Details

sample87.0ms

Algorithm

intervals

Results

22.0ms	222×	body	80	valid
8.0ms	256×	pre	80	true
5.0ms	13×	body	640	valid
3.0ms	11×	body	320	valid
3.0ms	6×	body	1280	valid
1.0ms	4×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2747
3	478
2	106
1	31
0	15

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.0b

localize33.0ms

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))))

8.0b

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

rewrite93.0ms

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:

28.0ms

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

43.0ms

(/ (/ (- 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)

series673.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms

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

305.0ms

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

265.0ms

(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	5000
2	2673
1	620
0	250

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- beta alpha))
0.6b	(cbrt (- beta alpha))
0.6b	(cbrt (- beta alpha))
8.0b	(fma (/ (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (fma 2.0 i (+ beta alpha))) (cbrt (fma 2.0 i (+ beta alpha))))) (/ (cbrt (- beta alpha)) (cbrt (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (- beta alpha))
9.0ms	(cbrt (- beta alpha))
3.0ms	(cbrt (- beta alpha))
0.0ms	(fma (/ (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (fma 2.0 i (+ beta alpha))) (cbrt (fma 2.0 i (+ beta alpha))))) (/ (cbrt (- beta alpha)) (cbrt (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

series890.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(cbrt (- beta alpha))
193.0ms	(cbrt (- beta alpha))
208.0ms	(cbrt (- beta alpha))
243.0ms	(fma (/ (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (fma 2.0 i (+ beta alpha))) (cbrt (fma 2.0 i (+ beta alpha))))) (/ (cbrt (- beta alpha)) (cbrt (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

simplify2.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	3929
2	760
1	235
0	106

prune755.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize34.0ms

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))))
2.1b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)
2.4b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))

rewrite205.0ms

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:

14.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
38.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
39.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)
90.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))

series1.1s

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
257.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
301.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)
391.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))

simplify1.5s

Counts

300 → 300

Iterations

Iter	Nodes
done	5000
1	1335
0	363

prune2.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

localize37.0ms

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))))
1.4b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
1.4b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
2.1b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha) 1.0)

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

429×	`times-frac`
377×	`*-un-lft-identity`
279×	`add-sqr-sqrt`
183×	`add-cube-cbrt`
164×	`associate-l`
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-r` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`div-sub` `pow-prod-down` `associate-l/` `-commutative`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `associate-/l/`

Counts

4 → 345

Calls

4 calls:

36.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
58.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
80.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
45.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
301.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
294.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
258.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha) 1.0)

simplify1.2s

Counts

357 → 357

Iterations

Iter	Nodes
done	5000
1	1119
0	403

prune2.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.8b

regimes457.0ms

Accuracy

0% (0.3b remaining)

Error of 12.0b against oracle of 11.8b and baseline of 12.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

610.0ms	6394×	body	80	valid
421.0ms	493×	body	1280	valid
206.0ms	563×	body	640	valid
198.0ms	8000×	pre	80	true
93.0ms	366×	body	320	valid
28.0ms	184×	body	160	valid