Details

sample125.0ms

Algorithm

intervals

Results

42.0ms	183×	body	80	valid
22.0ms	36×	body	1280	valid
22.0ms	31×	body	2560	valid
10.0ms	88×	body	80	nan
5.0ms	11×	body	640	valid
3.0ms	8×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	3×	body	160	valid

simplify143.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.0b	(- (* b b) (* 4 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
21.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

102.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
15.0ms	(- (* b b) (* 4 (* a c)))
19.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
55.0ms	(- (* b b) (* 4 (* a c)))
101.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
121.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify5.3s

Counts

173 → 173

Iterations

Iter	Nodes
3	6002
2	1722
1	597
0	239

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma (* a -4) c (* b b)))) (* 2 a))
1.1b	(- (- b) (sqrt (fma (* a -4) c (* b b))))
21.0b	(sqrt (fma (* a -4) c (* b b)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 142

Calls

3 calls:

47.0ms	(/ (- (- b) (sqrt (fma (* a -4) c (* b b)))) (* 2 a))
15.0ms	(- (- b) (sqrt (fma (* a -4) c (* b b))))
1.0ms	(sqrt (fma (* a -4) c (* b b)))

series304.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(/ (- (- b) (sqrt (fma (* a -4) c (* b b)))) (* 2 a))
107.0ms	(- (- b) (sqrt (fma (* a -4) c (* b b))))
93.0ms	(sqrt (fma (* a -4) c (* b b)))

simplify2.6s

Counts

151 → 151

Iterations

Iter	Nodes
3	4325
2	1264
1	480
0	203

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.4b

localize39.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (fma (* a -4) c (* b b))))
21.0b	(sqrt (fma (* a -4) c (* b b)))
21.0b	(sqrt (fma (* a -4) c (* b b)))
21.0b	(sqrt (fma (* a -4) c (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--`

Counts

4 → 139

Calls

4 calls:

21.0ms	(- (- b) (sqrt (fma (* a -4) c (* b b))))
3.0ms	(sqrt (fma (* a -4) c (* b b)))
3.0ms	(sqrt (fma (* a -4) c (* b b)))
3.0ms	(sqrt (fma (* a -4) c (* b b)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (- b) (sqrt (fma (* a -4) c (* b b))))
101.0ms	(sqrt (fma (* a -4) c (* b b)))
85.0ms	(sqrt (fma (* a -4) c (* b b)))
98.0ms	(sqrt (fma (* a -4) c (* b b)))

simplify4.1s

Counts

151 → 151

Iterations

Iter	Nodes
4	4991
3	1619
2	644
1	315
0	146

prune2.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.4b

localize37.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (fma (* a -4) c (* b b))))
21.0b	(sqrt (fma (* a -4) c (* b b)))
21.0b	(sqrt (fma (* a -4) c (* b b)))
21.0b	(sqrt (fma (* a -4) c (* b b)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--`

Counts

4 → 139

Calls

4 calls:

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

series461.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b) (sqrt (fma (* a -4) c (* b b))))
126.0ms	(sqrt (fma (* a -4) c (* b b)))
110.0ms	(sqrt (fma (* a -4) c (* b b)))
123.0ms	(sqrt (fma (* a -4) c (* b b)))

simplify4.3s

Counts

151 → 151

Iterations

Iter	Nodes
4	4991
3	1619
2	644
1	315
0	146

prune2.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.4b

regimes510.0ms

Accuracy

80% (5.5b remaining)

Error of 11.0b against oracle of 5.5b and baseline of 33.1b

bsearch489.0ms

Steps

Iters	Range		Point
9	1.7155709022758137e+74	7.648947555279674e+80	7.377921431051488e+75
10	-5.748517768285075e-159	-5.469432343389951e-172	-4.884190020998732e-159
8	-2.6710027588265904e-98	-8.066445726472055e-102	-5.61762387795767e-100
8	-2.1713506125136832e-64	-5.235448662345934e-68	-2.7503548021140933e-65

simplify19.0ms

Iterations

Iter	Nodes
3	47
2	47
1	45
0	38

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.1s	1092×	body	2560	valid
1.1s	866×	body	1280	valid
909.0ms	5873×	body	80	valid
370.0ms	2901×	body	80	nan
233.0ms	418×	body	640	valid
122.0ms	107×	body	5120	valid
120.0ms	238×	body	320	valid
32.0ms	127×	body	160	valid