Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	35×	body	640	valid
10.0ms	183×	body	80	valid
7.0ms	256×	pre	80	true
6.0ms	23×	body	1280	valid
2.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify559.0ms

Counts

1 → 1

Iterations

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

2 → 100

Calls

2 calls:

33.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
130.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series141.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
74.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

106 → 106

Iterations

Iter	Nodes
3	3192
2	975
1	338
0	128

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.6b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

182×	`*-un-lft-identity`
91×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
12×	`associate-/r/`
10×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 179

Calls

3 calls:

41.0ms	(/ alpha (+ (+ alpha beta) 2.0))
26.0ms	(/ beta (+ (+ alpha beta) 2.0))
156.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series262.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ alpha (+ (+ alpha beta) 2.0))
66.0ms	(/ beta (+ (+ alpha beta) 2.0))
125.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

188 → 188

Iterations

Iter	Nodes
3	3778
2	1181
1	487
0	221

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))
0.1b	(* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0)))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
25.0b	(cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0))))

rewrite593.0ms

Algorithm

rewrite-expression-head

Rules

327×	`*-un-lft-identity`
177×	`times-frac`
138×	`add-sqr-sqrt`
118×	`add-cube-cbrt`
117×	`distribute-lft-out`
63×	`prod-diff`
57×	`add-cbrt-cube` `add-exp-log`
42×	`associate-r`
39×	`swap-sqr`
30×	`pow1`
22×	`associate-l` `prod-exp` `cbrt-unprod`
21×	`fma-neg`
18×	`associate-/r/`
17×	`cbrt-undiv` `div-exp`
11×	`frac-times` `associate-*l/`
9×	`flip3-+` `flip-+` `div-inv`
7×	`cbrt-div` `pow-plus` `associate-*r/` `pow-prod-up`
6×	`add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`pow2` `pow-sqr`
2×	`pow3` `*-commutative` `difference-of-squares`
1×	`cbrt-prod` `sub-neg` `flip3--` `pow1/3` `diff-log` `rem-cbrt-cube` `flip--` `distribute-lft-out--`

Counts

4 → 303

Calls

4 calls:

188.0ms	(* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))
88.0ms	(* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0)))
178.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
126.0ms	(cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))
94.0ms	(* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0)))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
114.0ms	(cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0))))

simplify1.3s

Counts

315 → 315

Iterations

Iter	Nodes
2	2970
1	1012
0	351

prune3.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.5b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
25.0b	(cbrt (* (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ 1 (sqrt (+ (+ alpha beta) 2.0)))) (/ beta (sqrt (+ (+ alpha beta) 2.0)))))

rewrite849.0ms

Algorithm

rewrite-expression-head

Rules

197×	`*-un-lft-identity`
109×	`times-frac`
100×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
40×	`sqrt-prod`
21×	`fma-neg`
18×	`frac-times` `associate-*l/`
17×	`cbrt-div`
16×	`associate-/r*`
12×	`associate-/r/`
10×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`associate-*r/`
6×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`div-exp` `pow-flip`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `un-div-inv` `difference-of-squares`
1×	`cbrt-prod` `rec-exp` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `pow1/3` `diff-log` `1-exp` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 237

Calls

4 calls:

41.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
43.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
139.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
618.0ms	(cbrt (* (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ 1 (sqrt (+ (+ alpha beta) 2.0)))) (/ beta (sqrt (+ (+ alpha beta) 2.0)))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
80.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
102.0ms	(cbrt (* (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ 1 (sqrt (+ (+ alpha beta) 2.0)))) (/ beta (sqrt (+ (+ alpha beta) 2.0)))))

simplify1.0s

Counts

249 → 249

Iterations

Iter	Nodes
2	2049
1	817
0	375

prune3.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

regimes276.0ms

Accuracy

98.3% (0.2b remaining)

Error of 3.0b against oracle of 2.8b and baseline of 15.6b

bsearch2.0ms

simplify12.0ms

Iterations

Iter	Nodes
2	37
1	37
0	33

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	5894×	body	80	valid
421.0ms	853×	body	1280	valid
316.0ms	688×	body	640	valid
280.0ms	8000×	pre	80	true
97.0ms	379×	body	320	valid
62.0ms	186×	body	160	valid

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10

Iter	Nodes
15	445
14	445
13	442
12	437
11	416
10	364
9	276
8	211
7	186
6	152
5	112
4	69
3	50
2	33
1	20
0	10