Details

sample80.0ms

Algorithm

intervals

Results

43.0ms	256×	body	80	valid
19.0ms	256×	pre	80	true

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5013
3	1679
2	282
1	58
0	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.5b

localize41.0ms

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))))
39.2b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
46.7b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite657.0ms

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:

97.0ms	(* i (+ (+ alpha beta) i))
117.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
319.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
116.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.6s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* i (+ (+ alpha beta) i))
166.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
225.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.8s

Counts

205 → 205

Iterations

Iter	Nodes
done	5000
1	1251
0	351

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 36.6b

localize82.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
37.0b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
38.2b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-cbrt-cube` `add-exp-log`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 368

Calls

4 calls:

295.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
844.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
74.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
142.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.6s

Counts

4 → 12

Calls

4 calls:

458.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
2.8s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
135.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
171.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.4s

Counts

380 → 380

Iterations

Iter	Nodes
done	5000
1	1707
0	503

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 36.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.0b	(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
0.1b	(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
38.2b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1714×	`times-frac`
1388×	`*-un-lft-identity`
773×	`add-sqr-sqrt`
659×	`add-cube-cbrt`
392×	`distribute-lft-out`
278×	`associate-l`
96×	`associate-r`
85×	`associate-/r/`
74×	`associate-/l*`
71×	`add-cbrt-cube` `add-exp-log`
47×	`div-inv`
39×	`flip3-+` `flip-+`
38×	`cbrt-undiv` `div-exp`
30×	`difference-of-squares`
15×	`sqrt-prod` `distribute-lft-out--`
12×	`associate-/r*` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1`
5×	`associate-/l/`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 859

Calls

4 calls:

239.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
114.0ms	(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
734.0ms	(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
150.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.6s

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
83.0ms	(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
3.0s	(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
193.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.7s

Counts

871 → 871

Iterations

Iter	Nodes
done	5004
1	3239
0	959

prune5.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.5b

localize63.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

0.0b

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

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

950×	`times-frac`
828×	`*-un-lft-identity`
385×	`add-sqr-sqrt` `add-cube-cbrt`
252×	`distribute-lft-out`
74×	`associate-/l*`
48×	`associate-/r/`
30×	`associate-/r*`
27×	`div-inv`
22×	`flip3-+` `flip-+`
19×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

3 → 507

Calls

3 calls:

58.0ms

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

172.0ms

(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

100.0ms

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

series569.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms

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

358.0ms

(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

101.0ms

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

simplify2.0s

Counts

516 → 516

Iterations

Iter	Nodes
done	5000
1	1549
0	572

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.4b

regimes360.0ms

Accuracy

43.3% (9.2b remaining)

Error of 11.1b against oracle of 1.9b and baseline of 18.1b

bsearch132.0ms

Steps

Iters	Range		Point
7	4.180155208905662e+119	1.7530375893929083e+121	2.495505368754722e+120

simplify15.0ms

Iterations

Iter	Nodes
done	48
1	48
0	35

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
451.0ms	8000×	pre	80	true