Details

sample66.0ms

Algorithm

intervals

Results

20.0ms	201×	body	80	valid
13.0ms	15×	body	1280	valid
8.0ms	256×	pre	80	true
6.0ms	17×	body	640	valid
3.0ms	11×	body	320	valid
2.0ms	12×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2315
3	458
2	99
1	32
0	16

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
0.0b	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
12.9b	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
19.6b	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/l*`
4×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `swap-sqr` `associate-r` `associate-l*`
2×	`associate-/l/`
1×	`pow2` `distribute-rgt-in` `cbrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `pow-plus` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

1.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
16.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
1.0ms	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
40.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series806.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
108.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
300.0ms	(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
251.0ms	(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify2.9s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	3884
2	1077
1	377
0	168

prune740.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
0.3b	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.5b	(expm1 (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
2.8b	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
31×	`times-frac`
24×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`expm1-log1p` `flip3--` `div-sub` `fma-udef` `flip--` `expm1-udef`

Counts

4 → 107

Calls

4 calls:

37.0ms	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
56.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
1.0ms	(expm1 (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
1.0ms	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

series857.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
91.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
412.0ms	(expm1 (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
250.0ms	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

simplify1.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1296
1	460
0	199

prune838.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
0.3b	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.5b	(expm1 (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
2.8b	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
31×	`times-frac`
24×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `div-inv`
1×	`expm1-log1p` `flip3--` `div-sub` `fma-udef` `flip--` `expm1-udef`

Counts

4 → 107

Calls

4 calls:

40.0ms	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
38.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.0ms	(expm1 (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
0.0ms	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

series875.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (- beta alpha) (fma i 2 (+ beta alpha)))
119.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
383.0ms	(expm1 (fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
229.0ms	(fma (/ (- beta alpha) (fma i 2 (+ beta alpha))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

simplify1.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1296
1	460
0	199

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.5b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (fma i 2 (+ beta alpha)))
0.3b	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.5b	(expm1 (fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
4.3b	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
25×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `distribute-lft-out`
8×	`add-cbrt-cube`
7×	`associate-/r` `associate-/l`
5×	`pow1` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`div-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `associate-/r/` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `expm1-log1p` `1-exp` `fma-udef` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 100

Calls

4 calls:

5.0ms	(/ 1 (fma i 2 (+ beta alpha)))
31.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.0ms	(expm1 (fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
0.0ms	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

series882.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (fma i 2 (+ beta alpha)))
125.0ms	(/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
440.0ms	(expm1 (fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0))
215.0ms	(fma (* (- beta alpha) (/ 1 (fma i 2 (+ beta alpha)))) (/ (+ beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))) 1.0)

simplify2.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4037
2	1049
1	389
0	181

prune620.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.5b

regimes486.0ms

Accuracy

0% (0.4b remaining)

Error of 12.1b against oracle of 11.7b and baseline of 12.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.6s	6400×	body	80	valid
397.0ms	556×	body	640	valid
393.0ms	473×	body	1280	valid
375.0ms	8000×	pre	80	true
157.0ms	354×	body	320	valid
61.0ms	217×	body	160	valid