Details

sample160.0ms

Algorithm

intervals

Results

36.0ms	36×	body	2560	valid
32.0ms	86×	body	80	nan
32.0ms	187×	body	80	valid
21.0ms	25×	body	1280	valid
11.0ms	17×	body	640	valid
4.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify136.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.9b	(- (sqrt (fma b b (* (* a -4) c))) b)
1.0b	(fma b b (* (* a -4) c))
23.5b	(sqrt (fma b b (* (* a -4) c)))

rewrite36.0ms

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:

22.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
11.0ms	(- (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)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
93.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
80.0ms	(fma b b (* (* a -4) c))
82.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
3	2626
2	950
1	405
0	180

prune632.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
0.9b	(- (sqrt (fma b b (* (* a -4) c))) b)
1.0b	(fma b b (* (* a -4) c))
23.5b	(sqrt (fma b b (* (* a -4) c)))

rewrite59.0ms

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))
11.0ms	(- (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)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
119.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
62.0ms	(fma b b (* (* a -4) c))
102.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify3.3s

Counts

127 → 127

Iterations

Iter	Nodes
3	3169
2	1190
1	467
0	200

prune575.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.4b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma b b (* (* a -4) c))
1.0b	(fma b b (* (* a -4) c))
23.5b	(sqrt (fma b b (* (* a -4) c)))
23.5b	(sqrt (fma b b (* (* a -4) c)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

0.0ms	(fma b b (* (* a -4) c))
0.0ms	(fma b b (* (* a -4) c))
2.0ms	(sqrt (fma b b (* (* a -4) c)))
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma b b (* (* a -4) c))
65.0ms	(fma b b (* (* a -4) c))
105.0ms	(sqrt (fma b b (* (* a -4) c)))
105.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.0s

Counts

66 → 66

Iterations

Iter	Nodes
4	2419
3	634
2	216
1	92
0	49

prune491.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.4b

localize64.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (fma b b (* (* a -4) c)))
24.2b	(cbrt (fma b b (* (* a -4) c)))
24.2b	(cbrt (fma b b (* (* a -4) c)))
24.2b	(cbrt (fma b b (* (* a -4) c)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

1.0ms	(sqrt (fma b b (* (* a -4) c)))
1.0ms	(cbrt (fma b b (* (* a -4) c)))
1.0ms	(cbrt (fma b b (* (* a -4) c)))
1.0ms	(cbrt (fma b b (* (* a -4) c)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt (fma b b (* (* a -4) c)))
158.0ms	(cbrt (fma b b (* (* a -4) c)))
143.0ms	(cbrt (fma b b (* (* a -4) c)))
145.0ms	(cbrt (fma b b (* (* a -4) c)))

simplify3.0s

Counts

70 → 70

Iterations

Iter	Nodes
5	4129
4	1643
3	759
2	324
1	147
0	72

prune639.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.4b

regimes417.0ms

Accuracy

84.2% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 32.9b

bsearch255.0ms

Steps

Iters	Range		Point
8	5.833527798943191e-77	3.6732813120885656e-72	3.1295384133612364e-73
9	-2.2174027590176242e+73	-8.164533525332822e+65	-3.063397748446981e+71

simplify10.0ms

Iterations

Iter	Nodes
2	33
1	33
0	28

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	1026×	body	2560	valid
1.4s	5891×	body	80	valid
687.0ms	881×	body	1280	valid
373.0ms	2954×	body	80	nan
282.0ms	464×	body	640	valid
145.0ms	237×	body	320	valid
110.0ms	96×	body	5120	valid
27.0ms	104×	body	160	valid