Details

sample243.0ms

Algorithm

intervals

Results

53.0ms	191×	body	80	valid
13.0ms	25×	body	2560	valid
13.0ms	26×	body	1280	valid
9.0ms	18×	body	640	valid
8.0ms	92×	body	80	nan
4.0ms	6×	body	5120	valid
3.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify129.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize77.0ms

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))
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite155.0ms

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:

101.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
24.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
130.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify720.0ms

Counts: 92 → 92

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.1b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.4b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite298.0ms

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:

41.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
126.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
97.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
229.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
247.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts: 218 → 218

prune848.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* c a))))
2.0b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a) c)
2.1b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a) c)) a)
24.3b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite638.0ms

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:

48.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* c a))))
104.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a) c)
193.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a) c)) a)
11.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* c a))))
144.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a) c)
149.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a) c)) a)
89.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify1.6s

Counts: 1160 → 1160

prune4.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize33.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b_2) (sqrt (- (* b_2 b_2) (* c a))))
2.1b	(/ (/ 1 (/ (/ 1 1) (/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a)))) a)
2.1b	(/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a))
24.3b	(sqrt (- (* b_2 b_2) (* c a)))

rewrite6.3s

Algorithm

rewrite-expression-head

Rules

64767×	`times-frac`
29005×	`add-sqr-sqrt`
29004×	`*-un-lft-identity`
23336×	`add-cube-cbrt`
3143×	`associate-/l*`
2834×	`distribute-lft-out--` `difference-of-squares`
1606×	`div-inv`
1420×	`sqrt-prod`
1417×	`distribute-rgt-neg-in`
282×	`add-exp-log`
276×	`div-exp`
173×	`associate-/r/`
67×	`1-exp`
47×	`add-cbrt-cube`
40×	`rec-exp`
33×	`cbrt-undiv`
28×	`associate-/r*`
8×	`add-log-exp`
5×	`pow1`
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` `neg-log` `associate-/l/`

Counts

4 → 12800

Calls

4 calls:

38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* c a))))
1.8s	(/ (/ 1 (/ (/ 1 1) (/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a)))) a)
71.0ms	(/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a))
9.0ms	(sqrt (- (* b_2 b_2) (* c a)))

series1.3s

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* c a))))
267.0ms	(/ (/ 1 (/ (/ 1 1) (/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a)))) a)
822.0ms	(/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a))
114.0ms	(sqrt (- (* b_2 b_2) (* c a)))

simplify16.8s

Counts: 12812 → 12812

prune59.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.9b

regimes295.0ms

Accuracy

89.5% (2.8b remaining)

Error of 8.2b against oracle of 5.4b and baseline of 32.5b

bsearch263.0ms

Steps

Iters	Range	Point
10	1.1938117014962488e+94	7.783906932586822e+104	1.0868429336526664e+97
8	-1.373264203576674e-281	-7.437867491150874e-285	-1.4869025490520644e-284
7	-5.5142323965594324e+122	-4.933114397868945e+120	-7.617481894797657e+121

Iters

Range

Point

1.1938117014962488e+94

7.783906932586822e+104

1.0868429336526664e+97

-1.373264203576674e-281

-7.437867491150874e-285

-1.4869025490520644e-284

-5.5142323965594324e+122

-4.933114397868945e+120

-7.617481894797657e+121

simplify727.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

807.0ms	5781×	body	80	valid
603.0ms	1066×	body	2560	valid
290.0ms	894×	body	1280	valid
248.0ms	2846×	body	80	nan
187.0ms	502×	body	640	valid
51.0ms	118×	body	5120	valid
40.0ms	233×	body	320	valid
12.0ms	108×	body	160	valid