Details

sample294.0ms

Algorithm

intervals

Results

7.0ms	177×	body	80	valid
7.0ms	37×	body	2560	valid
5.0ms	31×	body	1280	valid
3.0ms	92×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
27.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite60.0ms

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:

34.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

112 → 112

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	164	1638
1	388	1535
2	1103	1355
3	3594	1340
done	5000	1338

prune294.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.0b

localize12.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.5b	(/ (/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.5b	(/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
27.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite116.0ms

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:

17.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
48.0ms	(/ (/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms	(/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
144.0ms	(/ (/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
174.0ms	(/ (+ (* a c) 0) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

296 → 296

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	388	10604
1	917	8205
2	3090	7301
done	5000	7299

prune585.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
27.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 196

Calls

4 calls:

30.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
33.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

208 → 208

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	299	4764
1	657	4148
2	1752	3649
3	4971	3500
done	5000	3500

prune325.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
0.4b	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
1.0b	(fma b_2 b_2 (- (* a c)))
27.3b	(sqrt (fma b_2 b_2 (- (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 110

Calls

4 calls:

15.0ms	(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
9.0ms	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
0.0ms	(fma b_2 b_2 (- (* a c)))
1.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (- (sqrt (fma b_2 b_2 (- (* a c)))) b_2) a)
80.0ms	(- (sqrt (fma b_2 b_2 (- (* a c)))) b_2)
39.0ms	(fma b_2 b_2 (- (* a c)))
72.0ms	(sqrt (fma b_2 b_2 (- (* a c))))

simplify1.7s

Counts

122 → 122

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	173	2260
1	386	1986
2	895	1763
3	2990	1683
done	5000	1681

prune258.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.9b

regimes201.0ms

Accuracy

88.3% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 33.1b

bsearch115.0ms

Steps

Iters	Range		Point
3	9.199102238044756e-11	1.1303867620315504e-10	1.1172319783923582e-10
10	5.915922603195057e-270	1.2341107315577453e-259	1.341950468971569e-262
8	-6.10058349091927e+155	-9.408528429616011e+151	-7.93152454634662e+153

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	39	64
1	51	56
2	56	56
done	56	56

end0.0ms

sample1.1s

Algorithm

intervals

Results

211.0ms	1046×	body	2560	valid
198.0ms	5915×	body	80	valid
191.0ms	450×	body	640	valid
132.0ms	862×	body	1280	valid
87.0ms	2863×	body	80	nan
27.0ms	113×	body	5120	valid
21.0ms	233×	body	320	valid
11.0ms	100×	body	160	valid