Details

sample98.0ms

Algorithm

intervals

Results

51.0ms	273×	body	80	valid
11.0ms	76×	body	80	nan

simplify204.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (29.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize177.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite176.0ms

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:

54.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
62.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
98.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

177 → 177

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	208	6992
1	458	4570
2	1227	3570
done	5001	2949

prune581.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize118.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b	(/ (/ (fma (/ (* a c) b) 2.0 (* -2 b)) 2.0) a)
6.5b	(/ (* a c) b)
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite133.0ms

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:

61.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
32.0ms	(/ (/ (fma (/ (* a c) b) 2.0 (* -2 b)) 2.0) a)
17.0ms	(/ (* a c) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
135.0ms	(/ (/ (fma (/ (* a c) b) 2.0 (* -2 b)) 2.0) a)
23.0ms	(/ (* a c) b)
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

214 → 214

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	355	7662
1	802	5645
2	2209	4723
done	5001	4083

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize143.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 140

Calls

3 calls:

90.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series484.0ms

Counts

3 → 9

Calls

3 calls:

263.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
120.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

149 → 149

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	218	6367
1	515	4384
2	1526	3474
done	5000	2823

prune615.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize162.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.1b	(/ (/ (fma (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) 2.0 (* -2 b)) 2.0) a)
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

124×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
103×	`add-cube-cbrt` `times-frac`
60×	`prod-diff`
34×	`sqrt-prod`
30×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`distribute-rgt-neg-in` `associate-r`
21×	`distribute-lft-neg-in`
13×	`associate-/l*`
11×	`cbrt-prod`
10×	`cbrt-undiv` `fma-neg` `div-exp`
8×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l` `div-inv`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `sqrt-div` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 240

Calls

4 calls:

31.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
23.0ms	(/ (/ (fma (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) 2.0 (* -2 b)) 2.0) a)
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
159.0ms	(/ (/ (fma (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) 2.0 (* -2 b)) 2.0) a)
122.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts

252 → 252

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	435	9292
1	1073	7240
2	3348	5628
done	5000	4542

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

regimes401.0ms

Accuracy

90% (1.5b remaining)

Error of 7.7b against oracle of 6.2b and baseline of 20.8b

bsearch212.0ms

Steps

Iters	Range		Point
5	1.0433798175544735e+152	3.237299440315181e+152	1.1155337065557208e+152
8	-1.173014798652874e+100	-8.67642318333193e+96	-1.1553711424735541e+100

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	50	132
1	61	130
done	61	130

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	8717×	body	80	valid
417.0ms	2914×	body	80	nan