Details

sample79.0ms

Algorithm

intervals

Results

19.0ms	181×	body	80	valid
14.0ms	32×	body	640	valid
12.0ms	22×	body	1280	valid
11.0ms	256×	pre	80	true
4.0ms	13×	body	320	valid
2.0ms	8×	body	160	valid

simplify642.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize16.0ms

Local error

Found 3 expressions with local error:

2.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.0b	(+ (+ alpha beta) 2.0)

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

113×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
38×	`distribute-lft-out`
35×	`fma-def`
27×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
10×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`sum-log` `flip3-+` `associate-/r/` `flip-+`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`+-commutative` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-+l+` `clear-num` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

3 → 124

Calls

3 calls:

Slowest

145.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
35.0ms	(+ (+ alpha beta) 2.0)
31.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series180.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

95.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
72.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
14.0ms	(+ (+ alpha beta) 2.0)

simplify466.0ms

Counts: 127 → 133

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.8b

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))

rewrite656.0ms

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 417

Calls

4 calls:

Slowest

455.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
143.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
24.0ms	(/ alpha (+ (+ alpha beta) 2.0))
23.0ms	(/ beta (+ (+ alpha beta) 2.0))

series322.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
83.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
75.0ms	(/ alpha (+ (+ alpha beta) 2.0))
55.0ms	(/ beta (+ (+ alpha beta) 2.0))

simplify696.0ms

Counts: 660 → 429

prune5.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize30.0ms

Local error

Found 4 expressions with local error:

9.1b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))

rewrite843.0ms

Algorithm

rewrite-expression-head

Rules

166×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
78×	`times-frac`
74×	`add-cube-cbrt`
63×	`prod-diff`
48×	`distribute-lft-out`
21×	`fma-neg`
14×	`log-prod`
10×	`associate-/r/`
8×	`log-div`
7×	`exp-sum` `add-exp-log` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`associate-/r*` `flip3-+` `flip3--` `flip-+` `div-inv` `flip--`
4×	`expm1-log1p-u` `exp-prod` `exp-diff` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `rem-exp-log`

Counts

4 → 191

Calls

4 calls:

Slowest

327.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
272.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
218.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
21.0ms	(/ alpha (+ (+ alpha beta) 2.0))

series477.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

209.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
111.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
78.0ms	(/ alpha (+ (+ alpha beta) 2.0))

simplify402.0ms

Counts: 306 → 203

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize33.0ms

Local error

Found 4 expressions with local error:

9.1b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.1b	(pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))

rewrite903.0ms

Algorithm

rewrite-expression-head

Rules

167×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
78×	`times-frac`
75×	`add-cube-cbrt`
63×	`prod-diff`
48×	`distribute-lft-out`
21×	`fma-neg`
14×	`log-prod`
10×	`associate-/r/`
8×	`log-div` `add-exp-log`
7×	`pow1` `unpow-prod-up` `distribute-lft-out--`
6×	`add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`associate-/r*` `flip3-+` `flip3--` `flip-+` `div-inv` `flip--`
4×	`expm1-log1p-u` `pow-unpow` `frac-sub` `insert-posit16` `log1p-expm1-u` `pow-sub`
3×	`unpow-prod-down` `associate-/l*`
2×	`pow-exp` `log-pow`
1×	`pow-to-exp` `cbrt-undiv` `e-exp-1` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `sqr-pow`

Counts

4 → 198

Calls

4 calls:

Slowest

446.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
234.0ms	(pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
187.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
28.0ms	(/ alpha (+ (+ alpha beta) 2.0))

series543.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(pow E (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
159.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
97.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
79.0ms	(/ alpha (+ (+ alpha beta) 2.0))

simplify505.0ms

Counts: 318 → 210

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

regimes249.0ms

Accuracy

99.1% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 16.2b

bsearch8.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

729.0ms	8000×	pre	80	true
529.0ms	5792×	body	80	valid
456.0ms	874×	body	1280	valid
342.0ms	730×	body	640	valid
99.0ms	402×	body	320	valid
32.0ms	202×	body	160	valid