Details

sample320.0ms

Algorithm

intervals

Results

30.0ms	9×	body	640	valid
21.0ms	177×	body	80	valid
19.0ms	32×	body	2560	valid
19.0ms	38×	body	1280	valid
8.0ms	90×	body	80	nan
5.0ms	7×	body	5120	valid
3.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify6.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize113.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

192.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
39.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify86.0ms

Counts: 103 → 103

prune517.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.6b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.2b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-/l*`
10×	`sqrt-prod` `associate-/r/`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 127

Calls

4 calls:

82.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
127.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
86.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series758.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
252.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
293.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Counts: 139 → 139

prune517.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
0.5b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `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` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

16.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
59.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
141.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
85.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Counts: 166 → 166

prune571.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.7b

localize35.0ms

Local error

Found 4 expressions with local error:

5.5b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
8.6b	(/ (* a c) (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))
15.5b	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`log-prod` `exp-sum`
10×	`add-cube-cbrt`
9×	`add-exp-log` `sqrt-prod` `add-cbrt-cube` `difference-of-squares`
7×	`pow1` `times-frac` `associate-/r*`
6×	`exp-prod` `add-log-exp`
4×	`flip3--` `sqrt-div` `flip--`
3×	`log-pow` `distribute-lft-out--`
2×	`cbrt-undiv` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `div-exp` `associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `rem-exp-log` `associate-/l*`

Counts

4 → 84

Calls

4 calls:

13.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
104.0ms	(/ (* a c) (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))
110.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
30.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series619.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
269.0ms	(/ (* a c) (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2))
133.0ms	(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
123.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Counts: 96 → 96

prune347.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.7b

regimes254.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 30.2b

bsearch215.0ms

Steps

Iters	Range		Point
9	1.126266178272183e+86	9.307219265615864e+90	7.493206037388171e+90
10	9.421053113373393e-302	2.626961042225499e-286	3.113957299494927e-289
7	-1.307088067977472e+71	-1.0608558557274316e+69	-1.2770913942233635e+71

simplify569.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

866.0ms	909×	body	1280	valid
588.0ms	1106×	body	2560	valid
586.0ms	5837×	body	80	valid
232.0ms	2929×	body	80	nan
138.0ms	100×	body	5120	valid
123.0ms	463×	body	640	valid
46.0ms	246×	body	320	valid
16.0ms	121×	body	160	valid