Details

sample94.0ms

Algorithm

intervals

Results

42.0ms	70×	body	1280	valid
19.0ms	50×	body	640	valid
9.0ms	20×	body	2560	valid
7.0ms	26×	body	320	valid
4.0ms	81×	body	80	valid
1.0ms	9×	body	160	valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
1	10
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b	(+ x (sqrt (fma x x 1.0)))
2.4b	(log (+ x (sqrt (fma x x 1.0))))
15.0b	(sqrt (fma x x 1.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `sqrt-prod` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 49

Calls

3 calls:

11.0ms	(+ x (sqrt (fma x x 1.0)))
7.0ms	(log (+ x (sqrt (fma x x 1.0))))
1.0ms	(sqrt (fma x x 1.0))

series407.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(+ x (sqrt (fma x x 1.0)))
242.0ms	(log (+ x (sqrt (fma x x 1.0))))
80.0ms	(sqrt (fma x x 1.0))

simplify692.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
2	1087
1	289
0	126

prune309.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (/ (/ (pow x 3) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (/ (/ (pow x 3) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series138.0ms

Counts

1 → 3

Calls

1 calls:

138.0ms

(fma (/ (/ (pow x 3) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify3.5s

Counts

13 → 13

Iterations

Iter	Nodes
done	5000
4	4906
3	569
2	144
1	49
0	27

prune93.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x 2 (/ 0.5 x))
0.0b	(- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.1b	(/ 0.125 (pow x 3))
12.6b	(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

163×	`add-sqr-sqrt`
152×	`times-frac`
141×	`*-un-lft-identity`
137×	`add-cube-cbrt`
120×	`prod-diff`
41×	`unpow-prod-down` `cube-prod`
15×	`sqr-pow`
13×	`cube-mult` `unpow3`
12×	`associate-/r*`
10×	`add-exp-log` `difference-of-squares`
9×	`log-prod`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `div-exp` `associate-/l*`
2×	`log-div` `flip3--` `fma-udef` `flip--` `distribute-lft-out--`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `associate--l+` `log-pow`

Counts

4 → 243

Calls

4 calls:

0.0ms	(fma x 2 (/ 0.5 x))
25.0ms	(- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3)))
6.0ms	(/ 0.125 (pow x 3))
49.0ms	(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma x 2 (/ 0.5 x))
61.0ms	(- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3)))
62.0ms	(/ 0.125 (pow x 3))
194.0ms	(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (pow x 3))))

simplify650.0ms

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
1	1050
0	418

prune861.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

2.4b	(log (+ x (* (fabs (cbrt (fma x x 1.0))) (sqrt (cbrt (fma x x 1.0))))))
4.0b	(+ x (* (fabs (cbrt (fma x x 1.0))) (sqrt (cbrt (fma x x 1.0)))))
15.4b	(cbrt (fma x x 1.0))
15.4b	(cbrt (fma x x 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod` `fma-def`
2×	`log-div` `flip3-+` `pow1/3` `flip-+`
1×	`+-commutative` `sum-log` `rem-log-exp` `log-pow`

Counts

4 → 58

Calls

4 calls:

4.0ms	(log (+ x (* (fabs (cbrt (fma x x 1.0))) (sqrt (cbrt (fma x x 1.0))))))
5.0ms	(+ x (* (fabs (cbrt (fma x x 1.0))) (sqrt (cbrt (fma x x 1.0)))))
1.0ms	(cbrt (fma x x 1.0))
1.0ms	(cbrt (fma x x 1.0))

series726.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(log (+ x (* (fabs (cbrt (fma x x 1.0))) (sqrt (cbrt (fma x x 1.0))))))
113.0ms	(+ x (* (fabs (cbrt (fma x x 1.0))) (sqrt (cbrt (fma x x 1.0)))))
273.0ms	(cbrt (fma x x 1.0))
249.0ms	(cbrt (fma x x 1.0))

simplify795.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1543
1	399
0	158

prune508.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.5b

bsearch89.0ms

Steps

Iters	Range		Point
9	7.294142785006675e-07	13.800596953327334	0.8895740307587359
7	-22.8286883066892	-0.10952899301968014	-1.0200493385609686

simplify3.0ms

Iterations

Iter	Nodes
done	34
1	34
0	33

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.1s	2422×	body	1280	valid
597.0ms	1486×	body	640	valid
378.0ms	801×	body	2560	valid
170.0ms	810×	body	320	valid
107.0ms	2073×	body	80	valid
102.0ms	408×	body	160	valid