Details

sample52.0ms

Algorithm

intervals

Results

14.0ms	256×	pre	80	true
10.0ms	189×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	24×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	4×	body	160	valid

simplify1.1s

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite314.0ms

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:

71.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
240.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series126.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
75.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts: 71 → 71

prune225.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

1.5s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
41.0ms	(/ alpha (+ (+ alpha beta) 2.0))
69.0ms	(/ beta (+ (+ alpha beta) 2.0))
250.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series399.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
91.0ms	(/ alpha (+ (+ alpha beta) 2.0))
68.0ms	(/ beta (+ (+ alpha beta) 2.0))
137.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify838.0ms

Counts: 149 → 149

prune520.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.2b	(- (cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) 1.0)
25.9b	(cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))

rewrite853.0ms

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity`
77×	`times-frac`
67×	`add-sqr-sqrt`
54×	`cbrt-prod`
52×	`add-cube-cbrt`
48×	`distribute-lft-out`
44×	`unpow-prod-down` `cube-prod`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `associate-/r*` `flip-+` `div-inv`
3×	`pow-unpow` `associate-/l*` `sqr-pow`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `flip--` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 177

Calls

4 calls:

49.0ms	(/ beta (+ (+ alpha beta) 2.0))
55.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
643.0ms	(- (cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) 1.0)
88.0ms	(cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))

series390.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ beta (+ (+ alpha beta) 2.0))
92.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
115.0ms	(- (cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) 1.0)
129.0ms	(cbrt (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))

simplify1.1s

Counts: 189 → 189

prune794.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`cbrt-prod` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
1.0ms	(cbrt beta)
318.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series981.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt beta)
293.0ms	(cbrt beta)
260.0ms	(cbrt beta)
103.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify652.0ms

Counts: 60 → 60

prune272.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.4b

regimes89.0ms

Accuracy

71.9% (3.5b remaining)

Error of 6.7b against oracle of 3.3b and baseline of 15.5b

bsearch56.0ms

Steps

Iters	Range		Point
7	1.6187759830994239e+40	3.492112297455384e+41	2.4810729294817534e+40

simplify465.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

281.0ms	5887×	body	80	valid
266.0ms	830×	body	1280	valid
255.0ms	8000×	pre	80	true
180.0ms	716×	body	640	valid
78.0ms	384×	body	320	valid
18.0ms	183×	body	160	valid