Details

sample16.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify9.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize7.0ms

Local error

Found 1 expressions with local error:

14.3b

(/ x (fma x x 1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
1×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

Slowest

4.0ms

(/ x (fma x x 1))

series69.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

69.0ms

(/ x (fma x x 1))

simplify2.0s

Counts: 33 → 33

prune232.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

14.2b	(sqrt (fma x x 1))
14.2b	(sqrt (fma x x 1))
0.0b	(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
0.0b	(/ x (sqrt (fma x x 1)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`*-un-lft-identity` `add-cube-cbrt`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 252

Calls

4 calls:

Slowest

9.0ms	(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
4.0ms	(/ x (sqrt (fma x x 1)))
1.0ms	(sqrt (fma x x 1))
1.0ms	(sqrt (fma x x 1))

series327.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

107.0ms	(/ x (sqrt (fma x x 1)))
79.0ms	(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
78.0ms	(sqrt (fma x x 1))
64.0ms	(sqrt (fma x x 1))

simplify877.0ms

Counts: 264 → 264

prune2.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (fma x x 1))
14.7b	(cbrt (fma x x 1))
14.2b	(sqrt (fma x x 1))
6.6b	(* (/ x (fabs (cbrt (fma x x 1)))) (/ (/ 1 (sqrt (fma x x 1))) (sqrt (cbrt (fma x x 1)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

439×	`times-frac`
321×	`add-sqr-sqrt`
248×	`sqrt-prod`
210×	`*-un-lft-identity`
202×	`associate-r`
198×	`add-cube-cbrt`
82×	`cbrt-prod`
39×	`add-exp-log`
32×	`unswap-sqr`
25×	`add-cbrt-cube`
17×	`div-exp`
13×	`associate-l`
11×	`div-inv`
10×	`prod-exp`
9×	`cbrt-undiv`
7×	`pow1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `pow1/3` `1-exp`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 322

Calls

4 calls:

Slowest

52.0ms	(* (/ x (fabs (cbrt (fma x x 1)))) (/ (/ 1 (sqrt (fma x x 1))) (sqrt (cbrt (fma x x 1)))))
2.0ms	(sqrt (fma x x 1))
2.0ms	(cbrt (fma x x 1))
2.0ms	(cbrt (fma x x 1))

series570.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

217.0ms	(* (/ x (fabs (cbrt (fma x x 1)))) (/ (/ 1 (sqrt (fma x x 1))) (sqrt (cbrt (fma x x 1)))))
161.0ms	(cbrt (fma x x 1))
135.0ms	(cbrt (fma x x 1))
56.0ms	(sqrt (fma x x 1))

simplify1.6s

Counts: 334 → 334

prune4.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

18.8b	(+ (/ 1 (pow x 5)) (- (/ 1 x) (/ 1 (* x (* x x)))))
0.2b	(/ 1 (pow x 5))
0.1b	(/ 1 (* x (* x x)))
0.1b	(* x (* x x))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
127×	`*-un-lft-identity`
113×	`add-sqr-sqrt`
112×	`add-cube-cbrt`
93×	`associate-+r+`
91×	`prod-diff`
39×	`add-exp-log`
36×	`div-inv`
33×	`pow1`
25×	`fma-def`
21×	`unpow-prod-down`
20×	`add-cbrt-cube`
12×	`div-exp` `prod-exp`
10×	`pow-prod-up` `distribute-lft-out`
9×	`pow-flip` `add-log-exp`
8×	`associate-/r*` `distribute-lft-out--`
7×	`sqr-pow`
6×	`rec-exp` `1-exp` `pow-prod-down` `cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
3×	`pow-to-exp` `associate-l` `frac-add` `pow-exp`
2×	`pow2` `clear-num` `sum-log` `frac-2neg` `pow-plus` `cube-unmult` `pow-sqr` `inv-pow`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-r` `*-commutative` `frac-sub` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 271

Calls

4 calls:

Slowest

91.0ms	(+ (/ 1 (pow x 5)) (- (/ 1 x) (/ 1 (* x (* x x)))))
35.0ms	(/ 1 (* x (* x x)))
13.0ms	(* x (* x x))
6.0ms	(/ 1 (pow x 5))

series233.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

81.0ms	(/ 1 (pow x 5))
60.0ms	(+ (/ 1 (pow x 5)) (- (/ 1 x) (/ 1 (* x (* x x)))))
47.0ms	(/ 1 (* x (* x x)))
45.0ms	(* x (* x x))

simplify1.1s

Counts: 283 → 283

prune2.9s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes45.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch99.0ms

end0.0ms

sample753.0ms

Algorithm

intervals

Results

634.0ms

8000×

body

valid