Details

sample58.0ms

Algorithm

intervals

Results

15.0ms	256×	pre	80	true
11.0ms	198×	body	80	valid
7.0ms	20×	body	1280	valid
4.0ms	20×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.8s

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: 13.5b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.1b

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

13.7b

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

rewrite68.0ms

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)))

25.0ms

(/ (/ (- 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)

series567.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms

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

246.0ms

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

214.0ms

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

simplify1.7s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	2673
1	620
0	250

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
0.1b	(/ (/ (- 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))
3.0b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

rewrite224.0ms

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:

27.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
41.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
89.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
35.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

series963.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
226.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
358.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
283.0ms	(+ (* (/ (/ (- 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

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- beta alpha))
0.7b	(cbrt (- beta alpha))
1.0b	(* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))
4.4b	(+ (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))))) (* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))) 1.0)

rewrite451.0ms

Algorithm

rewrite-expression-head

Rules

374×	`times-frac`
273×	`*-un-lft-identity`
239×	`add-sqr-sqrt`
232×	`cbrt-prod`
202×	`associate-l`
169×	`add-cube-cbrt`
29×	`distribute-lft-out`
23×	`distribute-lft-out--` `difference-of-squares`
13×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`div-inv`
7×	`unswap-sqr`
6×	`pow1` `cbrt-div` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-+l+` `flip3-+` `associate-r` `flip-+` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
2×	`frac-times` `flip3--` `pow1/3` `associate-*r/` `associate-/r/` `flip--`
1×	`+-commutative` `sum-log` `fma-def` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 289

Calls

4 calls:

6.0ms	(cbrt (- beta alpha))
7.0ms	(cbrt (- beta alpha))
174.0ms	(* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))
220.0ms	(+ (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))))) (* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))) 1.0)

series1.3s

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt (- beta alpha))
209.0ms	(cbrt (- beta alpha))
626.0ms	(* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))
252.0ms	(+ (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))))) (* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))) 1.0)

simplify3.6s

Counts

301 → 301

Iterations

Iter	Nodes
done	5000
1	1627
0	434

prune3.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- beta alpha))
0.7b	(cbrt (- beta alpha))
1.0b	(* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))
4.4b	(fma (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))))) (* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha)) 1.0)

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

374×	`times-frac`
273×	`*-un-lft-identity`
239×	`add-sqr-sqrt`
232×	`cbrt-prod`
202×	`associate-l`
169×	`add-cube-cbrt`
29×	`distribute-lft-out`
23×	`distribute-lft-out--` `difference-of-squares`
13×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`div-inv`
7×	`unswap-sqr`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+`
2×	`frac-times` `flip3--` `pow1/3` `associate-*r/` `associate-/r/` `flip--`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 281

Calls

4 calls:

3.0ms	(cbrt (- beta alpha))
4.0ms	(cbrt (- beta alpha))
188.0ms	(* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))
1.0ms	(fma (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))))) (* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha)) 1.0)

series5.1s

Counts

4 → 12

Calls

4 calls:

242.0ms	(cbrt (- beta alpha))
174.0ms	(cbrt (- beta alpha))
685.0ms	(* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha))
4.0s	(fma (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha)))))) (* (/ (/ (cbrt (- beta alpha)) (fma 2.0 i (+ beta alpha))) (cbrt (+ 2.0 (fma 2.0 i (+ beta alpha))))) (+ beta alpha)) 1.0)

simplify3.5s

Counts

293 → 293

Iterations

Iter	Nodes
done	5000
1	1542
0	417

prune3.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.1b

regimes567.0ms

Accuracy

0% (0.4b remaining)

Error of 12.6b against oracle of 12.3b and baseline of 12.6b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample1.9s

Algorithm

intervals

Results

635.0ms	6317×	body	80	valid
256.0ms	8000×	pre	80	true
255.0ms	528×	body	1280	valid
178.0ms	359×	body	320	valid
174.0ms	589×	body	640	valid
82.0ms	207×	body	160	valid