Details

sample103.0ms

Algorithm

intervals

Results

66.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	2000
3	1615
2	280
1	60
0	17

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ (+ alpha beta) i) i (* beta alpha))
0.1b	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
39.9b	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
46.7b	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-cbrt-cube` `add-exp-log`
22×	`times-frac`
17×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
15×	`add-sqr-sqrt`
11×	`-un-lft-identity` `add-cube-cbrt` `associate-/l`
9×	`pow1`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `difference-of-squares`
3×	`flip3--` `associate-l` `pow-prod-down` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`associate-r` `*-commutative` `fma-udef`

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma (+ (+ alpha beta) i) i (* beta alpha))
79.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
115.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
102.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma (+ (+ alpha beta) i) i (* beta alpha))
198.0ms	(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
451.0ms	(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
916.0ms	(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))

simplify1.3s

Counts

129 → 129

Iterations

Iter	Nodes
done	2005
2	2005
1	665
0	229

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 37.8b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
0.2b	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
36.8b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
37.5b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
131×	`*-un-lft-identity`
111×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
34×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
20×	`associate-/r/`
16×	`associate-/r*` `distribute-lft-out`
12×	`div-inv` `difference-of-squares`
11×	`cbrt-undiv` `div-exp`
6×	`flip3-+` `sqrt-prod` `flip-+` `distribute-lft-out--`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`associate-*l/` `prod-exp` `cbrt-unprod`

Counts

4 → 234

Calls

4 calls:

47.0ms	(/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
23.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
41.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
18.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

473.0ms	(/ (/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
479.0ms	(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (fma 2 i (+ alpha beta)))
292.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
434.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.3s

Counts

246 → 246

Iterations

Iter	Nodes
done	2001
2	2001
1	967
0	385

prune3.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (fma 2 i (+ alpha beta)) (sqrt (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
36.8b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
37.5b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
37.5b	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
126×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
74×	`sqrt-prod`
35×	`associate-/r*`
20×	`distribute-lft-out`
15×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
10×	`associate-/l*`
8×	`div-inv`
7×	`flip3-+` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`associate-*l/` `distribute-lft-out--` `associate-/l/`
1×	`flip3--` `sqrt-div` `prod-exp` `cbrt-unprod` `flip--`

Counts

4 → 209

Calls

4 calls:

21.0ms	(/ (fma 2 i (+ alpha beta)) (sqrt (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
41.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
9.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
9.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

series1.8s

Counts

4 → 12

Calls

4 calls:

663.0ms	(/ (fma 2 i (+ alpha beta)) (sqrt (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
228.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
403.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
465.0ms	(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

simplify1.3s

Counts

221 → 221

Iterations

Iter	Nodes
done	2000
2	2000
1	712
0	348

prune4.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 37.8b

localize125.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (sqrt (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))
36.8b	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
37.4b	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
37.4b	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-prod`
56×	`*-un-lft-identity`
48×	`add-sqr-sqrt` `times-frac`
38×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out` `associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `associate-*l/` `flip-+` `div-inv` `distribute-lft-out--` `associate-/l/`
1×	`sqrt-undiv` `flip3--` `prod-exp` `cbrt-unprod` `flip--`

Counts

4 → 139

Calls

4 calls:

21.0ms	(/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (sqrt (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))
68.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
2.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
3.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

series821.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (sqrt (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))
289.0ms	(/ (* (+ (+ alpha beta) i) i) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
71.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
91.0ms	(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

simplify1.2s

Counts

151 → 151

Iterations

Iter	Nodes
done	2000
3	2000
2	1563
1	541
0	236

prune2.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 37.8b

regimes253.0ms

Accuracy

0% (2.8b remaining)

Error of 36.8b against oracle of 34.1b and baseline of 36.8b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
420.0ms	8000×	pre	80	true