Details

sample90.0ms

Algorithm

intervals

Results

37.0ms	282×	body	80	valid
16.0ms	81×	body	80	nan

simplify239.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	20	38
1	39	38
2	79	37
3	142	37
4	171	37
5	181	37
6	185	37
done	185	37

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize124.0ms

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))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite196.0ms

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:

75.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
63.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
117.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
115.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
125.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

177 → 177

Iterations

Useful iterations: done (2.0s)

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

prune617.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize147.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b	(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* -2 b)))
6.8b	(/ (* a c) b)
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

35.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* -2 b)))
11.0ms	(/ (* a c) b)
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms	(/ (* 2.0 c) (fma (/ (* a c) b) 2.0 (* -2 b)))
44.0ms	(/ (* a c) b)
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

165 → 165

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	250	6245
1	573	4278
2	1778	3356
done	5000	2715

prune739.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize171.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.4b	(/ (* 2.0 c) (fma (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) 2.0 (* -2 b)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
63×	`add-cube-cbrt`
60×	`prod-diff`
34×	`sqrt-prod`
31×	`times-frac`
30×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`distribute-rgt-neg-in` `associate-r`
21×	`distribute-lft-neg-in`
11×	`cbrt-prod`
10×	`fma-neg`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `div-inv`
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 → 191

Calls

4 calls:

41.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
10.0ms	(/ (* 2.0 c) (fma (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) 2.0 (* -2 b)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
153.0ms	(/ (* 2.0 c) (fma (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) 2.0 (* -2 b)))
143.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

203 → 203

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	332	7322
1	844	5318
2	2950	4024
done	5000	3175

prune996.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.5b

localize129.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (/ a (* (cbrt b) (cbrt b))))
6.2b	(cbrt (/ a (* (cbrt b) (cbrt b))))
6.2b	(cbrt (/ a (* (cbrt b) (cbrt b))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 71

Calls

4 calls:

7.0ms	(cbrt (/ a (* (cbrt b) (cbrt b))))
7.0ms	(cbrt (/ a (* (cbrt b) (cbrt b))))
12.0ms	(cbrt (/ a (* (cbrt b) (cbrt b))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(cbrt (/ a (* (cbrt b) (cbrt b))))
203.0ms	(cbrt (/ a (* (cbrt b) (cbrt b))))
198.0ms	(cbrt (/ a (* (cbrt b) (cbrt b))))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

83 → 83

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	102	1084
1	210	1038
2	578	965
3	2016	953
done	5000	943

prune639.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

regimes368.0ms

Accuracy

89.8% (1.5b remaining)

Error of 8.1b against oracle of 6.6b and baseline of 20.9b

bsearch308.0ms

Steps

Iters	Range		Point
8	1.538525478595148e+72	6.402915924844171e+74	1.3910222191204909e+74
8	-1.173014798652874e+100	-8.67642318333193e+96	-1.1553711424735541e+100

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	55	168
1	65	168
done	65	168

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.4s	8755×	body	80	valid
346.0ms	2933×	body	80	nan