Details

sample787.0ms

Algorithm

intervals

Results

156.0ms	27×	body	1280	valid
143.0ms	330×	body	80	nan
133.0ms	17×	body	320	nan
73.0ms	176×	body	80	valid
27.0ms	25×	body	640	valid
23.0ms	18×	body	1280	nan
19.0ms	20×	body	640	nan
11.0ms	17×	body	320	valid
5.0ms	11×	body	160	valid
3.0ms	6×	body	160	nan

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4592
5	1370
4	472
3	215
2	101
1	44
0	18

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.3b

localize83.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
11.6b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.1b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite193.0ms

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:

77.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2) t)
38.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
60.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

458.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
61.0ms	(* (sqrt 2) t)
306.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
2.0s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify2.0s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1605
1	483
0	181

prune643.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.7b

localize56.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
5.5b	(/ (* l l) x)
9.5b	(/ (* t t) x)
25.8b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
9.0ms	(/ (* l l) x)
9.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2)))
34.0ms	(/ (* l l) x)
35.0ms	(/ (* t t) x)
208.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ (* l l) x) 2))))

simplify1.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	5020
2	1498
1	356
0	134

prune512.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
4.0b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
9.5b	(/ (* t t) x)
25.8b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

rewrite19.0ms

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:

7.0ms	(* (sqrt 2) t)
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
9.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sqrt 2) t)
86.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2)))
37.0ms	(/ (* t t) x)
238.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (* l (/ l x)) 2))))

simplify2.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4545
2	1019
1	317
0	132

prune669.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
4.0b	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
9.5b	(/ (* t t) x)
25.8b	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

rewrite19.0ms

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:

8.0ms	(* (sqrt 2) t)
0.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
9.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sqrt 2) t)
90.0ms	(fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2)))
28.0ms	(/ (* t t) x)
242.0ms	(sqrt (fma 2 (* t t) (fma (/ (* t t) x) 4 (* (/ l (/ x l)) 2))))

simplify3.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4708
2	1019
1	319
0	132

prune468.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

regimes895.0ms

Accuracy

77.6% (5.2b remaining)

Error of 9.0b against oracle of 3.8b and baseline of 27.2b

bsearch461.0ms

Steps

Iters	Range		Point
8	1.1851330097179606e+57	4.62892497053394e+59	4.561118037024944e+59
7	-1.2036851434557175e+108	-1.4050859331810362e+106	-6.081620194545127e+107

simplify18.0ms

Iterations

Iter	Nodes
done	46
1	46
0	41

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.1s	10190×	body	80	nan
1.6s	878×	body	1280	valid
1.5s	5134×	body	80	valid
1.2s	981×	body	640	valid
656.0ms	574×	body	1280	nan
481.0ms	562×	body	640	nan
378.0ms	665×	body	320	valid
289.0ms	363×	body	320	nan
121.0ms	342×	body	160	valid
65.0ms	194×	body	160	nan