Details

sample166.0ms

Algorithm

intervals

Results

19.0ms	39×	body	2560	valid
15.0ms	189×	body	80	valid
11.0ms	29×	body	1280	valid
8.0ms	87×	body	80	nan
4.0ms	15×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid

simplify66.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize20.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

Slowest

56.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
37.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series301.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

99.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))
76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms	(- (* b_2 b_2) (* a c))

simplify919.0ms

Counts: 100 → 100

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.8b

localize39.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `insert-posit16` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

Slowest

152.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(- (* b_2 b_2) (* a c))

series386.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

120.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))
98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms	(- (* b_2 b_2) (* a c))

simplify1.5s

Counts: 101 → 101

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize26.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

Slowest

56.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
39.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series772.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

519.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(- (* b_2 b_2) (* a c))

simplify957.0ms

Counts: 100 → 100

prune953.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

localize39.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b_2 b_2) (* a c)))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(- (* b_2 b_2) (* a c))
0.1b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 166

Calls

4 calls:

Slowest

77.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(- (* b_2 b_2) (* a c))

series461.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

187.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
115.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(- (* b_2 b_2) (* a c))

simplify683.0ms

Counts: 178 → 178

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.8b

regimes328.0ms

Accuracy

83.1% (4.5b remaining)

Error of 10.5b against oracle of 5.9b and baseline of 32.9b

bsearch135.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	1070×	body	2560	valid
857.0ms	5900×	body	80	valid
592.0ms	865×	body	1280	valid
291.0ms	2865×	body	80	nan
224.0ms	459×	body	640	valid
104.0ms	102×	body	5120	valid
87.0ms	208×	body	320	valid
57.0ms	113×	body	160	valid