Details

sample213.0ms

Algorithm

intervals

Results

22.0ms	194×	body	80	valid
22.0ms	35×	body	2560	valid
15.0ms	28×	body	1280	valid
7.0ms	79×	body	80	nan
5.0ms	11×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	4×	body	160	valid

simplify121.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

120.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize21.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite213.0ms

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

89.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
78.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(- (* b_2 b_2) (* a c))

series391.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

119.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))
105.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms	(- (* b_2 b_2) (* a c))

simplify5.9s

Counts

116 → 134

Calls

116 calls:

Slowest

483.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
431.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
340.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
250.0ms	(/ (* (* (- (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))
240.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

localize16.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite214.0ms

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

105.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
76.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

141.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
94.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))
46.0ms	(- (* b_2 b_2) (* a c))

simplify6.0s

Counts

116 → 134

Calls

116 calls:

Slowest

508.0ms	(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
370.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
361.0ms	(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
305.0ms	(/ (* (* (- (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))
293.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.5b

localize45.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 120

Calls

4 calls:

Slowest

56.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
49.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
120.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.9s

Counts

120 → 132

Calls

120 calls:

Slowest

388.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
302.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
296.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
271.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
253.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.5b

localize46.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b_2 b_2) (* a c)))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 120

Calls

4 calls:

Slowest

72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
46.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify5.9s

Counts

120 → 132

Calls

120 calls:

Slowest

388.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
333.0ms	(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
289.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
249.0ms	(- b_2 (* 1/2 (/ (* a c) b_2)))
221.0ms	(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.7s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.5b

regimes374.0ms

Accuracy

83.9% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 33.1b

bsearch112.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	5880×	body	80	valid
788.0ms	1024×	body	2560	valid
622.0ms	950×	body	1280	valid
327.0ms	2988×	body	80	nan
185.0ms	437×	body	640	valid
113.0ms	109×	body	5120	valid
90.0ms	226×	body	320	valid
50.0ms	121×	body	160	valid