Details

sample251.0ms

Algorithm

intervals

Results

37.0ms	44×	body	2560	valid
28.0ms	174×	body	80	valid
23.0ms	32×	body	1280	valid
13.0ms	96×	body	80	nan
10.0ms	17×	body	640	valid
8.0ms	7×	body	5120	valid
3.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify85.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize35.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b_2 b_2) (* a c)))
0.8b	(- (* b_2 b_2) (* a c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite178.0ms

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

102.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
55.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series421.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

134.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
117.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
104.0ms	(sqrt (- (* b_2 b_2) (* a c)))
66.0ms	(- (* b_2 b_2) (* a c))

simplify1.0s

Counts: 100 → 100

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize40.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b_2 b_2) (* a c)))
0.8b	(- (* b_2 b_2) (* a c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite179.0ms

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

91.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
60.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(- (* b_2 b_2) (* a c))

series342.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

125.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
89.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))
47.0ms	(- (* b_2 b_2) (* a c))

simplify1.2s

Counts: 100 → 100

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

localize34.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b_2 b_2) (* a c)))
0.8b	(- (* b_2 b_2) (* a c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite126.0ms

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

49.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
48.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

228.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
133.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))
51.0ms	(- (* b_2 b_2) (* a c))

simplify837.0ms

Counts: 178 → 178

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

localize53.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b_2 b_2) (* a c)))
0.8b	(- (* b_2 b_2) (* a c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.3b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

Slowest

120.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
45.0ms	(- (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))

series405.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

138.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
111.0ms	(sqrt (- (* b_2 b_2) (* a c)))
97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(- (* b_2 b_2) (* a c))

simplify1.8s

Counts: 104 → 104

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.7b

regimes399.0ms

Accuracy

82.5% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 32.8b

bsearch193.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.3s	1066×	body	2560	valid
812.0ms	5944×	body	80	valid
599.0ms	881×	body	1280	valid
372.0ms	2791×	body	80	nan
275.0ms	423×	body	640	valid
135.0ms	112×	body	5120	valid
69.0ms	213×	body	320	valid
22.0ms	106×	body	160	valid