Details

sample200.0ms

Algorithm

intervals

Results

28.0ms	189×	body	80	valid
23.0ms	30×	body	2560	valid
18.0ms	30×	body	1280	valid
10.0ms	79×	body	80	nan
9.0ms	19×	body	640	valid
3.0ms	3×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	5×	body	160	valid

simplify97.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

96.0ms

(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize34.0ms

Local error

Found 4 expressions with local error:

19.3b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

Slowest

131.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
64.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

134.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
118.0ms	(sqrt (- (* b_2 b_2) (* a c)))
114.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
48.0ms	(- (* b_2 b_2) (* a c))

simplify5.8s

Counts

116 → 134

Calls

116 calls:

Slowest

569.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
357.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
306.0ms	(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))
305.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
228.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize46.0ms

Local error

Found 4 expressions with local error:

19.3b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `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 → 123

Calls

4 calls:

Slowest

151.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
38.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(- (* b_2 b_2) (* a c))

series392.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

125.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
124.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))
50.0ms	(- (* b_2 b_2) (* a c))

simplify6.9s

Counts

105 → 135

Calls

105 calls:

Slowest

960.0ms	(* (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
409.0ms	(* (+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (+ (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
354.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
321.0ms	(* (- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3)) (/ 1 a))
300.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize34.0ms

Local error

Found 4 expressions with local error:

19.3b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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 → 122

Calls

4 calls:

Slowest

76.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
52.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

series335.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

120.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
87.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))
52.0ms	(- (* b_2 b_2) (* a c))

simplify5.9s

Counts

116 → 134

Calls

116 calls:

Slowest

490.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
357.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
332.0ms	(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))
332.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
248.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize28.0ms

Local error

Found 4 expressions with local error:

19.3b	(sqrt (- (* b_2 b_2) (* a c)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 200

Calls

4 calls:

Slowest

58.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(- (* b_2 b_2) (* a c))

series425.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

156.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))
98.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
66.0ms	(- (* b_2 b_2) (* a c))

simplify22.9s

Counts

247 → 212

Calls

247 calls:

Slowest

590.0ms	(/ (* (* 1 1) 1) (/ (* (* a a) a) (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
424.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
372.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
370.0ms	(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
356.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.3b

regimes595.0ms

Accuracy

87.6% (3.5b remaining)

Error of 8.8b against oracle of 5.3b and baseline of 33.5b

bsearch372.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.1s	5827×	body	80	valid
810.0ms	1090×	body	2560	valid
791.0ms	2869×	body	80	nan
612.0ms	927×	body	1280	valid
238.0ms	479×	body	640	valid
116.0ms	107×	body	5120	valid
103.0ms	238×	body	320	valid
58.0ms	120×	body	160	valid