Details

sample339.0ms

Algorithm

intervals

Results

6.0ms	36×	body	2560	valid
6.0ms	191×	body	80	valid
4.0ms	77×	body	80	nan
3.0ms	20×	body	1280	valid
2.0ms	18×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7
done	34	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

76.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
10.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753
done	5001	753

prune294.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.5b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 284

Calls

4 calls:

34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
63.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
147.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
177.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify137.0ms

Counts

296 → 296

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	919	5579
1	3918	4508
2	5001	4505
done	5001	4505

prune580.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.1b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.7b	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
162×	`times-frac`
118×	`add-cube-cbrt`
60×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
32×	`add-exp-log`
28×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
23×	`add-cbrt-cube`
21×	`distribute-lft-neg-in`
16×	`div-exp`
10×	`cbrt-undiv` `fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`prod-exp` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `neg-log` `associate-/r/` `associate-/l/`

Counts

4 → 258

Calls

4 calls:

34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
41.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
190.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
167.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Counts

270 → 270

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	986	4687
1	4287	3613
2	5001	3595
done	5001	3595

prune502.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
168×	`*-un-lft-identity`
159×	`times-frac`
116×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`neg-mul-1` `div-exp`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 249

Calls

4 calls:

49.0ms	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
12.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
34.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Counts

261 → 261

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	802	4368
1	3212	3287
2	5002	3111
done	5002	3111

prune349.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.3b

regimes153.0ms

Accuracy

82.6% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 30.1b

bsearch73.0ms

Steps

Iters	Range		Point
5	3.355600980676121e+98	1.2784432988208537e+99	6.385814412780331e+98
9	-7.880786648230988e-89	-3.5843833042003497e-96	-4.706781135059312e-92

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	18
1	46	18
2	46	18
done	46	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

201.0ms	1121×	body	2560	valid
183.0ms	5760×	body	80	valid
133.0ms	903×	body	1280	valid
83.0ms	2849×	body	80	nan
53.0ms	476×	body	640	valid
28.0ms	129×	body	5120	valid
18.0ms	216×	body	320	valid
6.0ms	105×	body	160	valid