Details

sample42.0ms

Algorithm

intervals

Results

12.0ms	53×	body	1280	valid
7.0ms	137×	body	80	valid
6.0ms	30×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	10×	body	160	valid

simplify258.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	350
14	350
13	346
12	340
11	329
10	222
9	96
8	75
7	58
6	39
5	27
4	21
3	19
2	16
1	12
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x 1.0))
3.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

947×	`*-un-lft-identity`
716×	`times-frac`
563×	`add-sqr-sqrt`
468×	`prod-diff`
407×	`add-cube-cbrt`
183×	`distribute-lft-out`
92×	`associate-/r/`
85×	`distribute-lft-out--`
76×	`difference-of-squares`
46×	`div-inv`
28×	`flip3-+` `flip-+`
19×	`flip3--` `flip--`
18×	`fma-neg`
4×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/l*`
2×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`

Counts

2 → 549

Calls

2 calls:

10.0ms	(/ x (+ x 1.0))
144.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series235.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ x (+ x 1.0))
185.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.7s

Counts

555 → 555

Iterations

Iter	Nodes
done	5002
2	3046
1	1162
0	496

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
28.7b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-exp-log`
4×	`associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`pow1` `associate-/l*`
2×	`expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `fma-udef` `div-inv` `pow-flip` `inv-pow`

Counts

2 → 49

Calls

2 calls:

10.0ms	(/ 1 (+ x 1.0))
0.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series228.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ 1 (+ x 1.0))
197.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify2.1s

Counts

55 → 55

Iterations

Iter	Nodes
done	5011
3	1967
2	587
1	206
0	95

prune279.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (fma x 1.0 3.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
2×	`fma-udef`
1×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

1 → 22

Calls

1 calls:

6.0ms

(* x (fma x 1.0 3.0))

series112.0ms

Counts

1 → 3

Calls

1 calls:

112.0ms

(* x (fma x 1.0 3.0))

simplify1.5s

Counts

25 → 25

Iterations

Iter	Nodes
done	5036
3	1067
2	245
1	92
0	43

prune81.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.1b	(/ (- (/ 3.0 x)) (* x x))
0.2b	(/ 1.0 (* x x))
6.0b	(- (/ (- (/ 3.0 x)) (* x x)) (+ (/ 1.0 (* x x)) (/ 3.0 x)))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

313×	`times-frac`
227×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
152×	`add-cube-cbrt`
136×	`prod-diff`
91×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
36×	`distribute-lft-out`
34×	`fma-neg`
33×	`associate-/l*`
22×	`div-inv`
14×	`add-cbrt-cube` `add-exp-log`
11×	`add-log-exp`
7×	`neg-mul-1` `fma-def`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`frac-sub`
2×	`neg-sub0` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `diff-log` `div-sub` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3--` `distribute-frac-neg` `flip--` `distribute-neg-frac` `associate--r+` `associate-/l/`

Counts

4 → 319

Calls

4 calls:

23.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
26.0ms	(/ (- (/ 3.0 x)) (* x x))
11.0ms	(/ 1.0 (* x x))
191.0ms	(- (/ (- (/ 3.0 x)) (* x x)) (+ (/ 1.0 (* x x)) (/ 3.0 x)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
60.0ms	(/ (- (/ 3.0 x)) (* x x))
28.0ms	(/ 1.0 (* x x))
45.0ms	(- (/ (- (/ 3.0 x)) (* x x)) (+ (/ 1.0 (* x x)) (/ 3.0 x)))

simplify1.7s

Counts

331 → 331

Iterations

Iter	Nodes
done	5007
2	3039
1	979
0	379

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.9b

bsearch109.0ms

Steps

Iters	Range		Point
9	44.35744796693956	12146952.384825662	10408.715590103024
10	-733100.9210806559	-4.034181863829644e-08	-17797.210498709817

simplify9.0ms

Iterations

Iter	Nodes
done	39
2	39
1	35
0	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

533.0ms	4078×	body	80	valid
428.0ms	1718×	body	1280	valid
287.0ms	1246×	body	640	valid
76.0ms	647×	body	320	valid
63.0ms	311×	body	160	valid