Details

sample358.0ms

Algorithm

intervals

Results

67.0ms	167×	body	80	valid
65.0ms	349×	body	80	nan
27.0ms	37×	body	640	valid
21.0ms	26×	body	1280	valid
16.0ms	17×	body	1280	nan
15.0ms	19×	body	640	nan
7.0ms	12×	body	320	valid
5.0ms	14×	body	160	valid
4.0ms	8×	body	320	nan
2.0ms	6×	body	160	nan

simplify1.2s

Counts: 1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize52.0ms

Local error

Found 4 expressions with local error:

20.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
11.8b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b	(* (sqrt 2) t)
0.0b	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))

rewrite186.0ms

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

79.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
49.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
37.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
15.0ms	(* (sqrt 2) t)

series2.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.9s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
316.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
172.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
55.0ms	(* (sqrt 2) t)

simplify1.1s

Counts: 136 → 136

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize42.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
7.9b	(/ (* t t) x)
5.8b	(/ (* l l) (/ x 2))
4.8b	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))

rewrite32.0ms

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

17.0ms	(/ (* t t) x)
11.0ms	(/ (* l l) (/ x 2))
2.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
0.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2)))))
78.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (/ (* l l) (/ x 2))))
44.0ms	(/ (* l l) (/ x 2))
21.0ms	(/ (* t t) x)

simplify2.1s

Counts: 112 → 112

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize69.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
7.9b	(/ (* t t) x)
4.8b	(fma (* t t) 2 (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))
0.5b	(* (sqrt 2) t)

rewrite37.0ms

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

18.0ms	(/ (* t t) x)
14.0ms	(* (sqrt 2) t)
3.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
1.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

354.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x)))))
199.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (* (* (sqrt 2) l) (/ (* (sqrt 2) l) x))))
49.0ms	(* (sqrt 2) t)
22.0ms	(/ (* t t) x)

simplify1.1s

Counts: 88 → 88

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

localize34.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (* (/ l x) (* l 2)))))
7.9b	(/ (* t t) x)
4.8b	(fma (* t t) 2 (fma (/ (* t t) x) 4 (* (/ l x) (* l 2))))
0.5b	(* (sqrt 2) t)

rewrite36.0ms

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

18.0ms	(/ (* t t) x)
15.0ms	(* (sqrt 2) t)
3.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (* (/ l x) (* l 2)))))
0.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (* (/ l x) (* l 2))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

213.0ms	(sqrt (fma (* t t) 2 (fma (/ (* t t) x) 4 (* (/ l x) (* l 2)))))
106.0ms	(fma (* t t) 2 (fma (/ (* t t) x) 4 (* (/ l x) (* l 2))))
54.0ms	(* (sqrt 2) t)
34.0ms	(/ (* t t) x)

simplify1.1s

Counts: 88 → 88

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.1b

regimes848.0ms

Accuracy

77.3% (5.4b remaining)

Error of 9.2b against oracle of 3.7b and baseline of 27.6b

bsearch2.3s

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.1s	9933×	body	80	nan
986.0ms	5194×	body	80	valid
960.0ms	608×	body	640	nan
854.0ms	988×	body	640	valid
788.0ms	828×	body	1280	valid
598.0ms	342×	body	320	nan
592.0ms	590×	body	1280	nan
359.0ms	629×	body	320	valid
176.0ms	190×	body	160	nan
162.0ms	361×	body	160	valid