Details

sample314.0ms

Algorithm

intervals

Results

46.0ms	338×	body	80	nan
37.0ms	33×	body	640	valid
24.0ms	163×	body	80	valid
16.0ms	25×	body	1280	valid
15.0ms	24×	body	640	nan
14.0ms	20×	body	1280	nan
9.0ms	16×	body	320	nan
8.0ms	22×	body	320	valid
4.0ms	13×	body	160	valid
2.0ms	8×	body	160	nan

simplify1.6s

Counts: 1 → 1

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.9b

localize77.0ms

Local error

Found 4 expressions with local error:

20.0b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.2b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b	(* (sqrt 2) t)
0.0b	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`associate-l`
29×	`times-frac`
21×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
8×	`difference-of-squares`
7×	`sqrt-prod` `distribute-lft-out`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `difference-of-sqr-1` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `unswap-sqr`
3×	`flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `sqrt-div` `pow-prod-down` `associate--l+` `associate-r/` `associate-/r/` `-commutative` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `associate-*l/` `div-inv`

Counts

4 → 124

Calls

4 calls:

Slowest

70.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
59.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
56.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
15.0ms	(* (sqrt 2) t)

series2.0s

Counts

4 → 12

Calls

4 calls:

Slowest

1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
297.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
121.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
78.0ms	(* (sqrt 2) t)

simplify1.1s

Counts: 136 → 136

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize55.0ms

Local error

Found 4 expressions with local error:

27.1b	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* 2 (* l l)) x))))
9.0b	(/ (* t t) x)
4.8b	(/ (* 2 (* l l)) x)
3.6b	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* 2 (* l l)) x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 77

Calls

4 calls:

Slowest

27.0ms	(/ (* 2 (* l l)) x)
24.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* 2 (* l l)) x))))
0.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* 2 (* l l)) x)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

562.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* 2 (* l l)) x))))
110.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* 2 (* l l)) x)))
35.0ms	(/ (* t t) x)
28.0ms	(/ (* 2 (* l l)) x)

simplify2.2s

Counts: 89 → 89

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize75.0ms

Local error

Found 4 expressions with local error:

27.1b	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x)))))
9.0b	(/ (* t t) x)
3.6b	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x))))
1.8b	(/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
44×	`add-sqr-sqrt`
43×	`*-un-lft-identity` `add-cube-cbrt`
34×	`add-exp-log`
33×	`cbrt-prod`
24×	`add-cbrt-cube`
21×	`associate-/r/`
17×	`cbrt-undiv` `div-exp`
11×	`associate-/l*`
9×	`associate-/r*` `div-inv`
7×	`frac-times` `associate-l/` `associate-r/`
5×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

4 → 153

Calls

4 calls:

Slowest

23.0ms	(/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x))
9.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x)))))
0.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

231.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x)))))
122.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x))))
67.0ms	(/ (/ 2 (* (/ (cbrt x) l) (/ (cbrt x) l))) (cbrt x))
27.0ms	(/ (* t t) x)

simplify837.0ms

Counts: 165 → 165

prune3.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.0b

localize73.0ms

Local error

Found 4 expressions with local error:

27.1b	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ (* (cbrt 2) (cbrt 2)) (/ (cbrt x) l)) (/ (cbrt x) (/ (cbrt 2) (/ (cbrt x) l)))))))
9.0b	(/ (* t t) x)
3.6b	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ (* (cbrt 2) (cbrt 2)) (/ (cbrt x) l)) (/ (cbrt x) (/ (cbrt 2) (/ (cbrt x) l))))))
1.0b	(cbrt 2)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

Slowest

18.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ (* (cbrt 2) (cbrt 2)) (/ (cbrt x) l)) (/ (cbrt x) (/ (cbrt 2) (/ (cbrt x) l)))))))
1.0ms	(cbrt 2)
0.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ (* (cbrt 2) (cbrt 2)) (/ (cbrt x) l)) (/ (cbrt x) (/ (cbrt 2) (/ (cbrt x) l))))))

series603.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

358.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ (* (cbrt 2) (cbrt 2)) (/ (cbrt x) l)) (/ (cbrt x) (/ (cbrt 2) (/ (cbrt x) l)))))))
218.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (/ (* (cbrt 2) (cbrt 2)) (/ (cbrt x) l)) (/ (cbrt x) (/ (cbrt 2) (/ (cbrt x) l))))))
26.0ms	(/ (* t t) x)
0.0ms	(cbrt 2)

simplify955.0ms

Counts: 75 → 75

prune1.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.0b

regimes1.3s

Accuracy

74.7% (5.9b remaining)

Error of 9.9b against oracle of 4.0b and baseline of 27.3b

bsearch1.3s

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.1s	10087×	body	80	nan
1.7s	849×	body	1280	valid
1.2s	5117×	body	80	valid
888.0ms	1042×	body	640	valid
630.0ms	583×	body	1280	nan
535.0ms	607×	body	640	nan
517.0ms	343×	body	160	valid
407.0ms	649×	body	320	valid
261.0ms	350×	body	320	nan
122.0ms	189×	body	160	nan