calls

4 calls:

0.0ms	(hypot (* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2)) (- phi1 phi2))
6.0ms	(* (hypot (* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
18.0ms	(* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2))
7.0ms	(cos (/ (+ phi2 phi1) 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

668.0ms	(hypot (* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2)) (- phi1 phi2))
615.0ms	(* (hypot (* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2)) (- phi1 phi2)) R)
215.0ms	(* (cos (/ (+ phi2 phi1) 2)) (- lambda1 lambda2))
35.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	2274
1	484
0	209

prune950.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))) (- lambda1 lambda2))
0.2b	(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
0.3b	(log1p (cos (/ (+ phi2 phi1) 2)))
3.0b	(cos (/ (+ phi2 phi1) 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`prod-diff` `add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`expm1-log1p-u` `associate-r`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`sub-neg` `associate-*r/`
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 → 81

Calls

4 calls:

24.0ms	(* (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))) (- lambda1 lambda2))
0.0ms	(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
0.0ms	(log1p (cos (/ (+ phi2 phi1) 2)))
7.0ms	(cos (/ (+ phi2 phi1) 2))

series417.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (expm1 (log1p (cos (/ (+ phi2 phi1) 2)))) (- lambda1 lambda2))
87.0ms	(expm1 (log1p (cos (/ (+ phi2 phi1) 2))))
65.0ms	(log1p (cos (/ (+ phi2 phi1) 2)))
36.0ms	(cos (/ (+ phi2 phi1) 2))

simplify952.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1021
1	303
0	155

prune919.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ phi2 phi1) 2)))
0.2b	(* (log (exp (cos (/ (+ phi2 phi1) 2)))) (- lambda1 lambda2))
0.5b	(log (exp (cos (/ (+ phi2 phi1) 2))))
3.0b	(cos (/ (+ phi2 phi1) 2))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `rem-exp-log`

Counts

4 → 93

Calls

4 calls:

8.0ms	(exp (cos (/ (+ phi2 phi1) 2)))
46.0ms	(* (log (exp (cos (/ (+ phi2 phi1) 2)))) (- lambda1 lambda2))
19.0ms	(log (exp (cos (/ (+ phi2 phi1) 2))))
11.0ms	(cos (/ (+ phi2 phi1) 2))

series324.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(exp (cos (/ (+ phi2 phi1) 2)))
204.0ms	(* (log (exp (cos (/ (+ phi2 phi1) 2)))) (- lambda1 lambda2))
30.0ms	(log (exp (cos (/ (+ phi2 phi1) 2))))
32.0ms	(cos (/ (+ phi2 phi1) 2))

simplify1.1s

Counts

105 → 105

Iterations

Iter	Nodes
done	5002
2	1141
1	328
0	167

prune939.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.7b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.2s	8371×	body	80	valid
2.1s	1368×	body	640	valid
1.2s	773×	body	1280	valid
971.0ms	731×	body	320	valid
206.0ms	387×	body	160	valid