Details

sample140.0ms

Algorithm

intervals

Results

33.0ms	34×	body	2560	valid
31.0ms	198×	body	80	valid
28.0ms	29×	body	1280	valid
14.0ms	91×	body	80	nan
5.0ms	8×	body	640	valid
4.0ms	7×	body	320	valid
2.0ms	2×	body	5120	valid
2.0ms	6×	body	160	valid

simplify95.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a -4) c)
1.3b	(- (sqrt (fma b b (* (* a -4) c))) b)
1.5b	(fma b b (* (* a -4) c))
27.8b	(sqrt (fma b b (* (* a -4) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

16.0ms	(* (* a -4) c)
12.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms	(fma b b (* (* a -4) c))
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* a -4) c)
104.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
62.0ms	(fma b b (* (* a -4) c))
100.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
3	2785
2	831
1	319
0	146

prune740.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
1.3b	(- (sqrt (fma b b (* -4 (* a c)))) b)
1.5b	(fma b b (* -4 (* a c)))
27.8b	(sqrt (fma b b (* -4 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

16.0ms	(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
7.0ms	(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms	(fma b b (* -4 (* a c)))
1.0ms	(sqrt (fma b b (* -4 (* a c))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
87.0ms	(- (sqrt (fma b b (* -4 (* a c)))) b)
58.0ms	(fma b b (* -4 (* a c)))
86.0ms	(sqrt (fma b b (* -4 (* a c))))

simplify848.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	2588
2	951
1	403
0	179

prune712.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
1.3b	(- (sqrt (fma b b (* -4 (* a c)))) b)
1.5b	(fma b b (* -4 (* a c)))
27.8b	(sqrt (fma b b (* -4 (* a c))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 115

Calls

4 calls:

26.0ms	(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
8.0ms	(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms	(fma b b (* -4 (* a c)))
1.0ms	(sqrt (fma b b (* -4 (* a c))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
102.0ms	(- (sqrt (fma b b (* -4 (* a c)))) b)
51.0ms	(fma b b (* -4 (* a c)))
82.0ms	(sqrt (fma b b (* -4 (* a c))))

simplify2.5s

Counts

127 → 127

Iterations

Iter	Nodes
3	3135
2	1185
1	465
0	199

prune917.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
1.3b	(- (sqrt (fma b b (* -4 (* a c)))) b)
1.5b	(fma b b (* -4 (* a c)))
27.8b	(sqrt (fma b b (* -4 (* a c))))

rewrite33.0ms

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*`
18×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
7×	`div-exp`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 192

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
13.0ms	(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms	(fma b b (* -4 (* a c)))
1.0ms	(sqrt (fma b b (* -4 (* a c))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
135.0ms	(- (sqrt (fma b b (* -4 (* a c)))) b)
75.0ms	(fma b b (* -4 (* a c)))
119.0ms	(sqrt (fma b b (* -4 (* a c))))

simplify4.5s

Counts

204 → 204

Iterations

Iter	Nodes
3	3963
2	1464
1	644
0	283

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.7b

regimes283.0ms

Accuracy

82.4% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.5b

bsearch172.0ms

Steps

Iters	Range		Point
8	2.764110880089542e-64	2.3245141193625934e-60	2.0617732603635578e-61
9	-229886301330938.94	-710549284.1101115	-227369802444031.66

simplify5.0ms

Iterations

Iter	Nodes
2	32
1	32
0	28

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.2s	5886×	body	80	valid
850.0ms	1054×	body	2560	valid
694.0ms	908×	body	1280	valid
463.0ms	232×	body	320	valid
429.0ms	2993×	body	80	nan
208.0ms	446×	body	640	valid
126.0ms	110×	body	5120	valid
26.0ms	113×	body	160	valid