Details

sample35.0ms

Algorithm

intervals

Results

13.0ms	268×	body	80	valid
4.0ms	85×	body	80	nan

simplify127.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	20	38
1	36	38
2	66	37
3	122	37
4	154	37
5	166	37
6	168	37
done	168	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize85.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

32.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
56.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

177 → 177

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	208	6992
1	458	4570
2	1226	3570
done	5000	2949

prune404.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.0b

localize93.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b	(/ (/ (fma 2.0 (/ (* a c) b) (* -2 b)) 2.0) a)
4.3b	(/ (* a c) b)
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
90×	`add-cube-cbrt`
78×	`times-frac`
60×	`prod-diff`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`associate-/r*` `div-inv`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `cbrt-unprod` `associate-/l/`

Counts

4 → 202

Calls

4 calls:

35.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (/ (fma 2.0 (/ (* a c) b) (* -2 b)) 2.0) a)
11.0ms	(/ (* a c) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(/ (/ (fma 2.0 (/ (* a c) b) (* -2 b)) 2.0) a)
20.0ms	(/ (* a c) b)
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

214 → 214

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	355	7662
1	802	5645
2	2206	4723
done	5001	4083

prune672.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/r*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 156

Calls

4 calls:

47.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
31.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify996.0ms

Counts

168 → 168

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	235	6633
1	542	4639
2	1653	3699
done	5000	3048

prune450.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize91.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
61×	`prod-diff`
57×	`add-cube-cbrt`
37×	`sqrt-prod`
27×	`associate-r`
26×	`add-exp-log`
25×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
16×	`add-cbrt-cube`
12×	`prod-exp`
11×	`fma-neg`
10×	`pow1` `add-log-exp`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`neg-mul-1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u`
3×	`diff-log` `pow-prod-down`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 177

Calls

4 calls:

82.0ms	(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

189 → 189

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	272	7070
1	663	4922
2	1996	3896
done	5001	3247

prune473.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.7b

regimes264.0ms

Accuracy

93.4% (1.0b remaining)

Error of 7.7b against oracle of 6.8b and baseline of 21.4b

bsearch305.0ms

Steps

Iters	Range	Point
9	8.777746745010686e+110	1.2290467223415774e+117	2.9765366996267504e+116
11	-1.5896185090842948e-298	2.4041921185404804e-297	-6.74259841072151e-308
7	-1.6239005782062206e+154	-7.680972122048022e+152	-2.6152573735422387e+153

Iters

Range

Point

8.777746745010686e+110

1.2290467223415774e+117

2.9765366996267504e+116

-1.5896185090842948e-298

2.4041921185404804e-297

-6.74259841072151e-308

-1.6239005782062206e+154

-7.680972122048022e+152

-2.6152573735422387e+153

simplify17.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	51	158
1	62	124
2	70	124
3	78	124
4	80	124
done	80	124

end0.0ms

sample975.0ms

Algorithm

intervals

Results

456.0ms	8763×	body	80	valid
136.0ms	2944×	body	80	nan