Details

sample54.0ms

Algorithm

intervals

Results

11.0ms	194×	body	80	valid
10.0ms	22×	body	640	valid
5.0ms	20×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	15×	body	320	valid
0.0ms	5×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2325
3	469
2	101
1	31
0	15

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.6b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b

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

14.7b

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

16.9b

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

24.0ms

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

0.0ms

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

25.0ms

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

series613.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms

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

268.0ms

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

223.0ms

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

simplify1.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	1555
1	375
0	143

prune662.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.1b

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

14.7b

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
156×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
24×	`associate-/l*`
20×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`flip3-+` `flip3--` `flip-+` `fma-udef` `flip--`

Counts

3 → 169

Calls

3 calls:

20.0ms

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

44.0ms

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

1.0ms

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

series622.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms

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

223.0ms

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

288.0ms

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

simplify1.8s

Counts

178 → 178

Iterations

Iter	Nodes
done	5006
2	1766
1	596
0	250

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
0.1b	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
1.5b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
3.1b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

305×	`times-frac`
278×	`*-un-lft-identity`
207×	`add-sqr-sqrt`
136×	`add-cube-cbrt`
82×	`associate-l`
40×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
24×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
12×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-r` `associate-/r/` `log1p-expm1-u`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`distribute-rgt-in` `frac-times` `associate-+l+` `clear-num` `frac-2neg` `distribute-lft-in` `associate-*r/`
1×	`+-commutative` `sum-log` `fma-def` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 288

Calls

4 calls:

13.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
30.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
85.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
30.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

series893.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
249.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
310.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
230.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

simplify2.9s

Counts

300 → 300

Iterations

Iter	Nodes
done	5000
2	4437
1	1311
0	363

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha))))
0.1b	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
1.5b	(* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
3.1b	(+ (* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

rewrite496.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
381×	`*-un-lft-identity`
374×	`add-sqr-sqrt`
249×	`add-cube-cbrt`
169×	`prod-diff`
54×	`associate-l`
49×	`div-inv`
40×	`distribute-lft-out--` `difference-of-squares`
26×	`distribute-lft-out`
13×	`fma-neg`
12×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-rgt-out--`
8×	`add-log-exp`
6×	`pow1`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-/r` `associate-r*` `associate-/r/` `log1p-expm1-u` `associate-/l/`
2×	`distribute-rgt-in` `frac-times` `cbrt-undiv` `associate-+l+` `distribute-lft-in` `flip3--` `div-exp` `prod-exp` `associate-*r/` `frac-sub` `cbrt-unprod` `flip--` `sub-div` `unswap-sqr`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 390

Calls

4 calls:

35.0ms	(- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha))))
152.0ms	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
184.0ms	(* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
77.0ms	(+ (* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

series876.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha))))
231.0ms	(/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
251.0ms	(* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
235.0ms	(+ (* (/ (- (/ beta (fma 2.0 i (+ beta alpha))) (/ alpha (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

simplify2.2s

Counts

402 → 402

Iterations

Iter	Nodes
done	5000
1	1636
0	551

prune4.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.2b

regimes434.0ms

Accuracy

0% (0.3b remaining)

Error of 12.1b against oracle of 11.8b and baseline of 12.1b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample2.1s

Algorithm

intervals

Results

705.0ms	6390×	body	80	valid
330.0ms	8000×	pre	80	true
286.0ms	522×	body	1280	valid
213.0ms	539×	body	640	valid
84.0ms	350×	body	320	valid
44.0ms	199×	body	160	valid