Details

sample115.0ms

Algorithm

intervals

Results

53.0ms	81×	body	1280	valid
25.0ms	46×	body	640	valid
15.0ms	26×	body	2560	valid
5.0ms	20×	body	320	valid
5.0ms	66×	body	80	valid
3.0ms	17×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	10
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize10.0ms

Local error

Found 2 expressions with local error:

1.1b	(+ x (hypot 1 x))
3.2b	(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))
4.0ms	(log (+ x (hypot 1 x)))

series235.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(+ x (hypot 1 x))
171.0ms	(log (+ x (hypot 1 x)))

simplify1.8s

Counts

42 → 42

Iterations

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

prune150.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
0.2b	(fma -1/6 (* (* x x) x) x)
20.8b	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

rewrite19.0ms

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:

18.0ms	(* (* x x) x)
0.0ms	(fma -1/6 (* (* x x) x) x)
0.0ms	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

series208.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (* x x) x)
94.0ms	(fma -1/6 (* (* x x) x) x)
72.0ms	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

simplify2.8s

Counts

62 → 62

Iterations

Iter	Nodes
4	5571
3	1215
2	332
1	132
0	70

prune181.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.4b	(/ -1/8 (* (* x x) x))
11.7b	(log (- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))))
19.4b	(- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

163×	`*-un-lft-identity`
124×	`add-sqr-sqrt`
114×	`times-frac`
103×	`add-cube-cbrt`
100×	`prod-diff`
47×	`unpow-prod-down`
27×	`distribute-lft-out`
25×	`fma-neg`
24×	`pow1`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`sqr-pow`
9×	`log-prod` `add-log-exp`
8×	`difference-of-squares`
6×	`pow-plus` `prod-exp` `pow-prod-up` `frac-sub` `cbrt-unprod` `div-inv`
5×	`log-div`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `flip3-+` `flip3--` `diff-log` `frac-add` `pow-sqr` `flip-+` `flip--`
1×	`clear-num` `associate-/r` `sum-log` `sub-neg` `frac-2neg` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `associate--r+` `unswap-sqr`

Counts

4 → 234

Calls

4 calls:

23.0ms	(* (* x x) x)
23.0ms	(/ -1/8 (* (* x x) x))
114.0ms	(log (- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))))
101.0ms	(- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* x x) x)
58.0ms	(/ -1/8 (* (* x x) x))
109.0ms	(log (- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))))
66.0ms	(- (/ -1/16 (pow x 5)) (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))

simplify1.2s

Counts

246 → 246

Iterations

Iter	Nodes
2	2526
1	844
0	354

prune836.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x)))
0.9b	(- x (hypot 1 x))
3.2b	(log (/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x))))
18.8b	(- (* x x) (* (hypot 1 x) (hypot 1 x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

21.0ms	(/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x)))
5.0ms	(- x (hypot 1 x))
10.0ms	(log (/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x))))
12.0ms	(- (* x x) (* (hypot 1 x) (hypot 1 x)))

series818.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x)))
72.0ms	(- x (hypot 1 x))
339.0ms	(log (/ (- (* x x) (* (hypot 1 x) (hypot 1 x))) (- x (hypot 1 x))))
164.0ms	(- (* x x) (* (hypot 1 x) (hypot 1 x)))

simplify2.3s

Counts

148 → 148

Iterations

Iter	Nodes
3	5614
2	1560
1	589
0	238

prune437.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.6b

bsearch110.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	0.00884177569185373
9	-32298.533864343164	-0.030639508246526274	-1.0612400279589977

simplify7.0ms

Iterations

Iter	Nodes
2	31
1	31
0	28

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	2289×	body	1280	valid
922.0ms	793×	body	2560	valid
724.0ms	1615×	body	640	valid
248.0ms	2105×	body	80	valid
206.0ms	764×	body	320	valid
69.0ms	434×	body	160	valid