Details

sample116.0ms

Algorithm

intervals

Results

37.0ms	205×	body	80	valid
20.0ms	21×	body	1280	valid
16.0ms	16×	body	640	valid
15.0ms	256×	pre	80	true
5.0ms	8×	body	320	valid
2.0ms	6×	body	160	valid

simplify912.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2067
4	2067
3	458
2	99
1	32
0	16

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ beta alpha) (- beta alpha))
0.0b	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
1.3b	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
24.4b	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `add-exp-log`
8×	`frac-times` `associate-/l/`
7×	`fma-def` `flip3-+` `flip-+`
6×	`pow1` `times-frac` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`cbrt-undiv` `sub-neg` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `-commutative` `fma-udef` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

28.0ms	(* (+ beta alpha) (- beta alpha))
0.0ms	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
35.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
45.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

series876.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (+ beta alpha) (- beta alpha))
137.0ms	(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))
261.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)
401.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

simplify876.0ms

Counts

131 → 131

Iterations

Iter	Nodes
done	2001
2	2001
1	682
0	225

prune609.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

12.1b

(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

20.8b

(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
13×	`add-cube-cbrt`
5×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `associate-/r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `div-inv` `flip--`

Counts

3 → 63

Calls

3 calls:

0.0ms

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

0.0ms

(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

19.0ms

(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

series634.0ms

Counts

3 → 9

Calls

3 calls:

156.0ms

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

265.0ms

(fma (/ (+ beta alpha) 1) (/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

213.0ms

(/ (- beta alpha) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

simplify922.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	2000
3	2000
2	718
1	286
0	131

prune468.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.5b

localize40.0ms

Local error

Found 4 expressions with local error:

12.1b	(fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)
20.8b	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
20.8b	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
20.8b	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cbrt-cube` `add-exp-log`
15×	`times-frac` `associate-/l*`
10×	`add-cube-cbrt`
6×	`cbrt-undiv` `div-exp` `associate-*r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `flip3--` `div-sub` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `flip--`
1×	`fma-udef`

Counts

4 → 110

Calls

4 calls:

0.0ms	(fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)
17.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
29.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
18.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

359.0ms	(fma (+ alpha beta) (/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0))) 1.0)
243.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
212.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
220.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

simplify1.1s

Counts

122 → 122

Iterations

Iter	Nodes
done	2065
3	2065
2	1307
1	312
0	121

prune952.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.4b

localize67.0ms

Local error

Found 4 expressions with local error:

20.8b	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
20.8b	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
20.8b	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
20.8b	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`add-cbrt-cube` `add-exp-log`
20×	`times-frac` `associate-/l*`
12×	`add-cube-cbrt`
8×	`cbrt-undiv` `div-exp` `associate-*r/` `associate-/r/` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `associate-/r*` `frac-2neg` `flip3-+` `flip3--` `div-sub` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `flip--` `add-log-exp`

Counts

4 → 132

Calls

4 calls:

27.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
23.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
37.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
17.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

series877.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
219.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
221.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))
231.0ms	(/ (- beta alpha) (* (fma 2 i (+ alpha beta)) (+ (fma 2 i (+ alpha beta)) 2.0)))

simplify1.3s

Counts

144 → 144

Iterations

Iter	Nodes
done	2004
3	2004
2	1001
1	251
0	92

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.4b

regimes618.0ms

Accuracy

81.6% (1.4b remaining)

Error of 13.6b against oracle of 12.2b and baseline of 19.8b

bsearch4.0ms

simplify23.0ms

Iterations

Iter	Nodes
done	50
1	50
0	39

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	6394×	body	80	valid
450.0ms	8000×	pre	80	true
392.0ms	513×	body	1280	valid
354.0ms	560×	body	640	valid
199.0ms	345×	body	320	valid
55.0ms	188×	body	160	valid