Details

sample575.0ms

Algorithm

intervals

Results

122.0ms	15×	body	320	valid
118.0ms	179×	body	80	valid
79.0ms	317×	body	80	nan
30.0ms	32×	body	640	valid
30.0ms	24×	body	1280	valid
20.0ms	23×	body	640	nan
17.0ms	15×	body	1280	nan
6.0ms	9×	body	320	nan
3.0ms	6×	body	160	valid
1.0ms	3×	body	160	nan

simplify413.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

412.0ms

(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.3b

localize79.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.3b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b	(* (sqrt 2) t)
0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite149.0ms

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

57.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
48.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
34.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
8.0ms	(* (sqrt 2) t)

series2.2s

Counts

4 → 12

Calls

4 calls:

Slowest

1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
463.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
225.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
52.0ms	(* (sqrt 2) t)

simplify8.4s

Counts

64 → 106

Calls

64 calls:

Slowest

355.0ms	(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
326.0ms	(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
321.0ms	(/ (* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* t t) t)) (* (* (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
304.0ms	(sqrt (+ (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (+ (* (* l l) (* l l)) (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
296.0ms	(* (* l l) (/ (+ x 1) (- x 1)))

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.6b

localize71.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.8b	(/ (* (* t t) 4) x)
5.2b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.5b	(* (sqrt 2) t)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `times-frac` `div-exp` `associate-r*`
2×	`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 → 78

Calls

4 calls:

Slowest

34.0ms	(/ (* (* t t) 4) x)
8.0ms	(* (sqrt 2) t)
3.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series618.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

426.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
87.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
74.0ms	(* (sqrt 2) t)
30.0ms	(/ (* (* t t) 4) x)

simplify2.9s

Counts

46 → 90

Calls

46 calls:

Slowest

263.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
250.0ms	(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
216.0ms	(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
199.0ms	(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
197.0ms	(* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* t t) t))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize57.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.8b	(/ (* (* t t) 4) x)
5.2b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

Slowest

59.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
36.0ms	(/ (* (* t t) 4) x)
2.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series727.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

495.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
103.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
84.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
45.0ms	(/ (* (* t t) 4) x)

simplify4.1s

Counts

45 → 90

Calls

45 calls:

Slowest

521.0ms	(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
354.0ms	(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
232.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
212.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
211.0ms	(/ (* (* (* (* t t) t) (* (* t t) t)) (* (* 4 4) 4)) (* (* x x) x))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize42.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.8b	(/ (* (* t t) 4) x)
5.2b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.5b	(* t (sqrt 2))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `times-frac` `div-exp` `associate-l*`
2×	`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 → 78

Calls

4 calls:

Slowest

22.0ms	(/ (* (* t t) 4) x)
15.0ms	(* t (sqrt 2))
1.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series733.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

526.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
98.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
75.0ms	(* t (sqrt 2))
33.0ms	(/ (* (* t t) 4) x)

simplify2.8s

Counts

47 → 90

Calls

47 calls:

Slowest

279.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
228.0ms	(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
214.0ms	(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
212.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
190.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

regimes535.0ms

Accuracy

78.1% (5.0b remaining)

Error of 9.0b against oracle of 3.9b and baseline of 26.9b

bsearch1.8s

end0.0ms

sample9.4s

Algorithm

intervals

Results

2.7s	10183×	body	80	nan
1.3s	854×	body	1280	valid
1.2s	5157×	body	80	valid
875.0ms	1025×	body	640	valid
825.0ms	611×	body	320	valid
791.0ms	634×	body	1280	nan
575.0ms	611×	body	640	nan
261.0ms	316×	body	320	nan
195.0ms	353×	body	160	valid
91.0ms	186×	body	160	nan