Details

sample97.0ms

Algorithm

intervals

Results

42.0ms	70×	body	1280	valid
22.0ms	50×	body	640	valid
10.0ms	20×	body	2560	valid
6.0ms	26×	body	320	valid
4.0ms	81×	body	80	valid
1.0ms	9×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.3b

localize18.0ms

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))

rewrite25.0ms

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)))
10.0ms	(log (+ x (sqrt (fma x x 1.0))))
3.0ms	(sqrt (fma x x 1.0))

series525.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(+ x (sqrt (fma x x 1.0)))
319.0ms	(log (+ x (sqrt (fma x x 1.0))))
121.0ms	(sqrt (fma x x 1.0))

simplify654.0ms

Counts

58 → 58

Iterations

Useful iterations: done (652.0ms)

Iter	Nodes	Cost
0	126	701
1	289	641
2	1087	577
done	5001	563

prune268.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

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

series192.0ms

Counts

1 → 3

Calls

1 calls:

192.0ms

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

simplify930.0ms

Counts

13 → 13

Iterations

Useful iterations: done (929.0ms)

Iter	Nodes	Cost
0	25	295
1	51	295
2	177	256
3	1262	256
done	5001	255

prune77.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

888×	`times-frac`
634×	`add-sqr-sqrt`
609×	`*-un-lft-identity`
603×	`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×	`add-exp-log` `difference-of-squares`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `div-exp` `associate-/l*`
2×	`distribute-lft-out--`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `frac-sub` `fma-udef` `flip--`

Counts

4 → 651

Calls

4 calls:

0.0ms	(fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3))))
67.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
6.0ms	(/ 0.125 (pow x 3))
1.0ms	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3))))
105.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
48.0ms	(/ 0.125 (pow x 3))
217.0ms	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify975.0ms

Counts

663 → 663

Iterations

Useful iterations: done (924.0ms)

Iter	Nodes	Cost
0	750	31474
1	1736	25737
done	5000	21190

prune2.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

2.4b	(log (+ x (* (sqrt (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0))))))
5.9b	(+ x (* (sqrt (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0)))))
15.0b	(sqrt (fma x x 1.0))
15.0b	(sqrt (fma x x 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

3.0ms	(log (+ x (* (sqrt (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0))))))
4.0ms	(+ x (* (sqrt (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0)))))
1.0ms	(sqrt (fma x x 1.0))
1.0ms	(sqrt (fma x x 1.0))

series824.0ms

Counts

4 → 12

Calls

4 calls:

578.0ms	(log (+ x (* (sqrt (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0))))))
77.0ms	(+ x (* (sqrt (sqrt (fma x x 1.0))) (sqrt (sqrt (fma x x 1.0)))))
98.0ms	(sqrt (fma x x 1.0))
70.0ms	(sqrt (fma x x 1.0))

simplify591.0ms

Counts

74 → 74

Iterations

Useful iterations: done (589.0ms)

Iter	Nodes	Cost
0	129	1216
1	306	770
2	1177	697
done	5001	682

prune321.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes88.0ms

Accuracy

99.3% (0.2b remaining)

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

bsearch95.0ms

Steps

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

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	55
1	34	55
done	34	55

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.6s	2422×	body	1280	valid
935.0ms	1486×	body	640	valid
379.0ms	801×	body	2560	valid
167.0ms	810×	body	320	valid
101.0ms	2073×	body	80	valid
50.0ms	408×	body	160	valid