Details

sample69.0ms

Algorithm

intervals

Results

19.0ms	205×	body	80	valid
10.0ms	256×	pre	80	true
9.0ms	20×	body	1280	valid
6.0ms	16×	body	640	valid
4.0ms	15×	body	320	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5022
4	2155
3	440
2	95
1	32
0	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

0.5b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

20.8b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite870.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `insert-posit16` `flip--`
2×	`clear-num` `frac-2neg` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 114

Calls

3 calls:

198.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

605.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

63.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series738.0ms

Counts

3 → 9

Calls

3 calls:

308.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

340.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

89.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify2.0s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	3058
1	697
0	228

prune583.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))
0.1b	(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta))))
0.5b	(log (exp (+ (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))) 1.0)))
0.5b	(+ (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))) 1.0)

rewrite826.0ms

Algorithm

rewrite-expression-head

Rules

120×	`*-un-lft-identity`
71×	`add-sqr-sqrt`
66×	`times-frac`
37×	`add-cube-cbrt`
36×	`distribute-lft-out`
35×	`associate-r`
18×	`add-cbrt-cube` `associate-l` `add-exp-log`
14×	`associate-/r/`
12×	`flip3-+` `flip-+`
11×	`distribute-lft-out--` `difference-of-squares`
8×	`frac-add`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
4×	`log-prod` `prod-exp` `log-pow` `cbrt-unprod` `insert-posit16` `unswap-sqr`
3×	`exp-prod` `div-inv`
2×	`associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-sub` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 164

Calls

4 calls:

79.0ms	(/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))
285.0ms	(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta))))
346.0ms	(log (exp (+ (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))) 1.0)))
110.0ms	(+ (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))
318.0ms	(* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta))))
370.0ms	(log (exp (+ (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))) 1.0)))
404.0ms	(+ (* (/ (+ alpha beta) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ (* 2 i) 2.0) (+ alpha beta)))) 1.0)

simplify2.7s

Counts

176 → 176

Iterations

Iter	Nodes
done	5002
2	3326
1	893
0	284

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.4b	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
6.8b	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

1015×	`times-frac`
755×	`*-un-lft-identity`
655×	`add-sqr-sqrt`
413×	`add-cube-cbrt`
333×	`sqrt-prod`
153×	`associate-r`
121×	`distribute-lft-out`
118×	`associate-l`
64×	`add-exp-log`
50×	`add-cbrt-cube`
45×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r/`
37×	`associate-/l*`
35×	`div-exp` `unswap-sqr`
34×	`div-inv`
24×	`cbrt-undiv`
20×	`flip3-+` `flip-+`
14×	`associate-/r*`
12×	`prod-exp`
9×	`cbrt-unprod`
8×	`sqrt-div`
6×	`pow1` `add-log-exp`
4×	`1-exp` `insert-posit16`
2×	`clear-num` `frac-2neg` `div-sub` `associate-/l/`
1×	`frac-times` `+-commutative` `sum-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 700

Calls

4 calls:

1.3s	(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
275.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
248.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
260.0ms	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

series1.3s

Counts

4 → 12

Calls

4 calls:

371.0ms	(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
266.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
205.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
463.0ms	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

simplify2.7s

Counts

712 → 712

Iterations

Iter	Nodes
done	5000
1	2321
0	732

prune4.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
6.8b	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
6.8b	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
6.8b	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

rewrite969.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
184×	`*-un-lft-identity`
102×	`add-sqr-sqrt` `add-cube-cbrt`
68×	`sqrt-prod`
41×	`distribute-lft-out`
16×	`associate-/l*`
11×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube` `div-inv`
7×	`associate-/r*`
5×	`div-exp`
4×	`pow1` `flip3-+` `flip-+` `insert-posit16`
3×	`cbrt-undiv` `+-commutative` `sum-log`
2×	`sqrt-div` `associate-/r/`
1×	`clear-num` `frac-2neg` `1-exp` `associate-/l/`

Counts

4 → 190

Calls

4 calls:

233.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
262.0ms	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
250.0ms	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
215.0ms	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
424.0ms	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
453.0ms	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
443.0ms	(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

simplify2.0s

Counts

202 → 202

Iterations

Iter	Nodes
done	5001
2	1672
1	627
0	274

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

regimes406.0ms

Accuracy

15.1% (5.6b remaining)

Error of 11.4b against oracle of 5.8b and baseline of 12.4b

bsearch200.0ms

Steps

Iters	Range		Point
10	1.0541557750928848e+125	2.8754037211585807e+137	3.234277159331003e+135

simplify21.0ms

Iterations

Iter	Nodes
done	59
1	59
0	46

end0.0ms

sample1.8s

Algorithm

intervals

Results

580.0ms	6361×	body	80	valid
354.0ms	8000×	pre	80	true
286.0ms	527×	body	640	valid
221.0ms	529×	body	1280	valid
134.0ms	382×	body	320	valid
29.0ms	201×	body	160	valid