Details

sample63.0ms

Algorithm

intervals

Results

21.0ms	201×	body	80	valid
11.0ms	25×	body	1280	valid
8.0ms	256×	pre	80	true
6.0ms	16×	body	640	valid
3.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2684
3	471
2	104
1	32
0	16

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b

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

13.3b

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

16.6b

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`times-frac` `associate-l` `associate-l/` `associate-/l`
3×	`expm1-log1p-u` `flip3-+` `associate-r` `flip-+` `fma-udef` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `pow-prod-down` `-commutative` `div-inv` `unswap-sqr`

Counts

3 → 67

Calls

3 calls:

14.0ms

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

1.0ms

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

32.0ms

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

series582.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms

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

216.0ms

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

228.0ms

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

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	2042
1	373
0	141

prune522.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.1b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.1b

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

13.3b

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 163

Calls

3 calls:

31.0ms

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

47.0ms

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

1.0ms

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

series570.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms

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

208.0ms

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

243.0ms

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

simplify1.8s

Counts

172 → 172

Iterations

Iter	Nodes
done	5000
2	2594
1	581
0	240

prune798.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
0.1b	(/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha)))
1.5b	(* (- beta alpha) (/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha))))
3.2b	(+ (* (- beta alpha) (/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha)))) 1.0)

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
258×	`*-un-lft-identity`
135×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
70×	`associate-r`
66×	`distribute-lft-out`
26×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r/`
10×	`flip3-+` `flip-+` `div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `flip3--` `associate-*l/` `flip--`
1×	`+-commutative` `sum-log` `fma-def` `pow-prod-down` `associate-r/` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 268

Calls

4 calls:

26.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
24.0ms	(/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha)))
60.0ms	(* (- beta alpha) (/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha))))
20.0ms	(+ (* (- beta alpha) (/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha)))) 1.0)

series921.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
232.0ms	(/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha)))
338.0ms	(* (- beta alpha) (/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha))))
237.0ms	(+ (* (- beta alpha) (/ (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (fma 2 i (+ beta alpha)))) 1.0)

simplify1.3s

Counts

280 → 280

Iterations

Iter	Nodes
done	5001
1	978
0	345

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
0.1b	(* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
1.3b	(+ (/ (* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (fma 2 i (+ beta alpha))) 1.0)
2.2b	(/ (* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (fma 2 i (+ beta alpha)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
39×	`times-frac`
35×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
19×	`distribute-lft-out`
7×	`associate-/r*` `fma-def` `associate-/l/`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
5×	`associate-l` `associate-/l*`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `flip3--` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `flip--`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr`
1×	`+-commutative` `sum-log` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 146

Calls

4 calls:

20.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
43.0ms	(* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
36.0ms	(+ (/ (* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (fma 2 i (+ beta alpha))) 1.0)
24.0ms	(/ (* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (fma 2 i (+ beta alpha)))

series830.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
108.0ms	(* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))))
267.0ms	(+ (/ (* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (fma 2 i (+ beta alpha))) 1.0)
338.0ms	(/ (* (- beta alpha) (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))) (fma 2 i (+ beta alpha)))

simplify2.2s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	4287
1	653
0	223

prune944.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.9b

regimes340.0ms

Accuracy

0% (0.3b remaining)

Error of 12.2b against oracle of 11.9b and baseline of 12.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.0s	6370×	body	80	valid
532.0ms	338×	body	320	valid
529.0ms	8000×	pre	80	true
450.0ms	530×	body	1280	valid
406.0ms	576×	body	640	valid
84.0ms	186×	body	160	valid