Details

sample145.0ms

Algorithm

intervals

Results

42.0ms	176×	body	80	valid
28.0ms	31×	body	2560	valid
21.0ms	30×	body	1280	valid
12.0ms	85×	body	80	nan
8.0ms	16×	body	640	valid
6.0ms	6×	body	5120	valid
4.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify121.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.2b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 156

Calls

3 calls:

35.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
5.0ms	(sqrt (fma (* -4 a) c (* b b)))

series294.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
95.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
107.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.4s

Counts

165 → 165

Iterations

Iter	Nodes
3	2842
2	1111
1	477
0	211

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
1.2b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
22.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`prod-diff`
53×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
12×	`add-exp-log`
11×	`times-frac`
10×	`fma-neg`
8×	`add-cbrt-cube`
7×	`neg-mul-1` `associate-l` `add-log-exp`
6×	`pow1`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `unswap-sqr`
2×	`frac-times` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

3 → 154

Calls

3 calls:

46.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series323.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
103.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
94.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.1s

Counts

163 → 163

Iterations

Iter	Nodes
3	3112
2	1319
1	538
0	230

prune856.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) a)
1.2b	(+ (sqrt (fma c (* -4 a) (* b b))) b)
22.9b	(sqrt (fma c (* -4 a) (* b b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
6×	`fma-def` `sqrt-prod`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `neg-mul-1`
3×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
2×	`flip3-+` `flip-+` `distribute-neg-frac` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `distribute-frac-neg` `div-inv`

Counts

3 → 107

Calls

3 calls:

24.0ms	(/ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) a)
7.0ms	(+ (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series330.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/ (- (+ (sqrt (fma c (* -4 a) (* b b))) b)) a)
106.0ms	(+ (sqrt (fma c (* -4 a) (* b b))) b)
126.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify826.0ms

Counts

116 → 116

Iterations

Iter	Nodes
3	2019
2	788
1	325
0	155

prune681.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize94.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (fma (* -4 a) c (* b b)))
22.9b	(sqrt (fma (* -4 a) c (* b b)))
23.5b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
62.2b	(fma (- (cbrt (sqrt (fma (* -4 a) c (* b b))))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b)))))))

rewrite3.0ms

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:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (fma (* -4 a) c (* b b)))
104.0ms	(sqrt (fma (* -4 a) c (* b b)))
183.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
653.0ms	(fma (- (cbrt (sqrt (fma (* -4 a) c (* b b))))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b)))))))

simplify2.1s

Counts

66 → 66

Iterations

Iter	Nodes
4	4777
3	1278
2	437
1	211
0	102

prune590.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

regimes338.0ms

Accuracy

81.7% (5.0b remaining)

Error of 10.7b against oracle of 5.7b and baseline of 33.2b

bsearch166.0ms

Steps

Iters	Range		Point
8	2.231296991249122e+66	2.5939819947174796e+69	2.559678284282607e+69
9	-2.273288360947074e-131	-1.9680749876012584e-137	-2.2415082771065304e-131

simplify12.0ms

Iterations

Iter	Nodes
3	39
2	39
1	36
0	27

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.3s	956×	body	1280	valid
1.1s	1048×	body	2560	valid
944.0ms	5790×	body	80	valid
922.0ms	2938×	body	80	nan
257.0ms	454×	body	640	valid
175.0ms	220×	body	320	valid
99.0ms	98×	body	5120	valid
29.0ms	105×	body	160	valid