Details

sample121.0ms

Algorithm

intervals

Results

9.0ms	35×	body	2560	valid
8.0ms	179×	body	80	valid
7.0ms	30×	body	1280	valid
5.0ms	76×	body	80	nan
3.0ms	8×	body	5120	valid
2.0ms	10×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
83.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Counts: 92 → 92

prune252.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.5b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.9b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
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 → 206

Calls

4 calls:

24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
83.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
59.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
159.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
189.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Counts: 218 → 218

prune535.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.3b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.5b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite383.0ms

Algorithm

rewrite-expression-head

Rules

3489×	`times-frac`
1831×	`add-sqr-sqrt`
1830×	`*-un-lft-identity`
1346×	`add-cube-cbrt`
267×	`associate-/l*`
242×	`distribute-lft-out--` `difference-of-squares`
124×	`sqrt-prod`
121×	`distribute-rgt-neg-in`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
8×	`add-log-exp`
6×	`associate-/r*`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 1148

Calls

4 calls:

23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
137.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
103.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
129.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify254.0ms

Counts: 1160 → 1160

prune2.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
1.6b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
25.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

22500×	`times-frac`
11592×	`add-sqr-sqrt`
11591×	`*-un-lft-identity`
8467×	`add-cube-cbrt`
8286×	`cbrt-prod`
1562×	`distribute-lft-out--` `difference-of-squares`
903×	`associate-/l*`
784×	`sqrt-prod`
781×	`distribute-rgt-neg-in`
181×	`div-inv`
23×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
8×	`add-log-exp`
7×	`associate-/r/`
5×	`pow1`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 6260

Calls

4 calls:

30.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
344.0ms	(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
76.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
128.0ms	(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
252.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts: 6272 → 6272

prune26.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

regimes234.0ms

Accuracy

80.2% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 30.2b

bsearch164.0ms

Steps

Iters	Range		Point
8	1.538525478595148e+72	6.402915924844171e+74	2.626711303971801e+73
9	-7.826064039423189e-132	-1.1138670077130767e-140	-7.664666030704839e-132

simplify2.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

580.0ms	2910×	body	80	nan
327.0ms	1026×	body	2560	valid
327.0ms	5865×	body	80	valid
301.0ms	907×	body	1280	valid
164.0ms	439×	body	640	valid
43.0ms	127×	body	5120	valid
35.0ms	245×	body	320	valid
10.0ms	110×	body	160	valid