Details

sample514.0ms

Algorithm

intervals

Results

107.0ms	330×	body	80	nan
62.0ms	157×	body	80	valid
26.0ms	31×	body	640	valid
25.0ms	28×	body	1280	valid
20.0ms	26×	body	640	nan
17.0ms	18×	body	1280	nan
15.0ms	28×	body	320	valid
5.0ms	12×	body	160	valid
3.0ms	9×	body	320	nan
2.0ms	6×	body	160	nan

simplify1.3s

Counts: 1 → 1

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize66.0ms

Local error

Found 4 expressions with local error:

18.3b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
17.0b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b	(* (sqrt 2) t)
0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 94

Calls

4 calls:

Slowest

70.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
48.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
40.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
14.0ms	(* (sqrt 2) t)

series2.3s

Counts

4 → 12

Calls

4 calls:

Slowest

1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
504.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
265.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
81.0ms	(* (sqrt 2) t)

simplify720.0ms

Counts: 106 → 106

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.5b

localize42.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
9.1b	(/ (* t t) x)
8.1b	(/ (* l l) (/ x 2))
3.4b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

Slowest

14.0ms	(/ (* l l) (/ x 2))
9.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

224.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
74.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))
30.0ms	(/ (* l l) (/ x 2))
24.0ms	(/ (* t t) x)

simplify2.6s

Counts: 112 → 112

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize53.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
9.1b	(/ (* t t) x)
3.4b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))
0.4b	(* (sqrt 2) t)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

Slowest

16.0ms	(/ (* t t) x)
7.0ms	(* (sqrt 2) t)
3.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

356.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
202.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))
75.0ms	(* (sqrt 2) t)
35.0ms	(/ (* t t) x)

simplify1.1s

Counts: 88 → 88

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize35.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
9.1b	(/ (* t t) x)
3.4b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))
0.4b	(* t (sqrt 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

Slowest

9.0ms	(/ (* t t) x)
7.0ms	(* t (sqrt 2))
1.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

377.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
201.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))
75.0ms	(* t (sqrt 2))
20.0ms	(/ (* t t) x)

simplify783.0ms

Counts: 88 → 88

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

regimes784.0ms

Accuracy

78.1% (5.1b remaining)

Error of 9.2b against oracle of 4.0b and baseline of 27.5b

bsearch462.0ms

end0.0ms

sample9.3s

Algorithm

intervals

Results

2.3s	10229×	body	80	nan
1.7s	821×	body	1280	valid
1.4s	1035×	body	640	valid
1.2s	5078×	body	80	valid
611.0ms	579×	body	1280	nan
507.0ms	638×	body	640	nan
499.0ms	660×	body	320	valid
209.0ms	311×	body	320	nan
147.0ms	406×	body	160	valid
77.0ms	210×	body	160	nan