Details

sample117.0ms

Algorithm

intervals

Results

64.0ms	87×	body	1280	valid
19.0ms	46×	body	640	valid
12.0ms	23×	body	2560	valid
7.0ms	28×	body	320	valid
4.0ms	65×	body	80	valid
1.0ms	7×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
0.9b	(+ x (hypot 1 x))
1.7b	(log (+ x (hypot 1 x)))

rewrite10.0ms

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:

0.0ms	(hypot 1 x)
5.0ms	(+ x (hypot 1 x))
4.0ms	(log (+ x (hypot 1 x)))

series753.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(hypot 1 x)
101.0ms	(+ x (hypot 1 x))
587.0ms	(log (+ x (hypot 1 x)))

simplify1.9s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
3	2188
2	682
1	244
0	108

prune242.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 3/40 (pow x 5) x)
0.4b	(* -1/6 x)
13.6b	(fma (* -1/6 x) (* x x) (fma 3/40 (pow x 5) x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

0.0ms	(fma 3/40 (pow x 5) x)
5.0ms	(* -1/6 x)
0.0ms	(fma (* -1/6 x) (* x x) (fma 3/40 (pow x 5) x))

series296.0ms

Counts

3 → 9

Calls

3 calls:

213.0ms	(fma 3/40 (pow x 5) x)
17.0ms	(* -1/6 x)
67.0ms	(fma (* -1/6 x) (* x x) (fma 3/40 (pow x 5) x))

simplify1.6s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	1165
2	322
1	124
0	66

prune207.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/8 (* x x)) x)
0.4b	(/ 1/8 (* x x))
11.4b	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 (* x x)) x))))
22.3b	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 (* x x)) x)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
59×	`*-un-lft-identity`
37×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`fma-def`
19×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`distribute-lft-out` `associate-/l*`
9×	`unpow-prod-down` `add-log-exp`
8×	`frac-add`
7×	`cbrt-undiv` `div-exp` `div-inv`
6×	`log-prod`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `associate-/r*` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `sqr-pow`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `associate-+r+` `rem-log-exp` `log-pow` `associate-/l/`

Counts

4 → 145

Calls

4 calls:

17.0ms	(/ (/ 1/8 (* x x)) x)
12.0ms	(/ 1/8 (* x x))
62.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 (* x x)) x))))
69.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 (* x x)) x)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (/ 1/8 (* x x)) x)
36.0ms	(/ 1/8 (* x x))
166.0ms	(log (+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 (* x x)) x))))
68.0ms	(+ (/ -1/16 (pow x 5)) (+ (/ -1/2 x) (/ (/ 1/8 (* x x)) x)))

simplify1.6s

Counts

157 → 157

Iterations

Iter	Nodes
done	5032
2	2147
1	617
0	241

prune610.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (hypot 1 x) x)
1.7b	(log (/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x))))
9.6b	(/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
14.9b	(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`times-frac`
13×	`log-prod`
9×	`prod-diff` `add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-neg` `associate-/l`
2×	`div-exp` `rem-log-exp` `div-inv`
1×	`cbrt-undiv` `log-div` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `log-pow` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

8.0ms	(- (hypot 1 x) x)
4.0ms	(log (/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x))))
8.0ms	(/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
1.0ms	(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))

series1.4s

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (hypot 1 x) x)
591.0ms	(log (/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x))))
489.0ms	(/ (fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x)) (fma (- (hypot 1 x) x) (hypot 1 x) (* x x)))
192.0ms	(fma (* (hypot 1 x) (hypot 1 x)) (hypot 1 x) (* (* x x) x))

simplify1.9s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
3	3306
2	1177
1	452
0	208

prune608.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch145.0ms

Steps

Iters	Range		Point
11	4.21785760657603e-35	57.56933376468871	0.007778482819478155
9	-34.11472770615283	-3.67231414207575e-08	-1.0840635159626253

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	2352×	body	1280	valid
1.1s	1515×	body	640	valid
564.0ms	786×	body	2560	valid
315.0ms	773×	body	320	valid
156.0ms	2138×	body	80	valid
75.0ms	436×	body	160	valid