Details

sample103.0ms

Algorithm

intervals

Results

52.0ms	79×	body	1280	valid
17.0ms	44×	body	640	valid
7.0ms	30×	body	320	valid
7.0ms	14×	body	2560	valid
4.0ms	81×	body	80	valid
1.0ms	8×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	10	8
done	10	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ (sqrt (fma x x 1.0)) x)
3.3b	(log (+ (sqrt (fma x x 1.0)) x))
13.1b	(sqrt (fma x x 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

16.0ms	(+ (sqrt (fma x x 1.0)) x)
12.0ms	(log (+ (sqrt (fma x x 1.0)) x))
3.0ms	(sqrt (fma x x 1.0))

series485.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(+ (sqrt (fma x x 1.0)) x)
312.0ms	(log (+ (sqrt (fma x x 1.0)) x))
79.0ms	(sqrt (fma x x 1.0))

simplify598.0ms

Counts

61 → 61

Iterations

Useful iterations: done (596.0ms)

Iter	Nodes	Cost
0	125	701
1	288	639
2	1075	573
done	5000	571

prune265.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

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

series185.0ms

Counts

1 → 3

Calls

1 calls:

185.0ms

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

simplify1.3s

Counts

13 → 13

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	25	295
1	51	295
2	177	256
3	1271	256
done	5002	255

prune92.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.2b	(/ 0.125 (pow x 3))
9.2b	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

888×	`times-frac`
633×	`add-sqr-sqrt`
608×	`*-un-lft-identity`
602×	`add-cube-cbrt`
520×	`prod-diff`
131×	`unpow-prod-down` `cube-prod`
55×	`div-inv`
45×	`sqr-pow`
43×	`cube-mult` `unpow3`
13×	`fma-neg`
12×	`associate-/r*`
10×	`difference-of-squares`
9×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `log-prod` `div-exp` `log1p-expm1-u` `associate-/l*`
2×	`distribute-lft-out--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--`

Counts

3 → 641

Calls

3 calls:

83.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
9.0ms	(/ 0.125 (pow x 3))
2.0ms	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series441.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
68.0ms	(/ 0.125 (pow x 3))
261.0ms	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify857.0ms

Counts

650 → 650

Iterations

Useful iterations: done (814.0ms)

Iter	Nodes	Cost
0	742	31264
1	1725	25528
done	5000	20811

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b

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

0.1b

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

27.5b

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

3 → 58

Calls

3 calls:

4.0ms

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

0.0ms

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

4.0ms

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

series763.0ms

Counts

3 → 9

Calls

3 calls:

376.0ms

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

168.0ms

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

218.0ms

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

simplify1.1s

Counts

67 → 67

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	100	2014
1	275	1787
2	1554	1553
done	5000	1549

prune234.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes65.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.4b

bsearch82.0ms

Steps

Iters	Range		Point
8	0.0004268116563047139	15.006088268796836	0.8844350792771517
8	-101.50163225226844	-0.031678663534995	-1.0087686302909924

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	55
1	35	55
done	35	55

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	2228×	body	1280	valid
617.0ms	1591×	body	640	valid
332.0ms	758×	body	2560	valid
163.0ms	796×	body	320	valid
106.0ms	2227×	body	80	valid
49.0ms	400×	body	160	valid