Details

sample115.0ms

Algorithm

intervals

Results

46.0ms	65×	body	1280	valid
27.0ms	66×	body	640	valid
13.0ms	24×	body	2560	valid
8.0ms	31×	body	320	valid
3.0ms	58×	body	80	valid
2.0ms	12×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
1	10
0	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ x (sqrt (+ (* x x) 1.0)))
2.9b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.9b	(sqrt (+ (* x x) 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

13.0ms	(+ x (sqrt (+ (* x x) 1.0)))
44.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms	(sqrt (+ (* x x) 1.0))

series809.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(+ x (sqrt (+ (* x x) 1.0)))
644.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
60.0ms	(sqrt (+ (* x x) 1.0))

simplify913.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
2	1498
1	343
0	140

prune420.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (/ (pow x 3) (* (sqrt 1.0) 1.0)) -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:

1.0ms

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

series198.0ms

Counts

1 → 3

Calls

1 calls:

198.0ms

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

simplify558.0ms

Counts

13 → 13

Iterations

Iter	Nodes
done	5001
3	667
2	152
1	49
0	26

prune85.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.125 (pow x 3))
0.5b	(/ 0.0625 (pow x 5))
12.4b	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
19.3b	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

1674×	`add-sqr-sqrt`
1602×	`times-frac`
1026×	`*-un-lft-identity`
895×	`prod-diff`
848×	`add-cube-cbrt`
522×	`associate--l+`
330×	`unpow-prod-down`
268×	`difference-of-squares`
181×	`cube-prod`
146×	`sqr-pow`
70×	`div-inv`
62×	`distribute-lft-out--`
43×	`cube-mult` `unpow3`
19×	`associate-/r*`
15×	`fma-neg` `add-exp-log`
10×	`log-prod`
9×	`add-log-exp`
8×	`add-cbrt-cube` `frac-sub`
6×	`div-exp` `associate-/l*`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow-exp`
1×	`associate--l-` `rem-log-exp` `log-pow`

Counts

4 → 1078

Calls

4 calls:

11.0ms	(/ 0.125 (pow x 3))
11.0ms	(/ 0.0625 (pow x 5))
317.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
730.0ms	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 0.125 (pow x 3))
71.0ms	(/ 0.0625 (pow x 5))
280.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
103.0ms	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify871.0ms

Counts

1090 → 1090

Iterations

Iter	Nodes
done	5001
1	1916
0	810

prune5.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.1b	(/ 0.125 (pow x 3))
10.7b	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite137.0ms

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×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `frac-sub` `flip--`

Counts

3 → 641

Calls

3 calls:

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)))))

series424.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
50.0ms	(/ 0.125 (pow x 3))
231.0ms	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify839.0ms

Counts

650 → 650

Iterations

Iter	Nodes
done	5000
1	1724
0	742

prune2.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.1b

bsearch119.0ms

Steps

Iters	Range		Point
9	0.030359728269424062	9645967.64350026	0.8817659968088067
11	-14746478108.679678	-8.433739504313006e-14	-1.021540982075884

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	33

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2320×	body	1280	valid
899.0ms	1556×	body	640	valid
456.0ms	793×	body	2560	valid
178.0ms	2100×	body	80	valid
164.0ms	812×	body	320	valid
50.0ms	419×	body	160	valid