Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	118	31
3	515	31
4	2648	31
done	5001	31

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

0.1b

(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))

2.7b

(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

872×	`times-frac`
765×	`*-un-lft-identity`
360×	`add-sqr-sqrt` `add-cube-cbrt`
229×	`distribute-lft-out`
72×	`associate-/l*`
31×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`associate-/l/`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `associate-/r/` `flip-+`

Counts

3 → 457

Calls

3 calls:

12.0ms

(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

41.0ms

(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))

8.0ms

(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series389.0ms

Counts

3 → 9

Calls

3 calls:

143.0ms

(/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

160.0ms

(/ (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))

85.0ms

(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.5s

Counts

466 → 466

Iterations

Useful iterations: 2 (728.0ms)

Iter	Nodes	Cost
0	503	23454
1	1204	22764
2	3825	21815
done	5000	21815

prune970.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
0.3b	(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
2.7b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
2.7b	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

461×	`times-frac`
368×	`*-un-lft-identity`
276×	`add-sqr-sqrt`
270×	`sqrt-prod`
216×	`add-cube-cbrt`
75×	`swap-sqr`
68×	`distribute-lft-out`
55×	`associate-r` `associate-l`
19×	`pow1` `div-inv`
16×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`sqrt-pow1` `pow1/2` `sqrt-div`
7×	`associate-/l/`
5×	`pow-prod-up`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `pow-sqr` `flip-+`
2×	`frac-times` `associate-r/` `associate-l/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `*-commutative`

Counts

4 → 333

Calls

4 calls:

39.0ms	(/ (* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
102.0ms	(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
8.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
8.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
150.0ms	(* (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (sqrt (/ (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))))
83.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
86.0ms	(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify1.2s

Counts

345 → 345

Iterations

Useful iterations: 2 (573.0ms)

Iter	Nodes	Cost
0	485	19230
1	883	13236
2	3248	12440
done	5000	12440

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
0.6b	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
2.6b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.6b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

1043×	`times-frac`
882×	`*-un-lft-identity`
810×	`sqrt-prod`
499×	`add-sqr-sqrt`
493×	`add-cube-cbrt`
218×	`distribute-lft-out`
71×	`associate-/l*`
18×	`div-inv`
14×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
6×	`pow1` `cbrt-undiv` `sqrt-div` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `hypot-def` `associate-/l/`

Counts

4 → 678

Calls

4 calls:

44.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
16.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
4.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
4.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
183.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
56.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
49.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify1.9s

Counts

690 → 690

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	652	33185
1	1494	30362
2	3759	29401
done	5000	29393

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
0.6b	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
2.6b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
2.6b	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

4013×	`times-frac`
2826×	`*-un-lft-identity`
2268×	`sqrt-prod`
1687×	`add-sqr-sqrt`
1681×	`add-cube-cbrt`
650×	`distribute-lft-out`
179×	`associate-/l*`
72×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r*`
9×	`cbrt-undiv` `div-exp`
6×	`pow1` `sqrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `hypot-def` `associate-/l/`

Counts

4 → 1651

Calls

4 calls:

84.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
16.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
4.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
8.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
177.0ms	(/ (/ (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (fma 1.0 2.0 (+ alpha beta))))
49.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))
60.0ms	(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify1.5s

Counts

1663 → 1663

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	1189	106149
1	2724	97138
done	5000	95854

prune4.0s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.9b

regimes66.0ms

Accuracy

57.1% (1.0b remaining)

Error of 2.1b against oracle of 1.1b and baseline of 3.5b

bsearch47.0ms

Steps

Iters	Range		Point
8	1.501308754378853e+168	5.852181614930846e+170	2.535503490869359e+170

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	36
1	20	36
done	20	36

end0.0ms

sample531.0ms

Algorithm

intervals

Results

301.0ms	8000×	body	80	valid
90.0ms	8000×	pre	80	true