Details

sample105.0ms

Algorithm

intervals

Results

43.0ms	273×	body	80	valid
12.0ms	82×	body	80	nan

simplify766.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	158
7	158
6	157
5	150
4	138
3	110
2	62
1	36
0	20

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize355.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 155

Calls

4 calls:

62.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
102.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
40.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
38.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
163.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
142.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
154.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify9.2s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
3	4467
2	1211
1	434
0	182

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

localize368.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.6b	(* (/ a b) (* c 2.0))
4.4b	(/ (* 2.0 c) (fma b -2 (* (/ a b) (* c 2.0))))
22.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
13×	`associate-l`
12×	`times-frac`
10×	`pow1` `fma-def`
8×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `distribute-rgt-neg-in` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `pow-prod-down` `sqrt-prod`
2×	`sum-log` `sqrt-div` `div-inv` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `associate-r` `neg-log` `associate-l/` `-commutative` `associate-+l-` `flip-+` `flip--` `associate-/l*`

Counts

4 → 106

Calls

4 calls:

103.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms	(* (/ a b) (* c 2.0))
35.0ms	(/ (* 2.0 c) (fma b -2 (* (/ a b) (* c 2.0))))
31.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(* (/ a b) (* c 2.0))
296.0ms	(/ (* 2.0 c) (fma b -2 (* (/ a b) (* c 2.0))))
160.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.8s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1938
1	533
0	203

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.8b

localize463.0ms

Local error

Found 4 expressions with local error:

10.0b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-div`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

63.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
36.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
56.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
38.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
143.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
154.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
144.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify7.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
3	2872
2	828
1	284
0	117

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.8b

localize420.0ms

Local error

Found 4 expressions with local error:

8.5b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`sqrt-prod`
2×	`neg-mul-1` `pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 87

Calls

4 calls:

44.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
37.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series911.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
138.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
232.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
274.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify4.2s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1364
1	443
0	181

prune2.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.8b

regimes805.0ms

Accuracy

93.6% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 19.8b

bsearch443.0ms

Steps

Iters	Range		Point
10	1.0955696400612189e+91	1.0202913897586463e+104	8.119950078133889e+99
9	-2.409563002992963e+162	-2.0274263258127503e+155	-2.0519886074223697e+155

simplify57.0ms

Iterations

Iter	Nodes
done	56
1	56
0	46

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	8746×	body	80	valid
808.0ms	2913×	body	80	nan