Details

sample153.0ms

Algorithm

intervals

Results

82.0ms	86×	body	1280	valid
27.0ms	49×	body	640	valid
15.0ms	21×	body	2560	valid
9.0ms	26×	body	320	valid
6.0ms	64×	body	80	valid
2.0ms	10×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.6b

localize9.0ms

Local error

Found 3 expressions with local error:

2.5b	(log (+ x (hypot 1 x)))
0.6b	(+ x (hypot 1 x))
0.0b	(hypot 1 x)

rewrite8.0ms

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:

Slowest

4.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))
0.0ms	(hypot 1 x)

series344.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

196.0ms	(log (+ x (hypot 1 x)))
92.0ms	(+ x (hypot 1 x))
56.0ms	(hypot 1 x)

simplify1.3s

Counts: 56 → 56

prune471.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 3 expressions with local error:

13.8b	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.3b	(* x -1/6)
0.0b	(fma 3/40 (pow x 5) x)

rewrite13.0ms

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:

Slowest

11.0ms	(* x -1/6)
1.0ms	(fma 3/40 (pow x 5) x)
1.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))

series308.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

211.0ms	(fma 3/40 (pow x 5) x)
68.0ms	(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
29.0ms	(* x -1/6)

simplify1.8s

Counts: 52 → 52

prune580.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

2.5b	(log (sqrt (+ x (hypot 1 x))))
2.5b	(log (sqrt (+ x (hypot 1 x))))
0.6b	(+ x (hypot 1 x))
0.6b	(+ x (hypot 1 x))

rewrite17.0ms

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:

Slowest

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

series556.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

194.0ms	(log (sqrt (+ x (hypot 1 x))))
159.0ms	(log (sqrt (+ x (hypot 1 x))))
114.0ms	(+ x (hypot 1 x))
89.0ms	(+ x (hypot 1 x))

simplify1.2s

Counts: 94 → 94

prune881.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

20.3b	(+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)))
12.9b	(log (+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x))))
0.5b	(/ 1/8 (* x x))
0.1b	(/ (/ 1/8 (* x x)) x)

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 474

Calls

4 calls:

Slowest

115.0ms	(+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)))
66.0ms	(log (+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x))))
12.0ms	(/ (/ 1/8 (* x x)) x)
6.0ms	(/ 1/8 (* x x))

series715.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

459.0ms	(/ (/ 1/8 (* x x)) x)
137.0ms	(log (+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x))))
87.0ms	(+ (/ -1/16 (pow x 5)) (- (/ (/ 1/8 (* x x)) x) (/ 1/2 x)))
33.0ms	(/ 1/8 (* x x))

simplify1.6s

Counts: 486 → 486

prune5.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes59.0ms

Accuracy

99.8% (0.1b remaining)

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

bsearch178.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.6s	2418×	body	1280	valid
798.0ms	1498×	body	640	valid
651.0ms	811×	body	2560	valid
238.0ms	745×	body	320	valid
172.0ms	2135×	body	80	valid
77.0ms	393×	body	160	valid