Details

sample399.0ms

Algorithm

intervals

Results

71.0ms	168×	body	80	valid
59.0ms	292×	body	80	nan
47.0ms	10×	body	160	valid
28.0ms	27×	body	1280	valid
27.0ms	25×	body	1280	nan
24.0ms	29×	body	640	valid
18.0ms	22×	body	640	nan
17.0ms	22×	body	320	valid
6.0ms	12×	body	320	nan
2.0ms	6×	body	160	nan

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2040
6	2040
5	1370
4	472
3	215
2	101
1	44
0	18

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
0.4b	(* (sqrt 2) t)
13.5b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
22.3b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`associate-l`
29×	`times-frac`
21×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
8×	`difference-of-squares`
7×	`sqrt-prod` `distribute-lft-out`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `difference-of-sqr-1` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `unswap-sqr`
3×	`flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `sqrt-div` `pow-prod-down` `associate--l+` `associate-r/` `associate-/r/` `-commutative` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `associate-*l/` `div-inv`

Counts

4 → 124

Calls

4 calls:

68.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
7.0ms	(* (sqrt 2) t)
40.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
65.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.0s

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))
44.0ms	(* (sqrt 2) t)
310.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.2s

Counts

136 → 136

Iterations

Iter	Nodes
done	2002
2	2002
1	818
0	247

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.0b

localize44.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* (/ (* l l) x) 2)))
7.6b	(/ (* l l) x)
11.9b	(/ (* t t) x)
27.8b	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (/ (* l l) x) 2))))

rewrite39.0ms

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 (* t t) 2 (fma 4 (/ (* t t) x) (* (/ (* l l) x) 2)))
17.0ms	(/ (* l l) x)
17.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (/ (* l l) x) 2))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* (/ (* l l) x) 2)))
41.0ms	(/ (* l l) x)
36.0ms	(/ (* t t) x)
263.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (/ (* l l) x) 2))))

simplify1.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	2015
3	2015
2	1507
1	357
0	134

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
3.8b	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2)))
11.9b	(/ (* t t) x)
27.8b	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2))))

rewrite24.0ms

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:

13.0ms	(* (sqrt 2) t)
0.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2)))
9.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt 2) t)
83.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2)))
41.0ms	(/ (* t t) x)
194.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2))))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	2000
3	2000
2	1004
1	318
0	132

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
3.8b	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2)))
11.9b	(/ (* t t) x)
27.8b	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
17×	`pow1`
15×	`add-cbrt-cube`
9×	`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×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp`
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 → 76

Calls

4 calls:

49.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
0.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2)))
9.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
75.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2)))
26.0ms	(/ (* t t) x)
205.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* (* l (/ l x)) 2))))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	2002
3	2002
2	1224
1	352
0	137

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

regimes792.0ms

Accuracy

78.1% (5.1b remaining)

Error of 9.0b against oracle of 3.9b and baseline of 27.2b

bsearch409.0ms

Steps

Iters	Range		Point
6	4.7332403373153464e+123	3.3768436627244136e+124	3.3304656260583313e+124
10	-1.5304224262738304e+84	-6.960410891925428e+71	-6.377624199137871e+80

simplify25.0ms

Iterations

Iter	Nodes
done	52
1	52
0	45

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.8s	9884×	body	80	nan
1.3s	868×	body	1280	valid
1.2s	5062×	body	80	valid
821.0ms	1015×	body	640	valid
733.0ms	613×	body	1280	nan
620.0ms	609×	body	640	nan
466.0ms	686×	body	320	valid
261.0ms	344×	body	320	nan
131.0ms	369×	body	160	valid
93.0ms	192×	body	160	nan