Details

sample70.0ms

Algorithm

intervals

Results

17.0ms	282×	body	80	valid
11.0ms	27×	body	1280	valid
10.0ms	35×	body	640	valid
8.0ms	28×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	32	32
2	69	32
3	238	32
4	742	32
5	1972	32
6	4486	32
done	5001	32

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

65.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
98.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series595.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
434.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify488.0ms

Counts

147 → 147

Iterations

Useful iterations: done (480.0ms)

Iter	Nodes	Cost
0	455	7854
1	1320	7209
done	5000	6835

prune447.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
109.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
30.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
436.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify488.0ms

Counts

128 → 128

Iterations

Useful iterations: done (478.0ms)

Iter	Nodes	Cost
0	449	7330
1	1286	6543
done	5001	6035

prune483.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.0b

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
2.5b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/`
96×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
118.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(cos (/ (+ phi1 phi2) 2.0))
434.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cbrt (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify470.0ms

Counts

112 → 112

Iterations

Useful iterations: done (460.0ms)

Iter	Nodes	Cost
0	424	7796
1	1243	7316
done	5000	6477

prune597.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 23.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
2.5b	(cos (/ (+ phi1 phi2) 2.0))
5.9b	(exp (log (sqrt (+ (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))))
33.6b	(sqrt (+ (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `associate-*r/` `flip--`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `exp-diff`
64×	`associate-*l/`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`unpow-prod-down` `log-prod` `exp-prod` `exp-sum` `sqrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `log-pow`
2×	`pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-exp` `rem-exp-log` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

3.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
10.0ms	(cos (/ (+ phi1 phi2) 2.0))
73.0ms	(exp (log (sqrt (+ (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))))
75.0ms	(sqrt (+ (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series1.5s

Counts

4 → 12

Calls

4 calls:

87.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
29.0ms	(cos (/ (+ phi1 phi2) 2.0))
688.0ms	(exp (log (sqrt (+ (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))))
684.0ms	(sqrt (+ (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify522.0ms

Counts

205 → 205

Iterations

Useful iterations: done (510.0ms)

Iter	Nodes	Cost
0	699	13391
1	1542	12116
done	5000	11808

prune742.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 15.9b

regimes683.0ms

Accuracy

39.9% (11.0b remaining)

Error of 31.1b against oracle of 20.0b and baseline of 38.4b

bsearch126.0ms

Steps

Iters	Range		Point
5	1.0089552931209797e+74	3.624693707620505e+74	1.4975036163339162e+74
6	-2.5565135935631026e+148	-5.0947934852509e+147	-2.5324828700327777e+148

simplify21.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	86
1	63	86
2	72	86
3	77	86
4	87	86
5	93	86
done	93	86

end0.0ms

sample2.1s

Algorithm

intervals

Results

738.0ms	8358×	body	80	valid
359.0ms	1256×	body	640	valid
312.0ms	779×	body	1280	valid
151.0ms	757×	body	320	valid
54.0ms	413×	body	160	valid