Details

sample172.0ms

Algorithm

intervals

Results

20.0ms	38×	body	2560	valid
18.0ms	190×	body	80	valid
16.0ms	36×	body	1280	valid
6.0ms	79×	body	80	nan
4.0ms	11×	body	640	valid
2.0ms	4×	body	5120	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify116.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite344.0ms

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:

143.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
114.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
48.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
190.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

112 → 112

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	164	1638
1	405	1539
2	1668	1355
done	5000	1344

prune407.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.9b	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.7b	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite322.0ms

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:

35.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
140.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
88.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series766.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
291.0ms	(/ (/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
281.0ms	(/ (+ 0 (* c a)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify605.0ms

Counts

296 → 296

Iterations

Useful iterations: done (594.0ms)

Iter	Nodes	Cost
0	390	10604
1	974	8179
done	5000	7437

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.9b	(/ (* (+ 0 (* c a)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
7.7b	(* (+ 0 (* c a)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
60×	`add-cube-cbrt` `prod-diff`
37×	`sqrt-prod`
28×	`add-exp-log`
27×	`associate-r`
26×	`times-frac`
25×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube`
10×	`fma-neg`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `neg-mul-1`
6×	`associate-/l/`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-*l/` `cbrt-unprod` `flip-+` `log1p-expm1-u`
3×	`flip3--` `associate-l` `associate-/r*` `flip--` `unswap-sqr`
2×	`rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `-commutative` `associate-/l`

Counts

4 → 196

Calls

4 calls:

60.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(/ (* (+ 0 (* c a)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
160.0ms	(* (+ 0 (* c a)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series765.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
336.0ms	(/ (* (+ 0 (* c a)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
235.0ms	(* (+ 0 (* c a)) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify674.0ms

Counts

208 → 208

Iterations

Useful iterations: done (661.0ms)

Iter	Nodes	Cost
0	320	6943
1	855	4840
done	5000	4022

prune742.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize38.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.8b	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`times-frac`
10×	`add-cube-cbrt`
8×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-neg-in` `div-inv`

Counts

4 → 86

Calls

4 calls:

65.0ms	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
59.0ms	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series845.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
295.0ms	(sqrt (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	131	1862
1	306	1648
2	1250	1584
done	5002	1564

prune593.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes213.0ms

Accuracy

83.3% (4.5b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 33.0b

bsearch181.0ms

Steps

Iters	Range		Point
9	3.58845601849977e-79	3.3299624871078663e-72	4.603517726908401e-74
9	-4.955433086253459e+131	-5.661938264600021e+124	-3.4127765686872833e+126

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	37
1	30	37
done	30	37

end0.0ms

sample2.9s

Algorithm

intervals

Results

843.0ms	903×	body	1280	valid
498.0ms	1056×	body	2560	valid
475.0ms	5921×	body	80	valid
297.0ms	2891×	body	80	nan
98.0ms	460×	body	640	valid
77.0ms	85×	body	5120	valid
41.0ms	221×	body	320	valid
13.0ms	119×	body	160	valid