Details

sample156.0ms

Algorithm

intervals

Results

74.0ms	93×	body	1280	valid
21.0ms	44×	body	640	valid
20.0ms	32×	body	2560	valid
7.0ms	24×	body	320	valid
4.0ms	51×	body	80	valid
2.0ms	12×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	10
0	7

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 48.9b

localize9.0ms

Local error

Found 2 expressions with local error:

1.0b	(+ x (hypot 1 x))
2.6b	(log (+ x (hypot 1 x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `log-prod` `add-cube-cbrt` `add-log-exp`
3×	`pow1` `fma-def` `add-exp-log`
2×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `rem-log-exp` `log-pow`

Counts

2 → 36

Calls

2 calls:

4.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))

series214.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(+ x (hypot 1 x))
138.0ms	(log (+ x (hypot 1 x)))

simplify1.8s

Counts

42 → 42

Iterations

Iter	Nodes
4	3762
3	1360
2	535
1	214
0	93

prune273.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma -1/6 (* (* x x) x) x)
0.1b	(* (* x x) x)
19.0b	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma -1/6 (* (* x x) x) x)
23.0ms	(* (* x x) x)
0.0ms	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

series229.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(fma -1/6 (* (* x x) x) x)
37.0ms	(* (* x x) x)
75.0ms	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

simplify2.8s

Counts

62 → 62

Iterations

Iter	Nodes
4	5740
3	1305
2	365
1	134
0	70

prune330.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ -1/16 (pow x 5))
0.3b	(/ -1/8 (* (* x x) x))
16.3b	(log (- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))))
21.8b	(- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
138×	`add-sqr-sqrt`
135×	`times-frac`
118×	`add-cube-cbrt`
100×	`prod-diff`
59×	`unpow-prod-down`
27×	`distribute-lft-out`
25×	`fma-neg`
21×	`sqr-pow`
19×	`add-exp-log`
15×	`add-cbrt-cube`
9×	`log-prod` `add-log-exp`
8×	`associate-/r*` `difference-of-squares`
7×	`div-inv`
6×	`div-exp` `frac-sub` `associate-/l*`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `diff-log` `frac-add` `flip-+` `flip--`
1×	`pow-to-exp` `sum-log` `sub-neg` `rem-log-exp` `pow-exp` `log-pow` `associate--r+`

Counts

4 → 251

Calls

4 calls:

6.0ms	(/ -1/16 (pow x 5))
20.0ms	(/ -1/8 (* (* x x) x))
81.0ms	(log (- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))))
109.0ms	(- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ -1/16 (pow x 5))
56.0ms	(/ -1/8 (* (* x x) x))
138.0ms	(log (- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))))
61.0ms	(- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))

simplify1.1s

Counts

263 → 263

Iterations

Iter	Nodes
2	2605
1	850
0	361

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ -1/4 (* x x))
0.1b	(* (* x x) (* x x))
0.3b	(/ 3/32 (* (* x x) (* x x)))
9.5b	(+ (+ (/ 3/32 (* (* x x) (* x x))) (log 1/2)) (+ (log (/ -1 x)) (/ -1/4 (* x x))))

rewrite567.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
39×	`add-cbrt-cube` `add-exp-log`
36×	`*-un-lft-identity` `pow-prod-up`
23×	`pow-prod-down` `distribute-lft-out`
22×	`pow-sqr`
18×	`pow-plus`
17×	`prod-exp` `cbrt-unprod`
13×	`pow2`
12×	`add-log-exp`
9×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`sum-log`
7×	`cbrt-undiv` `div-exp` `log-pow`
6×	`times-frac` `associate-/l*`
5×	`fma-def` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `frac-add` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`
1×	`+-commutative` `log-div` `associate-+l+` `associate-+r+` `associate-+r-` `swap-sqr` `associate-r` `associate-l` `*-commutative` `associate-+l-` `unswap-sqr`

Counts

4 → 158

Calls

4 calls:

7.0ms	(/ -1/4 (* x x))
29.0ms	(* (* x x) (* x x))
35.0ms	(/ 3/32 (* (* x x) (* x x)))
494.0ms	(+ (+ (/ 3/32 (* (* x x) (* x x))) (log 1/2)) (+ (log (/ -1 x)) (/ -1/4 (* x x))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ -1/4 (* x x))
44.0ms	(* (* x x) (* x x))
49.0ms	(/ 3/32 (* (* x x) (* x x)))
105.0ms	(+ (+ (/ 3/32 (* (* x x) (* x x))) (log 1/2)) (+ (log (/ -1 x)) (/ -1/4 (* x x))))

simplify820.0ms

Counts

170 → 170

Iterations

Iter	Nodes
2	2654
1	611
0	210

prune797.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.1b

bsearch124.0ms

Steps

Iters	Range		Point
10	0.002603609100038161	6235082944194588.0	0.008530104512022981
8	-145.89507053458865	-0.006947246361207331	-1.0432984552881022

simplify7.0ms

Iterations

Iter	Nodes
2	32
1	32
0	30

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	2366×	body	1280	valid
776.0ms	1506×	body	640	valid
607.0ms	860×	body	2560	valid
498.0ms	2063×	body	80	valid
305.0ms	799×	body	320	valid
68.0ms	406×	body	160	valid