Details

sample43.0ms

Algorithm

intervals

Results

11.0ms	208×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	15×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize20.0ms

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))))

11.4b

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

rewrite75.0ms

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:

16.0ms

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

50.0ms

(/ (/ (- 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)

series616.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms

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

236.0ms

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

283.0ms

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

simplify2.6s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
2	2673
1	620
0	250

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.1b

localize35.0ms

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))))
1.7b	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
3.5b	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

rewrite179.0ms

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)))
33.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
88.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
28.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- beta alpha) (fma 2.0 i (+ beta alpha)))
315.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
395.0ms	(* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha))
284.0ms	(+ (* (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))) (+ beta alpha)) 1.0)

simplify1.8s

Counts

300 → 300

Iterations

Iter	Nodes
done	5001
1	1337
0	363

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.1b

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))))
0.2b	(* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
1.6b	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
3.5b	(+ (* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

rewrite255.0ms

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-+` `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 → 345

Calls

4 calls:

33.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
70.0ms	(* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
86.0ms	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
24.0ms	(+ (* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))
266.0ms	(* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
251.0ms	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
431.0ms	(+ (* alpha (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha))))) 1.0)

simplify1.5s

Counts

357 → 357

Iterations

Iter	Nodes
done	5001
1	1239
0	414

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma 2.0 i (+ beta alpha)))
0.6b	(cbrt (fma 2.0 i (+ beta alpha)))
1.6b	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
9.3b	(+ (* alpha (* (/ (/ 1 (* (cbrt (fma 2.0 i (+ beta alpha))) (cbrt (fma 2.0 i (+ beta alpha))))) 1) (/ (/ (- beta alpha) (cbrt (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))) 1.0)

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

139×	`times-frac`
125×	`*-un-lft-identity`
96×	`add-sqr-sqrt`
82×	`associate-r`
63×	`add-cube-cbrt`
19×	`distribute-lft-out`
13×	`add-cbrt-cube` `add-exp-log`
12×	`distribute-lft-out--` `difference-of-squares`
6×	`cbrt-prod` `pow1` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `pow1/3` `associate-/r/` `flip-+`
1×	`+-commutative` `sum-log` `fma-def` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 146

Calls

4 calls:

1.0ms	(cbrt (fma 2.0 i (+ beta alpha)))
1.0ms	(cbrt (fma 2.0 i (+ beta alpha)))
72.0ms	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
226.0ms	(+ (* alpha (* (/ (/ 1 (* (cbrt (fma 2.0 i (+ beta alpha))) (cbrt (fma 2.0 i (+ beta alpha))))) 1) (/ (/ (- beta alpha) (cbrt (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))) 1.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

370.0ms	(cbrt (fma 2.0 i (+ beta alpha)))
345.0ms	(cbrt (fma 2.0 i (+ beta alpha)))
327.0ms	(* beta (/ (/ (- beta alpha) (fma 2.0 i (+ beta alpha))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))
417.0ms	(+ (* alpha (* (/ (/ 1 (* (cbrt (fma 2.0 i (+ beta alpha))) (cbrt (fma 2.0 i (+ beta alpha))))) 1) (/ (/ (- beta alpha) (cbrt (fma 2.0 i (+ beta alpha)))) (+ 2.0 (fma 2.0 i (+ beta alpha)))))) 1.0)

simplify3.0s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	4187
1	845
0	288

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

regimes353.0ms

Accuracy

14.5% (5.8b remaining)

Error of 11.7b against oracle of 5.9b and baseline of 12.7b

bsearch147.0ms

Steps

Iters	Range		Point
9	2.5571677378596085e+141	6.851744006698495e+147	6.401252237322337e+145

simplify18.0ms

Iterations

Iter	Nodes
done	47
1	47
0	38

end0.0ms

sample2.5s

Algorithm

intervals

Results

726.0ms	6316×	body	80	valid
640.0ms	8000×	pre	80	true
324.0ms	519×	body	1280	valid
232.0ms	582×	body	640	valid
138.0ms	385×	body	320	valid
33.0ms	198×	body	160	valid