Details

sample77.0ms

Algorithm

intervals

Results

36.0ms	76×	body	1280	valid
16.0ms	56×	body	640	valid
6.0ms	19×	body	2560	valid
4.0ms	26×	body	320	valid
2.0ms	60×	body	80	valid
2.0ms	19×	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: 53.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.8b	(+ x (sqrt (+ (* x x) 1.0)))
3.9b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.2b	(sqrt (+ (* x x) 1.0))

rewrite72.0ms

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:

28.0ms	(+ x (sqrt (+ (* x x) 1.0)))
34.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms	(sqrt (+ (* x x) 1.0))

series857.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(+ x (sqrt (+ (* x x) 1.0)))
708.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
69.0ms	(sqrt (+ (* x x) 1.0))

simplify897.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
2	1498
1	343
0	140

prune442.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize18.0ms

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:

0.0ms

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

series153.0ms

Counts

1 → 3

Calls

1 calls:

152.0ms

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

simplify595.0ms

Counts

13 → 13

Iterations

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

prune97.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.8b	(+ x (hypot x (sqrt 1.0)))
3.9b	(log (+ x (hypot x (sqrt 1.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

1.0ms	(hypot x (sqrt 1.0))
6.0ms	(+ x (hypot x (sqrt 1.0)))
4.0ms	(log (+ x (hypot x (sqrt 1.0))))

series729.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(hypot x (sqrt 1.0))
165.0ms	(+ x (hypot x (sqrt 1.0)))
439.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify595.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
2	1059
1	273
0	118

prune228.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.0625 (pow x 5))
0.2b	(/ 0.125 (pow x 3))
15.6b	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
20.3b	(- (- (/ 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:

6.0ms	(/ 0.0625 (pow x 5))
6.0ms	(/ 0.125 (pow x 3))
366.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
728.0ms	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ 0.0625 (pow x 5))
47.0ms	(/ 0.125 (pow x 3))
247.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
85.0ms	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify1.0s

Counts

1090 → 1090

Iterations

Iter	Nodes
done	5000
1	1918
0	810

prune6.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes40.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.3b

bsearch100.0ms

Steps

Iters	Range		Point
10	5.09324609688744e-06	47495130.80298876	0.0009623921030137705
10	-1138.2876542095912	-1.6260248627107784e-07	-1.0218942286122286

simplify7.0ms

Iterations

Iter	Nodes
done	35
1	35
0	32

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	2336×	body	1280	valid
718.0ms	816×	body	2560	valid
548.0ms	1547×	body	640	valid
193.0ms	2122×	body	80	valid
153.0ms	778×	body	320	valid
105.0ms	401×	body	160	valid