Details

sample368.0ms

Algorithm

intervals

Results

59.0ms	330×	body	80	nan
55.0ms	157×	body	80	valid
23.0ms	28×	body	1280	valid
22.0ms	31×	body	640	valid
18.0ms	26×	body	640	nan
16.0ms	18×	body	1280	nan
14.0ms	28×	body	320	valid
5.0ms	12×	body	160	valid
3.0ms	9×	body	320	nan
2.0ms	6×	body	160	nan

simplify1.9s

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize80.0ms

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))))

rewrite161.0ms

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×	`sqrt-div` `insert-posit16`
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` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

Slowest

60.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
47.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
34.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
14.0ms	(* (sqrt 2) t)

series2.4s

Counts

4 → 12

Calls

4 calls:

Slowest

1.6s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
505.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
236.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
59.0ms	(* (sqrt 2) t)

simplify3.6s

Counts: 96 → 96

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.3b

localize46.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (/ (* 4 t) (/ x t))))
8.1b	(/ (* l l) x)
3.2b	(+ (* (+ (* t t) (/ (* l l) x)) 2) (/ (* 4 t) (/ x t)))
0.4b	(* (sqrt 2) t)

rewrite105.0ms

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` `add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-*l/` `frac-add` `flip-+` `insert-posit16`
3×	`associate-/r` `times-frac` `associate-r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 77

Calls

4 calls:

Slowest

37.0ms	(+ (* (+ (* t t) (/ (* l l) x)) 2) (/ (* 4 t) (/ x t)))
35.0ms	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (/ (* 4 t) (/ x t))))
18.0ms	(/ (* l l) x)
14.0ms	(* (sqrt 2) t)

series585.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

412.0ms	(sqrt (+ (* (+ (* t t) (/ (* l l) x)) 2) (/ (* 4 t) (/ x t))))
85.0ms	(+ (* (+ (* t t) (/ (* l l) x)) 2) (/ (* 4 t) (/ x t)))
57.0ms	(* (sqrt 2) t)
31.0ms	(/ (* l l) x)

simplify2.1s

Counts: 89 → 89

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize35.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2)))
9.1b	(* (/ 4 x) (* t t))
3.2b	(+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2))
0.4b	(* (sqrt 2) t)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-l`
18×	`add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
10×	`times-frac`
9×	`associate-*l/`
7×	`prod-exp` `sqrt-prod` `cbrt-unprod`
6×	`add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-r` `pow-prod-down` `frac-add` `flip-+` `insert-posit16` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `*-commutative`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 91

Calls

4 calls:

Slowest

43.0ms	(+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2))
33.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2)))
28.0ms	(* (/ 4 x) (* t t))
7.0ms	(* (sqrt 2) t)

series580.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

400.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2)))
90.0ms	(+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2))
51.0ms	(* (sqrt 2) t)
39.0ms	(* (/ 4 x) (* t t))

simplify643.0ms

Counts: 103 → 103

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize76.0ms

Local error

Found 4 expressions with local error:

26.4b	(sqrt (+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2)))
9.1b	(* (/ 4 x) (* t t))
3.2b	(+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2))
0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
22×	`pow1` `add-cbrt-cube`
16×	`add-sqr-sqrt`
14×	`associate-l` `prod-exp` `cbrt-unprod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow-prod-down`
10×	`times-frac`
9×	`associate-*l/`
6×	`add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `insert-posit16`
3×	`sqrt-prod`
2×	`cbrt-undiv` `div-exp` `associate-r` `*-commutative` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 91

Calls

4 calls:

Slowest

41.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
36.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2)))
28.0ms	(* (/ 4 x) (* t t))
27.0ms	(+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2))

series672.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

479.0ms	(sqrt (+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2)))
83.0ms	(+ (* (/ 4 x) (* t t)) (* (+ (* t t) (* (/ l x) l)) 2))
78.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
33.0ms	(* (/ 4 x) (* t t))

simplify767.0ms

Counts: 103 → 103

prune1.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.3b

regimes892.0ms

Accuracy

78.3% (5.1b remaining)

Error of 9.1b against oracle of 4.0b and baseline of 27.5b

bsearch494.0ms

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.4s	10229×	body	80	nan
1.0s	5078×	body	80	valid
925.0ms	821×	body	1280	valid
876.0ms	1035×	body	640	valid
656.0ms	579×	body	1280	nan
565.0ms	638×	body	640	nan
505.0ms	660×	body	320	valid
164.0ms	311×	body	320	nan
140.0ms	406×	body	160	valid
70.0ms	210×	body	160	nan