Details

sample62.0ms

Algorithm

intervals

Results

15.0ms	197×	body	80	valid
8.0ms	22×	body	1280	valid
7.0ms	256×	pre	80	true
5.0ms	17×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	7×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	106	27
3	477	26
4	2270	26
done	5001	26

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

0.0b

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

2.0b

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
7×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

3 → 93

Calls

3 calls:

46.0ms

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

23.0ms

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

1.0ms

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

series466.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

114.0ms

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

220.0ms

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

simplify2.3s

Counts

102 → 102

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	172	1935
1	391	1877
2	1094	1746
3	3541	1744
done	5002	1741

prune494.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0b	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
0.2b	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
2.5b	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
38×	`times-frac`
31×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube`
11×	`distribute-lft-out`
7×	`pow1` `associate-/r` `associate-/l`
5×	`div-exp` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `flip--` `cbrt-unprod` `associate-/l/`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 133

Calls

4 calls:

12.0ms	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
20.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
87.0ms	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
1.0ms	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series611.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
119.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
148.0ms	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
244.0ms	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.6s

Counts

145 → 145

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	213	2499
1	496	2253
2	1488	2040
done	5000	2039

prune570.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.3b	(* (* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.3b	(* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
9.3b	(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
53×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
42×	`associate-r`
40×	`times-frac`
31×	`add-cube-cbrt`
16×	`sqrt-div`
13×	`pow1`
11×	`add-exp-log` `frac-times` `associate-*l/` `add-cbrt-cube`
9×	`distribute-lft-out`
6×	`flip3--` `associate-l` `associate-/r/` `flip--`
4×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `flip-+` `div-inv`
2×	`*-commutative`
1×	`pow-flip` `pow1/2` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 142

Calls

4 calls:

21.0ms	(sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
147.0ms	(* (* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
83.0ms	(* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.0ms	(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series787.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
146.0ms	(* (* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
232.0ms	(* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
218.0ms	(fma (* (* (- beta alpha) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify2.0s

Counts

154 → 154

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	255	3798
1	585	2989
2	1537	2595
done	5000	2578

prune748.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.3b	(* (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.3b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
7.1b	(fma (* (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
110×	`times-frac`
93×	`sqrt-prod`
59×	`add-cube-cbrt`
41×	`associate-l`
21×	`associate-r`
17×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares`
12×	`unswap-sqr`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sqrt-div` `associate-/r*`
5×	`associate-/l*`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`frac-times` `flip3--` `pow-flip` `frac-2neg` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--` `fma-udef` `inv-pow`

Counts

4 → 203

Calls

4 calls:

13.0ms	(sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
154.0ms	(* (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
35.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
1.0ms	(fma (* (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series712.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
113.0ms	(* (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))))
175.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
214.0ms	(fma (* (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.6s

Counts

215 → 215

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	299	5718
1	688	5358
2	1647	5036
done	5000	5014

prune808.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.8b

regimes199.0ms

Accuracy

0% (0.3b remaining)

Error of 12.6b against oracle of 12.3b and baseline of 12.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	42
1	26	42
done	26	42

end0.0ms

sample2.0s

Algorithm

intervals

Results

638.0ms	8000×	pre	80	true
466.0ms	6321×	body	80	valid
240.0ms	525×	body	1280	valid
138.0ms	575×	body	640	valid
118.0ms	399×	body	320	valid
23.0ms	180×	body	160	valid