Details

sample130.0ms

Algorithm

intervals

Results

66.0ms	78×	body	1280	valid
22.0ms	48×	body	640	valid
9.0ms	31×	body	320	valid
8.0ms	15×	body	2560	valid
5.0ms	70×	body	80	valid
2.0ms	14×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
1	10
0	7

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize32.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ x (sqrt (fma x x 1.0)))
4.0b	(log (+ x (sqrt (fma x x 1.0))))
12.8b	(sqrt (fma x x 1.0))

rewrite30.0ms

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` `insert-posit16` `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 → 52

Calls

3 calls:

10.0ms	(+ x (sqrt (fma x x 1.0)))
13.0ms	(log (+ x (sqrt (fma x x 1.0))))
5.0ms	(sqrt (fma x x 1.0))

series501.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(+ x (sqrt (fma x x 1.0)))
286.0ms	(log (+ x (sqrt (fma x x 1.0))))
79.0ms	(sqrt (fma x x 1.0))

simplify3.9s

Counts

61 → 61

Iterations

Iter	Nodes
done	5025
3	2803
2	839
1	291
0	129

prune703.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma -1/6 (* (/ x 1.0) (/ (* x x) (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
0.1b	(* (/ x 1.0) (/ (* x x) (sqrt 1.0)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`add-cbrt-cube` `add-exp-log`
22×	`times-frac`
13×	`associate-l`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-r`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`unswap-sqr`
5×	`sqrt-prod`
4×	`pow1`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

2 → 67

Calls

2 calls:

2.0ms	(fma -1/6 (* (/ x 1.0) (/ (* x x) (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
74.0ms	(* (/ x 1.0) (/ (* x x) (sqrt 1.0)))

series316.0ms

Counts

2 → 6

Calls

2 calls:

183.0ms	(fma -1/6 (* (/ x 1.0) (/ (* x x) (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
133.0ms	(* (/ x 1.0) (/ (* x x) (sqrt 1.0)))

simplify3.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
2	1720
1	397
0	132

prune605.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sqrt 1.0) x)
0.7b	(+ x (hypot (sqrt 1.0) x))
4.0b	(log (+ x (hypot (sqrt 1.0) x)))

rewrite36.0ms

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` `insert-posit16` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `sum-log` `rem-log-exp` `log-pow`

Counts

3 → 47

Calls

3 calls:

2.0ms	(hypot (sqrt 1.0) x)
16.0ms	(+ x (hypot (sqrt 1.0) x))
15.0ms	(log (+ x (hypot (sqrt 1.0) x)))

series827.0ms

Counts

3 → 9

Calls

3 calls:

146.0ms	(hypot (sqrt 1.0) x)
225.0ms	(+ x (hypot (sqrt 1.0) x))
456.0ms	(log (+ x (hypot (sqrt 1.0) x)))

simplify3.9s

Counts

56 → 56

Iterations

Iter	Nodes
done	5007
3	2755
2	763
1	277
0	121

prune577.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.0625 (pow x 5))
0.2b	(/ 0.125 (* x (* x x)))
14.6b	(log (- (- (/ 0.125 (* x (* x x))) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
21.0b	(- (- (/ 0.125 (* x (* x x))) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

358×	`add-sqr-sqrt`
284×	`times-frac`
270×	`*-un-lft-identity`
241×	`prod-diff`
208×	`add-cube-cbrt`
93×	`associate--l+`
68×	`unpow-prod-down`
60×	`difference-of-squares`
32×	`distribute-lft-out--`
28×	`div-inv`
24×	`sqr-pow`
19×	`add-exp-log`
15×	`add-cbrt-cube`
9×	`log-prod` `add-log-exp`
8×	`associate-/r*` `frac-sub`
6×	`fma-neg` `div-exp` `associate-/l*`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `cbrt-undiv` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log` `prod-exp` `cbrt-unprod`
2×	`clear-num` `sub-neg` `frac-2neg`
1×	`associate--l-` `pow-to-exp` `rem-log-exp` `pow-exp` `log-pow`

Counts

4 → 375

Calls

4 calls:

20.0ms	(/ 0.0625 (pow x 5))
42.0ms	(/ 0.125 (* x (* x x)))
467.0ms	(log (- (- (/ 0.125 (* x (* x x))) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
775.0ms	(- (- (/ 0.125 (* x (* x x))) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series531.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 0.0625 (pow x 5))
67.0ms	(/ 0.125 (* x (* x x)))
287.0ms	(log (- (- (/ 0.125 (* x (* x x))) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
106.0ms	(- (- (/ 0.125 (* x (* x x))) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify6.6s

Counts

387 → 387

Iterations

Iter	Nodes
done	5000
2	4692
1	1446
0	591

prune3.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes114.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.2b

bsearch121.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	0.000899647441404317
10	-26711381.42537418	-6.803810524357175e-07	-1.0026376323582022

simplify11.0ms

Iterations

Iter	Nodes
done	37
1	37
0	33

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	2363×	body	1280	valid
877.0ms	1540×	body	640	valid
329.0ms	774×	body	2560	valid
148.0ms	785×	body	320	valid
99.0ms	2145×	body	80	valid
43.0ms	393×	body	160	valid