Details

sample258.0ms

Algorithm

intervals

Results

72.0ms	307×	body	80	nan
23.0ms	162×	body	80	valid
20.0ms	36×	body	640	valid
16.0ms	21×	body	1280	nan
15.0ms	23×	body	1280	valid
10.0ms	27×	body	320	valid
7.0ms	13×	body	640	nan
4.0ms	12×	body	320	nan
2.0ms	8×	body	160	valid
0.0ms	1×	body	160	nan

simplify227.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

226.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.2b

localize72.0ms

Local error

Found 4 expressions with local error:

21.0b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
12.0b	(- (* (/ (+ 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))))

rewrite191.0ms

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

85.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
46.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
41.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
15.0ms	(* (sqrt 2) t)

series2.2s

Counts

4 → 12

Calls

4 calls:

Slowest

1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
469.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
226.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
63.0ms	(* (sqrt 2) t)

simplify9.2s

Counts

64 → 106

Calls

64 calls:

Slowest

605.0ms	(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
375.0ms	(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)))))
344.0ms	(/ (* (* (* (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)))))
340.0ms	(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
314.0ms	(/ (* (* (* (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)))))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.0b

localize36.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.3b	(/ (* (* t t) 4) x)
5.6b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.5b	(* (sqrt 2) t)

rewrite58.0ms

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

39.0ms	(/ (* (* t t) 4) x)
14.0ms	(* (sqrt 2) t)
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))

series595.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

437.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
77.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
55.0ms	(* (sqrt 2) t)
26.0ms	(/ (* (* t t) 4) x)

simplify2.7s

Counts

46 → 90

Calls

46 calls:

Slowest

255.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
211.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
208.0ms	(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
202.0ms	(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
193.0ms	(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)))))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

localize72.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.3b	(/ (* (* t t) 4) x)
5.6b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.2b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite60.0ms

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

36.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
22.0ms	(/ (* (* t t) 4) x)
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))

series704.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

481.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
108.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
66.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
49.0ms	(/ (* (* t t) 4) x)

simplify4.1s

Counts

45 → 90

Calls

45 calls:

Slowest

475.0ms	(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
365.0ms	(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)))
288.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
244.0ms	(/ (* (* (* (* t t) t) (* (* t t) t)) (* (* 4 4) 4)) (* (* x x) x))
225.0ms	(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

localize62.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.3b	(/ (* (* t t) 4) x)
5.6b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.5b	(* t (sqrt 2))

rewrite37.0ms

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

21.0ms	(/ (* (* t t) 4) x)
12.0ms	(* t (sqrt 2))
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))

series650.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

471.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
102.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
52.0ms	(* t (sqrt 2))
25.0ms	(/ (* (* t t) 4) x)

simplify2.8s

Counts

47 → 90

Calls

47 calls:

Slowest

287.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
238.0ms	(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
215.0ms	(/ (* (* (* (* t t) t) (* (* t t) t)) (* (* 4 4) 4)) (* (* x x) x))
199.0ms	(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
190.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

regimes613.0ms

Accuracy

78% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.6b

bsearch1.0s

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.0s	10060×	body	80	nan
1.6s	5077×	body	80	valid
1.4s	815×	body	1280	valid
967.0ms	593×	body	1280	nan
904.0ms	1049×	body	640	valid
440.0ms	539×	body	640	nan
423.0ms	677×	body	320	valid
202.0ms	382×	body	160	valid
168.0ms	327×	body	320	nan
58.0ms	176×	body	160	nan