Details

sample93.0ms

Algorithm

intervals

Results

25.0ms	24×	body	640	valid
20.0ms	207×	body	80	valid
8.0ms	256×	pre	80	true
6.0ms	13×	body	1280	valid
2.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 i (+ beta alpha))
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))))
11.6b	(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
157×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
79×	`add-cube-cbrt`
24×	`associate-/l*`
20×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*` `div-inv`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-/r/` `fma-udef`
1×	`flip3-+` `flip3--` `flip-+` `flip--`

Counts

4 → 179

Calls

4 calls:

0.0ms	(fma 2.0 i (+ beta alpha))
17.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
23.0ms	(/ (/ (- 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)

series608.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma 2.0 i (+ beta alpha))
125.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
234.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
211.0ms	(fma (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha) 1.0)

simplify1.9s

Counts

191 → 191

Iterations

Iter	Nodes
done	5000
2	3241
1	660
0	255

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.2b

localize48.0ms

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))))
0.9b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
2.6b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

rewrite188.0ms

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:

13.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
26.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
105.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
22.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

series975.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
252.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
377.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
261.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

simplify1.5s

Counts

300 → 300

Iterations

Iter	Nodes
done	5001
1	1337
0	363

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))
0.9b	(* (/ (cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
2.6b	(+ (* (/ (cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)
11.6b	(cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
95×	`add-sqr-sqrt`
93×	`times-frac`
54×	`add-cube-cbrt`
41×	`associate-l`
25×	`swap-sqr`
23×	`associate-r`
21×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`distribute-lft-out--`
13×	`pow1`
12×	`difference-of-squares`
8×	`frac-times`
7×	`cbrt-div` `associate-*l/`
6×	`prod-exp` `associate-*r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
5×	`cbrt-prod` `cbrt-undiv` `div-exp` `div-inv` `distribute-lft-out`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `associate-/r/` `*-commutative`
1×	`pow2` `+-commutative` `sum-log` `fma-def` `pow-plus` `pow1/3` `pow3` `pow-sqr` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 178

Calls

4 calls:

77.0ms	(* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))
60.0ms	(* (/ (cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
17.0ms	(+ (* (/ (cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)
89.0ms	(cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

212.0ms	(* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))
384.0ms	(* (/ (cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
283.0ms	(+ (* (/ (cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha))))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)
131.0ms	(cbrt (* (* (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))) (/ (- beta alpha) (fma 2.0 i (+ beta alpha)))))

simplify1.5s

Counts

190 → 190

Iterations

Iter	Nodes
done	5001
1	1049
0	296

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.2b

localize61.0ms

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))))
0.6b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
0.8b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
2.6b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha) 1.0)

rewrite228.0ms

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:

30.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
69.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
91.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
19.0ms	(+ (* (/ (/ (- 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:

258.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
299.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
310.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
262.0ms	(+ (* (/ (/ (- 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

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.2b

regimes626.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample2.4s

Algorithm

intervals

Results

762.0ms	542×	body	1280	valid
566.0ms	6362×	body	80	valid
288.0ms	8000×	pre	80	true
217.0ms	583×	body	640	valid
82.0ms	329×	body	320	valid
65.0ms	184×	body	160	valid