Details

sample135.0ms

Algorithm

intervals

Results

33.0ms	32×	body	2560	valid
26.0ms	184×	body	80	valid
25.0ms	37×	body	1280	valid
13.0ms	108×	body	80	nan
8.0ms	15×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

62.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
62.0ms	(- (* b_2 b_2) (* a c))
95.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

187 → 187

Iterations

Iter	Nodes
3	4034
2	1423
1	576
0	248

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize41.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.4b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
18.0b	(- (* b_2 b_2) (* b_2 b_2))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
33×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `associate-+l-`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `distribute-rgt-out--` `pow1/2` `+-inverses` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 204

Calls

4 calls:

114.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
94.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms	(- (* b_2 b_2) (* b_2 b_2))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
149.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.0ms	(- (* b_2 b_2) (* b_2 b_2))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify852.0ms

Counts

216 → 216

Iterations

Iter	Nodes
2	2029
1	786
0	327

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ a (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
14.9b	(/ a (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`div-exp`
13×	`prod-exp`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `cbrt-undiv`
6×	`times-frac` `associate-/l*` `add-log-exp`
5×	`associate-/r/` `cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`sqrt-prod`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-l/` `div-inv` `pow-flip`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-*r/` `inv-pow`

Counts

4 → 103

Calls

4 calls:

130.0ms	(/ 1 (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ a (* a c))))
14.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ a (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ a (* a c))))
44.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(/ a (* a c))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify6.4s

Counts

115 → 115

Iterations

Iter	Nodes
3	8574
2	1629
1	473
0	198

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite95.0ms

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 121

Calls

4 calls:

34.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
37.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
36.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

133 → 133

Iterations

Iter	Nodes
3	3023
2	1006
1	405
0	191

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

regimes431.0ms

Accuracy

94.5% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 29.1b

bsearch259.0ms

Steps

Iters	Range	Point
9	1.9710174875302874e+32	1.945305249879839e+37	5.3869004057037945e+35
6	-1.0679744695448512e-282	-9.594308287007325e-284	-9.739621771792007e-284
8	-3.568388406125044e+108	-1.2407302225025659e+104	-2.4629151126589693e+107

Iters

Range

Point

1.9710174875302874e+32

1.945305249879839e+37

5.3869004057037945e+35

-1.0679744695448512e-282

-9.594308287007325e-284

-9.739621771792007e-284

-3.568388406125044e+108

-1.2407302225025659e+104

-2.4629151126589693e+107

simplify5.0ms

Iterations

Iter	Nodes
2	35
1	35
0	31

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.0s	945×	body	1280	valid
863.0ms	988×	body	2560	valid
832.0ms	5915×	body	80	valid
355.0ms	2876×	body	80	nan
233.0ms	477×	body	640	valid
94.0ms	111×	body	5120	valid
64.0ms	190×	body	320	valid
26.0ms	114×	body	160	valid