Details

sample115.0ms

Algorithm

intervals

Results

42.0ms	36×	body	2560	valid
21.0ms	184×	body	80	valid
16.0ms	29×	body	1280	valid
8.0ms	77×	body	80	nan
5.0ms	10×	body	640	valid
3.0ms	10×	body	320	valid
3.0ms	4×	body	5120	valid
1.0ms	4×	body	160	valid

simplify119.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
1.1b	(- (sqrt (fma b b (* (* a -4) c))) b)
1.5b	(fma b b (* (* a -4) c))
23.1b	(sqrt (fma b b (* (* a -4) c)))

rewrite40.0ms

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:

17.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
19.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms	(fma b b (* (* a -4) c))
3.0ms	(sqrt (fma b b (* (* a -4) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
111.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
56.0ms	(fma b b (* (* a -4) c))
131.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.1s

Counts

126 → 126

Iterations

Iter	Nodes
3	2626
2	950
1	405
0	180

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
1.1b	(- (sqrt (fma b b (* (* a -4) c))) b)
1.5b	(fma b b (* (* a -4) c))
23.1b	(sqrt (fma b b (* (* a -4) c)))

rewrite55.0ms

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:

44.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms	(fma b b (* (* a -4) c))
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
112.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
88.0ms	(fma b b (* (* a -4) c))
118.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify3.0s

Counts

127 → 127

Iterations

Iter	Nodes
3	3169
2	1190
1	467
0	200

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* -4 a) c))) b) a)
1.1b	(- (sqrt (fma b b (* (* -4 a) c))) b)
1.5b	(fma b b (* (* -4 a) c))
23.1b	(sqrt (fma b b (* (* -4 a) c)))

rewrite42.0ms

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:

23.0ms	(/ (- (sqrt (fma b b (* (* -4 a) c))) b) a)
14.0ms	(- (sqrt (fma b b (* (* -4 a) c))) b)
0.0ms	(fma b b (* (* -4 a) c))
2.0ms	(sqrt (fma b b (* (* -4 a) c)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (- (sqrt (fma b b (* (* -4 a) c))) b) a)
124.0ms	(- (sqrt (fma b b (* (* -4 a) c))) b)
70.0ms	(fma b b (* (* -4 a) c))
106.0ms	(sqrt (fma b b (* (* -4 a) c)))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
3	2638
2	952
1	404
0	180

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma b b (* (* -4 a) c))) b) (/ 1 a))
1.1b	(- (sqrt (fma b b (* (* -4 a) c))) b)
1.5b	(fma b b (* (* -4 a) c))
23.1b	(sqrt (fma b b (* (* -4 a) c)))

rewrite53.0ms

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:

27.0ms	(* (- (sqrt (fma b b (* (* -4 a) c))) b) (/ 1 a))
21.0ms	(- (sqrt (fma b b (* (* -4 a) c))) b)
0.0ms	(fma b b (* (* -4 a) c))
2.0ms	(sqrt (fma b b (* (* -4 a) c)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (- (sqrt (fma b b (* (* -4 a) c))) b) (/ 1 a))
148.0ms	(- (sqrt (fma b b (* (* -4 a) c))) b)
85.0ms	(fma b b (* (* -4 a) c))
90.0ms	(sqrt (fma b b (* (* -4 a) c)))

simplify3.4s

Counts

127 → 127

Iterations

Iter	Nodes
3	3147
2	1186
1	466
0	200

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

regimes344.0ms

Accuracy

84.2% (4.4b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 33.4b

bsearch247.0ms

Steps

Iters	Range		Point
10	8.951341119180922e-71	6.02619389320856e-56	3.289226058156428e-70
8	-5.520406447692031e+155	-8.116303404487084e+152	-4.82289647433212e+153

simplify8.0ms

Iterations

Iter	Nodes
2	30
1	30
0	26

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.0s	5824×	body	80	valid
989.0ms	1114×	body	2560	valid
650.0ms	912×	body	1280	valid
548.0ms	414×	body	640	valid
334.0ms	2907×	body	80	nan
130.0ms	232×	body	320	valid
124.0ms	110×	body	5120	valid
22.0ms	100×	body	160	valid