Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	197×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	24×	body	640	valid
2.0ms	19×	body	320	valid
2.0ms	10×	body	1280	valid
0.0ms	6×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (50.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize12.0ms

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)))

1.6b

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

rewrite47.0ms

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:

25.0ms

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

18.0ms

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

0.0ms

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

series312.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms

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

72.0ms

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

148.0ms

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

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

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

prune312.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.4b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
8.7b	(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
134×	`times-frac`
83×	`sqrt-prod`
72×	`add-cube-cbrt`
41×	`associate-r`
32×	`add-exp-log`
27×	`associate-l`
20×	`add-cbrt-cube`
18×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/` `associate-/l*`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `fma-udef` `inv-pow`

Counts

4 → 238

Calls

4 calls:

90.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
24.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
16.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms	(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series514.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
133.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
128.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
85.0ms	(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.1s

Counts

250 → 250

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	297	6664
1	774	6016
2	2259	5067
done	5000	5055

prune605.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.6b	(* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
9.9b	(fma (* (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

320×	`sqrt-prod`
216×	`add-sqr-sqrt`
198×	`times-frac`
188×	`*-un-lft-identity`
104×	`add-cube-cbrt`
50×	`sqrt-pow1`
46×	`swap-sqr`
39×	`pow1`
36×	`unswap-sqr`
30×	`pow-flip` `associate-r` `associate-l`
26×	`distribute-lft-out`
18×	`pow1/2`
16×	`sqrt-div`
14×	`add-exp-log` `associate-/r*`
13×	`pow-prod-up`
12×	`associate-/r/`
10×	`add-cbrt-cube` `inv-pow`
8×	`div-inv`
7×	`pow-prod-down` `pow-sqr`
6×	`flip3-+` `flip-+` `associate-/l*`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 304

Calls

4 calls:

13.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
13.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
90.0ms	(* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
0.0ms	(fma (* (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series449.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
122.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
126.0ms	(* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
79.0ms	(fma (* (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.6s

Counts

316 → 316

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	286	9590
1	493	6230
2	1092	5844
3	3383	5656
done	5001	5516

prune660.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
9.9b	(fma (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
77×	`times-frac`
72×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `sqrt-prod`
21×	`associate-/r*`
14×	`add-exp-log` `distribute-lft-out`
11×	`associate-/l*`
10×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`pow-flip` `sqrt-div` `associate-/r/`
5×	`div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv`
2×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/` `inv-pow`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

4 → 182

Calls

4 calls:

27.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
13.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
13.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms	(fma (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series468.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
124.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
126.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
81.0ms	(fma (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (* (sqrt (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.8s

Counts

194 → 194

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	217	4273
1	468	3822
2	1093	3432
3	2992	3275
done	5000	3274

prune519.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

regimes156.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.4b and baseline of 12.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	53
1	25	53
done	25	53

end0.0ms

sample838.0ms

Algorithm

intervals

Results

238.0ms	6310×	body	80	valid
113.0ms	8000×	pre	80	true
95.0ms	490×	body	1280	valid
85.0ms	591×	body	640	valid
45.0ms	414×	body	320	valid
17.0ms	195×	body	160	valid