Details

sample133.0ms

Algorithm

intervals

Results

48.0ms	58×	body	1280	valid
25.0ms	34×	body	2560	valid
25.0ms	46×	body	640	valid
13.0ms	25×	body	320	valid
7.0ms	77×	body	80	valid
3.0ms	16×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	13
2	13
1	12
0	7

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
1.3b	(+ x (hypot 1 x))
3.2b	(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)
4.0ms	(+ x (hypot 1 x))
5.0ms	(log (+ x (hypot 1 x)))

series301.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(hypot 1 x)
78.0ms	(+ x (hypot 1 x))
175.0ms	(log (+ x (hypot 1 x)))

simplify2.4s

Counts

56 → 56

Iterations

Iter	Nodes
4	4224
3	1536
2	601
1	244
0	108

prune532.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
0.2b	(fma 3/40 (pow x 5) x)
22.3b	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

rewrite15.0ms

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:

14.0ms	(* (* x x) x)
0.0ms	(fma 3/40 (pow x 5) x)
0.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

series335.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (* x x) x)
191.0ms	(fma 3/40 (pow x 5) x)
91.0ms	(fma -1/6 (* (* x x) x) (fma 3/40 (pow x 5) x))

simplify2.8s

Counts

62 → 62

Iterations

Iter	Nodes
4	5482
3	1165
2	320
1	129
0	69

prune526.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ x (hypot 1 x))
1.3b	(+ x (hypot 1 x))
3.1b	(log (sqrt (+ x (hypot 1 x))))
3.1b	(log (sqrt (+ x (hypot 1 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

4.0ms	(+ x (hypot 1 x))
4.0ms	(+ x (hypot 1 x))
8.0ms	(log (sqrt (+ x (hypot 1 x))))
4.0ms	(log (sqrt (+ x (hypot 1 x))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ x (hypot 1 x))
70.0ms	(+ x (hypot 1 x))
177.0ms	(log (sqrt (+ x (hypot 1 x))))
163.0ms	(log (sqrt (+ x (hypot 1 x))))

simplify1.2s

Counts

94 → 94

Iterations

Iter	Nodes
4	2924
3	1125
2	492
1	217
0	101

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ -1/16 (pow x 5))
0.3b	(/ -1/8 (* (* x x) x))
9.5b	(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
14.9b	(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

rewrite417.0ms

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:

10.0ms	(/ -1/16 (pow x 5))
27.0ms	(/ -1/8 (* (* x x) x))
149.0ms	(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
219.0ms	(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ -1/16 (pow x 5))
79.0ms	(/ -1/8 (* (* x x) x))
179.0ms	(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
91.0ms	(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

simplify938.0ms

Counts

263 → 263

Iterations

Iter	Nodes
2	2569
1	838
0	361

prune2.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.3b

bsearch98.0ms

Steps

Iters	Range		Point
8	0.00023203888932163942	0.10106394179147121	0.007378209414887432
8	-174.255226838109	-0.11981472621416538	-1.0788943454777058

simplify7.0ms

Iterations

Iter	Nodes
2	35
1	35
0	30

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.2s	2403×	body	1280	valid
884.0ms	1500×	body	640	valid
709.0ms	774×	body	320	valid
583.0ms	821×	body	2560	valid
201.0ms	2090×	body	80	valid
84.0ms	412×	body	160	valid