Details

sample79.0ms

Algorithm

intervals

Results

33.0ms	213×	body	80	valid
8.0ms	256×	pre	80	true
6.0ms	12×	body	1280	valid
6.0ms	15×	body	640	valid
2.0ms	7×	body	320	valid
2.0ms	9×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize43.0ms

Local error

Found 3 expressions with local error:

0.0b

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

10.2b

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

17.2b

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

rewrite44.0ms

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` `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 → 67

Calls

3 calls:

16.0ms

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

0.0ms

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

27.0ms

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

series691.0ms

Counts

3 → 9

Calls

3 calls:

155.0ms

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

259.0ms

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

277.0ms

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

simplify1.9s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	1555
1	375
0	143

prune649.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.9b

localize28.0ms

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))))

10.2b

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

rewrite49.0ms

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:

14.0ms

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

27.0ms

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

0.0ms

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

series582.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms

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

245.0ms

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

224.0ms

(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	5006
2	1766
1	596
0	250

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.8b

localize35.0ms

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))))
1.4b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
2.9b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

rewrite169.0ms

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:

20.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
24.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
90.0ms	(* (/ (/ (- 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)

series916.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
250.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
321.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
241.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

simplify2.8s

Counts

300 → 300

Iterations

Iter	Nodes
done	5000
2	4437
1	1311
0	363

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
0.8b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
0.9b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
2.9b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha) 1.0)

rewrite241.0ms

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:

23.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
62.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
91.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
37.0ms	(+ (* (/ (/ (- 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:

291.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
288.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha)
267.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) beta)
279.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) alpha) 1.0)

simplify2.3s

Counts

357 → 357

Iterations

Iter	Nodes
done	5000
2	3267
1	1102
0	403

prune2.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.7b

regimes987.0ms

Accuracy

0% (0.4b remaining)

Error of 12.3b against oracle of 11.9b and baseline of 12.3b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample1.8s

Algorithm

intervals

Results

466.0ms	6375×	body	80	valid
352.0ms	8000×	pre	80	true
310.0ms	502×	body	1280	valid
216.0ms	582×	body	640	valid
120.0ms	354×	body	320	valid
27.0ms	187×	body	160	valid