Details

sample850.0ms

Algorithm

intervals

Results

606.0ms	34×	body	1280	valid
65.0ms	171×	body	80	valid
17.0ms	32×	body	2560	valid
9.0ms	105×	body	80	nan
4.0ms	13×	body	640	valid
2.0ms	10×	body	160	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	139
7	139
6	137
5	134
4	131
3	113
2	62
1	29
0	14

prune88.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
2.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite759.0ms

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-/l*`
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-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

304.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
28.0ms	(- (* b b) (* 4.0 (* a c)))
374.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
30.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
115.0ms	(- (* b b) (* 4.0 (* a c)))
149.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
136.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify8.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	1843
1	607
0	243

prune3.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize104.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
1.3b	(fma b b (- (* 4.0 (* a c))))
2.4b	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
22.3b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 149

Calls

4 calls:

197.0ms	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
1.0ms	(fma b b (- (* 4.0 (* a c))))
32.0ms	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
2.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
167.0ms	(fma b b (- (* 4.0 (* a c))))
400.0ms	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
420.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify5.5s

Counts

161 → 161

Iterations

Iter	Nodes
done	5001
2	1468
1	527
0	221

prune3.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* 4.0 (* a c)))
2.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

199.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
17.0ms	(- (* b b) (* 4.0 (* a c)))
65.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series1.6s

Counts

4 → 12

Calls

4 calls:

463.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
96.0ms	(- (* b b) (* 4.0 (* a c)))
502.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
535.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify9.4s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
2	1987
1	670
0	269

prune3.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.9b

localize125.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
11.4b	(/ (/ (+ (- (* b b) (* b b)) (* (* c a) 4.0)) 2.0) a)
18.3b	(- (* b b) (* b b))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite522.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
48×	`add-sqr-sqrt`
47×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `sqrt-prod` `flip--`
2×	`sub-neg` `fma-neg` `sqrt-div` `diff-log` `div-sub` `prod-diff`
1×	`associate-+l-` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `+-inverses` `clear-num` `associate-/l/` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 126

Calls

4 calls:

194.0ms	(- (* b b) (* 4.0 (* a c)))
163.0ms	(/ (/ (+ (- (* b b) (* b b)) (* (* c a) 4.0)) 2.0) a)
17.0ms	(- (* b b) (* b b))
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(- (* b b) (* 4.0 (* a c)))
111.0ms	(/ (/ (+ (- (* b b) (* b b)) (* (* c a) 4.0)) 2.0) a)
4.0ms	(- (* b b) (* b b))
398.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.5s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
2	1652
1	583
0	248

prune2.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

regimes512.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 30.2b

bsearch522.0ms

Steps

Iters	Range	Point
7	6.896997489231346e+142	2.39218470372122e+144	6.994525771494005e+142
9	1.431611294151488e-203	4.1417548827777133e-196	1.5861830220858986e-203
6	-4.525167845450207e+100	-9.36795079059543e+99	-1.6507168034351889e+100

Iters

Range

Point

6.896997489231346e+142

2.39218470372122e+144

6.994525771494005e+142

1.431611294151488e-203

4.1417548827777133e-196

1.5861830220858986e-203

-4.525167845450207e+100

-9.36795079059543e+99

-1.6507168034351889e+100

simplify27.0ms

Iterations

Iter	Nodes
done	55
2	55
1	47
0	36

end0.0ms

sample12.4s

Algorithm

intervals

Results

4.2s	1056×	body	2560	valid
3.0s	449×	body	640	valid
1.6s	5836×	body	80	valid
1.2s	909×	body	1280	valid
762.0ms	230×	body	320	valid
443.0ms	2825×	body	80	nan
358.0ms	103×	body	5120	valid
86.0ms	127×	body	160	valid