Details

sample31.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
4.0ms	33×	body	640	valid
4.0ms	256×	pre	80	true
3.0ms	20×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	6×	body	160	valid

simplify51.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
170.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series116.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify32.0ms

Counts: 71 → 71

prune153.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite670.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

409.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
37.0ms	(/ alpha (+ (+ alpha beta) 2.0))
35.0ms	(/ beta (+ (+ alpha beta) 2.0))
183.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series249.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify44.0ms

Counts: 123 → 123

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.9b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite631.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
24×	`distribute-lft-out`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 110

Calls

4 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
36.0ms	(/ beta (+ (+ alpha beta) 2.0))
374.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
180.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series263.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
53.0ms	(/ beta (+ (+ alpha beta) 2.0))
83.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify35.0ms

Counts: 122 → 122

prune322.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
1.9b	(log (exp (/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.9b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite723.0ms

Algorithm

rewrite-expression-head

Rules

232×	`*-un-lft-identity`
131×	`times-frac`
88×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
23×	`log-pow`
22×	`exp-prod`
21×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
12×	`pow1` `associate-/r/`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `associate-/r*` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`log-prod` `associate-/l*`
1×	`pow2` `frac-times` `sub-neg` `log-div` `flip3--` `frac-2neg` `pow-plus` `exp-diff` `diff-log` `div-sub` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 194

Calls

4 calls:

36.0ms	(/ beta (+ (+ alpha beta) 2.0))
154.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
469.0ms	(log (exp (/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
53.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series361.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ beta (+ (+ alpha beta) 2.0))
63.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
146.0ms	(log (exp (/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
99.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify100.0ms

Counts: 206 → 206

prune528.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

regimes117.0ms

Accuracy

76.4% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.5b

bsearch57.0ms

Steps

Iters	Range		Point
8	976503.8483825806	50707504882.44517	45468567748.04238

simplify1.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

287.0ms	5869×	body	80	valid
184.0ms	8000×	pre	80	true
180.0ms	836×	body	1280	valid
116.0ms	691×	body	640	valid
38.0ms	405×	body	320	valid
14.0ms	199×	body	160	valid