Details

sample141.0ms

Algorithm

intervals

Results

39.0ms	184×	body	80	valid
30.0ms	36×	body	2560	valid
21.0ms	29×	body	1280	valid
11.0ms	77×	body	80	nan
6.0ms	10×	body	640	valid
6.0ms	10×	body	320	valid
4.0ms	4×	body	5120	valid
1.0ms	4×	body	160	valid

simplify130.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize30.0ms

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)))

rewrite32.0ms

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 (* (* a -4) c))) b) a)
13.0ms	(- (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)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
115.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
64.0ms	(fma b b (* (* a -4) c))
129.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
3	2626
2	950
1	405
0	180

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize23.0ms

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)))

rewrite47.0ms

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:

37.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
7.0ms	(- (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)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
138.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
88.0ms	(fma b b (* (* a -4) c))
104.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify3.3s

Counts

127 → 127

Iterations

Iter	Nodes
3	3169
2	1190
1	467
0	200

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize44.0ms

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)))

rewrite30.0ms

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:

18.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) 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)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
109.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
76.0ms	(fma b b (* (* a -4) c))
135.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
3	2626
2	950
1	405
0	180

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize22.0ms

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)))

rewrite56.0ms

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:

45.0ms	(* (- (sqrt (fma b b (* (* -4 a) c))) b) (/ 1 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)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (- (sqrt (fma b b (* (* -4 a) c))) b) (/ 1 a))
92.0ms	(- (sqrt (fma b b (* (* -4 a) c))) b)
74.0ms	(fma b b (* (* -4 a) c))
89.0ms	(sqrt (fma b b (* (* -4 a) c)))

simplify3.3s

Counts

127 → 127

Iterations

Iter	Nodes
3	3147
2	1186
1	466
0	200

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

regimes391.0ms

Accuracy

84.2% (4.4b remaining)

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

bsearch236.0ms

Steps

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

simplify5.0ms

Iterations

Iter	Nodes
2	30
1	30
0	26

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.1s	1114×	body	2560	valid
967.0ms	5824×	body	80	valid
712.0ms	912×	body	1280	valid
484.0ms	110×	body	5120	valid
384.0ms	2907×	body	80	nan
241.0ms	414×	body	640	valid
124.0ms	232×	body	320	valid
25.0ms	100×	body	160	valid