Details

sample343.0ms

Algorithm

intervals

Results

87.0ms	332×	body	80	nan
71.0ms	37×	body	640	valid
33.0ms	161×	body	80	valid
28.0ms	27×	body	1280	valid
18.0ms	22×	body	640	nan
16.0ms	17×	body	1280	nan
9.0ms	18×	body	320	valid
5.0ms	8×	body	320	nan
5.0ms	13×	body	160	valid
2.0ms	5×	body	160	nan

simplify650.0ms

Calls

1 calls:

Slowest

649.0ms

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

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.3b

localize83.0ms

Local error

Found 4 expressions with local error:

20.4b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.6b	(- (* (/ (+ 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))))

rewrite4.4s

Algorithm

rewrite-expression-head

Rules

2006×	`add-sqr-sqrt`
1306×	`*-un-lft-identity`
990×	`associate-l`
959×	`times-frac`
720×	`prod-diff`
610×	`add-cube-cbrt`
504×	`sqrt-prod`
413×	`difference-of-squares`
381×	`unswap-sqr`
337×	`associate-r`
201×	`swap-sqr`
176×	`distribute-lft-out`
148×	`*-commutative`
140×	`distribute-lft-out--`
64×	`difference-of-sqr-1`
48×	`fma-neg`
34×	`associate-/r/`
25×	`associate-/r*`
19×	`flip3--` `flip--`
17×	`div-inv`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate--l+` `insert-posit16` `log1p-expm1-u`
2×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `distribute-lft-in` `div-exp` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down`

Calls

4 calls:

Slowest

1.7s	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.1s	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2) t)

series2.2s

Calls

4 calls:

Slowest

1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
486.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
257.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
43.0ms	(* (sqrt 2) t)

simplify7.6m

Calls

2421 calls:

Slowest

926.0ms	(fma (/ 1 (+ (sqrt x) (sqrt 1))) (* (/ (+ x 1) (- (sqrt x) (sqrt 1))) (+ (* l l) (* 2 (* t t)))) (- (* (sqrt (* l l)) (sqrt (* l l)))))
807.0ms	(fma (/ (sqrt (+ x 1)) (+ (sqrt x) 1)) (* (/ (sqrt (+ x 1)) (- (sqrt x) 1)) (+ (* l l) (* 2 (* t t)))) (- (* (* l l) 1)))
803.0ms	(fma (/ 1 (+ (sqrt x) 1)) (* (/ (+ x 1) (- (sqrt x) 1)) (+ (* l l) (* 2 (* t t)))) (- (* (* l l) 1)))
793.0ms	(/ (* (sqrt 2) (* (cbrt t) (cbrt t))) (sqrt (+ (sqrt (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (* (sqrt l) (sqrt l)))))
786.0ms	(/ (* (sqrt (cbrt 2)) t) (sqrt (- (sqrt (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) l)))

prune21.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.9b

localize44.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.1b	(/ (* (* t t) 4) x)
3.4b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b	(* (sqrt 2) t)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
84×	`times-frac`
78×	`associate-l`
65×	`*-un-lft-identity` `add-cube-cbrt`
30×	`unswap-sqr`
28×	`associate-/l*`
27×	`associate-r`
16×	`swap-sqr`
15×	`add-cbrt-cube` `add-exp-log`
13×	`*-commutative`
7×	`pow1` `sqrt-prod`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `fma-udef` `div-inv`

Calls

4 calls:

Slowest

58.0ms	(/ (* (* t t) 4) x)
14.0ms	(* (sqrt 2) t)
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))

series715.0ms

Calls

4 calls:

Slowest

509.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
90.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
63.0ms	(* (sqrt 2) t)
53.0ms	(/ (* (* t t) 4) x)

simplify11.0s

Calls

229 calls:

Slowest

430.0ms	(/ (* (* t t) (* (cbrt 4) (cbrt 4))) (* (cbrt x) (cbrt x)))
402.0ms	(/ (* (* t t) (sqrt 4)) (* (cbrt x) (cbrt x)))
280.0ms	(/ (* (* (cbrt t) (cbrt t)) (* (cbrt t) (cbrt t))) (* (cbrt x) (cbrt x)))
267.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
226.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize81.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.1b	(/ (* (* t t) 4) x)
3.4b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

392×	`add-sqr-sqrt`
195×	`unswap-sqr`
162×	`cbrt-prod`
133×	`associate-l`
84×	`times-frac` `sqrt-prod`
80×	`*-un-lft-identity` `add-cube-cbrt`
56×	`associate-r`
48×	`add-cbrt-cube`
47×	`swap-sqr`
40×	`cbrt-unprod`
28×	`associate-/l*`
25×	`add-exp-log`
19×	`*-commutative`
17×	`pow1`
11×	`prod-exp`
8×	`pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `div-inv`

Calls

4 calls:

Slowest

72.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
40.0ms	(/ (* (* t t) 4) x)
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))

series717.0ms

Calls

4 calls:

Slowest

529.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
80.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
57.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
51.0ms	(/ (* (* t t) 4) x)

simplify24.7s

Calls

433 calls:

Slowest

567.0ms	(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* t t) t)))
514.0ms	(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t)))
513.0ms	(* (* (sqrt 2) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* t t) t)))
510.0ms	(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* t t) t)))
500.0ms	(* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt 2)) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (* t t) t)))

prune5.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.8b

localize64.0ms

Local error

Found 4 expressions with local error:

27.0b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
10.1b	(/ (* (* t t) 4) x)
3.4b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b	(* (* (cbrt (sqrt 2)) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)))

rewrite570.0ms

Algorithm

rewrite-expression-head

Rules

7445×	`add-sqr-sqrt`
6325×	`cbrt-prod`
5709×	`unswap-sqr`
1749×	`sqrt-prod`
354×	`swap-sqr`
316×	`cbrt-unprod`
262×	`associate-l`
257×	`add-cbrt-cube`
171×	`associate-r`
93×	`*-un-lft-identity` `add-cube-cbrt`
84×	`times-frac`
71×	`*-commutative`
49×	`add-exp-log`
41×	`pow1`
30×	`prod-exp`
28×	`associate-/l*`
27×	`pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `div-inv`

Calls

4 calls:

Slowest

342.0ms	(* (* (cbrt (sqrt 2)) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)))
76.0ms	(/ (* (* t t) 4) x)
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))

series694.0ms

Calls

4 calls:

Slowest

477.0ms	(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))
82.0ms	(* (* (cbrt (sqrt 2)) (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (cbrt (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)))
49.0ms	(/ (* (* t t) 4) x)