Details

sample32.0ms

Algorithm

intervals

Results

5.0ms	167×	body	80	valid
4.0ms	28×	body	1280	valid
4.0ms	33×	body	640	valid
4.0ms	256×	pre	80	true
1.0ms	15×	body	320	valid
1.0ms	13×	body	160	valid

simplify6.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	244
1	20	244
2	33	244
3	50	244
4	69	244
5	124	244
6	209	244
7	290	244
8	348	244
9	467	244
10	582	244
11	669	244
12	795	244
13	995	244
14	1236	244
15	1474	244
16	1722	244
17	1985	244
18	2315	244
19	2829	244
20	3229	244
21	3572	244
22	3954	244
23	4303	244
24	4583	244
25	4885	244
done	5000	244

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
3.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite251.0ms

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:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
199.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series178.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
107.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

106 → 106

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	128	23780
1	340	21276
2	1160	20829
done	5000	20754

prune564.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
3.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.1s

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` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

648.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
42.0ms	(/ alpha (+ (+ alpha beta) 2.0))
280.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series313.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
82.0ms	(/ beta (+ (+ alpha beta) 2.0))
57.0ms	(/ alpha (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify4.1s

Counts

425 → 425

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	402	232467
1	991	202239
2	2694	173816
done	5004	168488

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize104.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
3.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite367.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

24.0ms	(cbrt (+ (+ alpha beta) 2.0))
25.0ms	(cbrt (+ (+ alpha beta) 2.0))
26.0ms	(cbrt (+ (+ alpha beta) 2.0))
279.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series499.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (+ (+ alpha beta) 2.0))
135.0ms	(cbrt (+ (+ alpha beta) 2.0))
130.0ms	(cbrt (+ (+ alpha beta) 2.0))
106.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.2s

Counts

164 → 164

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	204	71367
1	470	57635
2	1174	46828
3	3825	44314
done	5000	44239

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize98.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
3.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

18.0ms	(cbrt (+ (+ alpha beta) 2.0))
13.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(cbrt (+ (+ alpha beta) 2.0))
187.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series517.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(cbrt (+ (+ alpha beta) 2.0))
149.0ms	(cbrt (+ (+ alpha beta) 2.0))
134.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.9s

Counts

164 → 164

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	204	71367
1	470	57635
2	1174	46828
3	3825	44314
done	5000	44239

prune1.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

regimes341.0ms

Accuracy

77.6% (2.9b remaining)

Error of 6.1b against oracle of 3.2b and baseline of 16.1b

bsearch65.0ms

Steps

Iters	Range		Point
7	247318.98015239072	31866126.207131654	16738773.274129016

simplify8.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	34	1292
1	37	1292
done	37	1292

end0.0ms

sample1.7s

Algorithm

intervals

Results

656.0ms	857×	body	1280	valid
321.0ms	5809×	body	80	valid
225.0ms	8000×	pre	80	true
150.0ms	745×	body	640	valid
96.0ms	376×	body	320	valid
58.0ms	213×	body	160	valid