Details

sample75.0ms

Algorithm

intervals

Results

42.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
4	11139
3	1615
2	280
1	60
0	17

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.1b

localize54.0ms

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))))
35.2b	(/ (/ (* (* 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))
44.1b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite662.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `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 → 201

Calls

4 calls:

74.0ms	(* i (+ (+ alpha beta) i))
104.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
309.0ms	(/ (/ (* (* 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))
168.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.5s

Counts

4 → 12

Calls

4 calls:

40.0ms	(* i (+ (+ alpha beta) i))
178.0ms	(* (* 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))
249.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.0s

Counts

213 → 213

Iterations

Iter	Nodes
2	7204
1	1272
0	359

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.2b

localize91.0ms

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))))
34.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.8b	(/ (+ (* 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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 376

Calls

4 calls:

291.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
841.0ms	(* (/ (/ (* 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))))
72.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
180.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.1s

Counts

4 → 12

Calls

4 calls:

478.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.4s	(* (/ (/ (* 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))))
110.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
175.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.8s

Counts

388 → 388

Iterations

Iter	Nodes
2	7286
1	1713
0	511

prune6.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.1b

localize79.0ms

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)))
0.0b	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
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))))
34.8b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

1852×	`times-frac`
1455×	`*-un-lft-identity`
892×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
380×	`distribute-lft-out`
278×	`associate-l`
99×	`associate-/r/`
96×	`associate-r`
86×	`associate-/l*`
74×	`add-cbrt-cube` `add-exp-log`
62×	`difference-of-squares`
54×	`div-inv`
44×	`flip3-+` `flip-+`
40×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 956

Calls

4 calls:

334.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
181.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
876.0ms	(* (/ (/ 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))))
205.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.5s

Counts

4 → 12

Calls

4 calls:

542.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
399.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.3s	(* (/ (/ 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))))
219.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.5s

Counts

968 → 968

Iterations

Iter	Nodes
1	3388
0	1042

prune17.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize63.0ms

Local error

Found 3 expressions with local error:

0.0b

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

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)))

rewrite351.0ms

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×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`

Counts

3 → 513

Calls

3 calls:

83.0ms

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

65.0ms

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

177.0ms

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

series596.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms

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

144.0ms

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

372.0ms

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

simplify3.7s

Counts

522 → 522

Iterations

Iter	Nodes
2	5262
1	1514
0	578

prune8.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

regimes348.0ms

Accuracy

36.2% (10.4b remaining)

Error of 12.5b against oracle of 2.1b and baseline of 18.4b

bsearch449.0ms

Steps

Iters	Range		Point
7	5.10633297233485e+153	4.121021321028831e+155	8.296142771618488e+154
6	3.1819839989364968e+143	1.9564396141384856e+144	1.1670218513000327e+144
7	4.6213351350430846e+131	1.4905430430158114e+133	6.635668102175435e+131
6	4.790332713009464e+113	3.8021573547113504e+114	3.744674797319727e+114

simplify39.0ms

Iterations

Iter	Nodes
2	64
1	64
0	49

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
362.0ms	8000×	pre	80	true