Details

sample156.0ms

Algorithm

intervals

Results

20.0ms	43×	body	2560	valid
14.0ms	185×	body	80	valid
11.0ms	25×	body	1280	valid
9.0ms	119×	body	80	nan
3.0ms	5×	body	5120	valid
3.0ms	10×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify57.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.2b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite181.0ms

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:

94.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
49.0ms	(- (* b_2 b_2) (* a c))
105.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts: 92 → 92

prune415.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.0b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite303.0ms

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:

36.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
106.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
118.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
205.0ms	(/ (/ (+ 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)))))
110.0ms	(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: 6.1b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.3b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.8b	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp` `sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`cbrt-undiv`
8×	`add-log-exp`
6×	`prod-exp` `div-inv`
5×	`pow1`
4×	`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 → 180

Calls

4 calls:

23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
40.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
269.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
250.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts: 192 → 192

prune632.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.5b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.8b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
26.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite591.0ms

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))))
89.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
202.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
27.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
129.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
178.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
92.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts: 1160 → 1160

prune4.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

regimes320.0ms

Accuracy

89.3% (2.9b remaining)

Error of 8.3b against oracle of 5.5b and baseline of 32.5b

bsearch227.0ms

Steps

Iters	Range		Point
9	555.6593536559827	215074437.79861602	148410.07195430735
9	-1.8468183666089936e-283	-2.8481806021794936e-290	-4.603808643431252e-290
6	-5.879772917858402e+57	-1.39221916616404e+57	-5.004804434998936e+57

simplify1.2s

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	5799×	body	80	valid
555.0ms	1146×	body	2560	valid
303.0ms	859×	body	1280	valid
238.0ms	3012×	body	80	nan
106.0ms	439×	body	640	valid
65.0ms	126×	body	5120	valid
62.0ms	113×	body	160	valid
44.0ms	242×	body	320	valid