Details

sample88.0ms

Algorithm

intervals

Results

36.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5013
3	1566
2	267
1	58
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize212.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.0b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.1b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
42×	`add-sqr-sqrt`
32×	`frac-times`
31×	`*-un-lft-identity`
30×	`associate-*r/`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
11×	`pow1`
9×	`associate-/l/`
8×	`associate-r`
7×	`div-inv`
5×	`associate-/r*`
4×	`associate-l` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 193

Calls

4 calls:

210.0ms	(* i (+ (+ alpha beta) i))
387.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
811.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
487.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series3.2s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* i (+ (+ alpha beta) i))
225.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
2.5s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
458.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify3.6s

Counts

205 → 205

Iterations

Iter	Nodes
done	5001
1	1258
0	352

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.8b

localize209.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
33.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

264×	`times-frac`
191×	`add-sqr-sqrt`
178×	`*-un-lft-identity`
110×	`add-cube-cbrt`
96×	`associate-r`
74×	`add-cbrt-cube` `add-exp-log`
42×	`associate-l`
40×	`associate-/r/`
35×	`cbrt-undiv` `div-exp`
30×	`difference-of-squares`
21×	`flip3-+` `flip-+`
20×	`div-inv`
19×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
15×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/l*`
10×	`associate-/r*`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 308

Calls

4 calls:

657.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.5s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
279.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
508.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series5.7s

Counts

4 → 12

Calls

4 calls:

426.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
4.8s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
168.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
273.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify4.5s

Counts

320 → 320

Iterations

Iter	Nodes
done	5001
1	1625
0	467

prune4.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.7b

localize254.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
0.2b	(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
33.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite4.7s

Algorithm

rewrite-expression-head

Rules

220×	`add-exp-log`
136×	`add-cbrt-cube`
91×	`times-frac` `div-exp`
87×	`prod-exp`
73×	`add-sqr-sqrt` `*-un-lft-identity`
54×	`cbrt-undiv`
49×	`add-cube-cbrt` `cbrt-unprod`
43×	`associate-l`
39×	`associate-r`
18×	`associate-/r/`
11×	`pow1`
10×	`flip3-+` `flip-+`
9×	`rec-exp` `1-exp` `div-inv` `distribute-lft-out`
6×	`frac-times` `associate-/r` `associate-l/` `associate-*r/` `difference-of-squares`
4×	`pow-prod-down` `insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr` `associate-/l/`
3×	`sqrt-prod` `distribute-lft-out--`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`flip3--` `un-div-inv` `flip--`

Counts

4 → 246

Calls

4 calls:

1.3s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
2.7s	(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
187.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
427.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series7.0s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
5.2s	(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
162.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
281.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify4.2s

Counts

258 → 258

Iterations

Iter	Nodes
done	5000
1	1377
0	413

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.7b

localize467.0ms

Local error

Found 4 expressions with local error:

33.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
34.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
8×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*` `associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `associate-*r/` `insert-posit16` `div-inv` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

247.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
239.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
421.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
425.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series832.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
156.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
235.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
262.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify3.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1824
1	380
0	126

prune2.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 33.7b

regimes870.0ms

Accuracy

36.2% (2.5b remaining)

Error of 36.9b against oracle of 34.4b and baseline of 38.3b

bsearch95.0ms

Steps

Iters	Range		Point
7	1.5185210340582453e+216	6.531618038873483e+217	1.605441052792236e+216

simplify20.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
378.0ms	8000×	pre	80	true