Details

sample94.0ms

Algorithm

intervals

Results

28.0ms	22×	body	640	valid
20.0ms	204×	body	80	valid
8.0ms	256×	pre	80	true
6.0ms	13×	body	1280	valid
3.0ms	9×	body	320	valid
2.0ms	8×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (75.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.1b

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

2.3b

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

rewrite57.0ms

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:

21.0ms

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

29.0ms

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

0.0ms

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

series403.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms

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

104.0ms

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

210.0ms

(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	1095	1746
3	3539	1744
done	5000	1741

prune435.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.1b

localize44.0ms

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)))
7.2b	(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)

rewrite270.0ms

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:

191.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
29.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
24.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
1.0ms	(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)

series814.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
258.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
197.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
108.0ms	(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)

simplify1.6s

Counts

250 → 250

Iterations

Useful iterations: done (1.6s)

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

prune913.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.1b

localize22.0ms

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)))
7.7b	(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)

rewrite91.0ms

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:

37.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
25.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
16.0ms	(/ 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)

series703.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
179.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
202.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
129.0ms	(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)

simplify2.5s

Counts

194 → 194

Iterations

Useful iterations: done (2.5s)

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

prune884.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.6b	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
9.1b	(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) (fabs (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
16×	`sqrt-prod`
8×	`add-exp-log` `cbrt-prod`
7×	`associate-/r*`
6×	`pow1` `add-cbrt-cube` `distribute-lft-out`
4×	`expm1-log1p-u` `cbrt-div` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `flip3-+` `flip-+` `associate-/l*`
2×	`pow1/3` `sqrt-div` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

4 → 95

Calls

4 calls:

30.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
8.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
9.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
1.0ms	(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) (fabs (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series3.3s

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
452.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
444.0ms	(cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0))
2.2s	(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) (fabs (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (sqrt (cbrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify2.5s

Counts

107 → 107

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	189	2604
1	392	2408
2	912	2024
3	2796	1925
done	5000	1892

prune639.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

regimes240.0ms

Accuracy

0% (0.4b remaining)

Error of 12.6b against oracle of 12.2b and baseline of 12.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	52
1	24	52
done	24	52

end0.0ms

sample2.0s

Algorithm

intervals

Results

598.0ms	6338×	body	80	valid
356.0ms	8000×	pre	80	true
285.0ms	528×	body	1280	valid
221.0ms	574×	body	640	valid
81.0ms	353×	body	320	valid
31.0ms	207×	body	160	valid