Details

sample100.0ms

Algorithm

intervals

Results

23.0ms	201×	body	80	valid
14.0ms	25×	body	1280	valid
11.0ms	16×	body	640	valid
10.0ms	256×	pre	80	true
3.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify5.1s

Counts

1 → 1

Iterations

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

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.0b

localize122.0ms

Local error

Found 3 expressions with local error:

0.0b

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

13.3b

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

16.6b

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

rewrite120.0ms

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` `insert-posit16` `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 → 70

Calls

3 calls:

52.0ms

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

2.0ms

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

59.0ms

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

series940.0ms

Counts

3 → 9

Calls

3 calls:

156.0ms

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

426.0ms

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

357.0ms

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

simplify3.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5003
2	1561
1	378
0	146

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.1b

localize109.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

13.3b

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

rewrite167.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`flip3-+` `flip3--` `flip-+` `fma-udef` `flip--`

Counts

3 → 172

Calls

3 calls:

47.0ms

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

101.0ms

(/ (/ (- 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)

series961.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms

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

382.0ms

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

452.0ms

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

simplify4.3s

Counts

181 → 181

Iterations

Iter	Nodes
done	5002
2	1760
1	599
0	253

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize155.0ms

Local error

Found 4 expressions with local error:

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

rewrite464.0ms

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/` `insert-posit16` `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 → 292

Calls

4 calls:

65.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
56.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
215.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
83.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
338.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
508.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
439.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

simplify7.7s

Counts

304 → 304

Iterations

Iter	Nodes
done	5001
2	4334
1	1313
0	367

prune3.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.9b

localize181.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
0.7b	(* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
1.1b	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
3.2b	(+ (* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

rewrite904.0ms

Algorithm

rewrite-expression-head

Rules

429×	`times-frac`
377×	`*-un-lft-identity`
279×	`add-sqr-sqrt`
183×	`add-cube-cbrt`
164×	`associate-r`
58×	`distribute-lft-out`
39×	`distribute-lft-out--` `difference-of-squares`
27×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/l*`
16×	`div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`pow1`
6×	`associate-l` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
2×	`div-sub` `pow-prod-down` `associate-r/` `-commutative`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `associate-/l/`

Counts

4 → 349

Calls

4 calls:

77.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
191.0ms	(* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
148.0ms	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
421.0ms	(+ (* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

series1.7s

Counts

4 → 12

Calls

4 calls:

319.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
350.0ms	(* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
422.0ms	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
610.0ms	(+ (* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

simplify7.1s

Counts

361 → 361

Iterations

Iter	Nodes
done	5002
2	3816
1	1177
0	418

prune4.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

regimes1.1s

Accuracy

5.1% (5.9b remaining)

Error of 12.0b against oracle of 6.1b and baseline of 12.3b

bsearch144.0ms

Steps

Iters	Range		Point
6	1.4152141949557758e+58	6.729550462449917e+58	6.642737521362061e+58

simplify21.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	6370×	body	80	valid
378.0ms	8000×	pre	80	true
313.0ms	576×	body	640	valid
308.0ms	530×	body	1280	valid
110.0ms	338×	body	320	valid
43.0ms	186×	body	160	valid