Details

sample130.0ms

Algorithm

intervals

Results

38.0ms	26×	body	2560	valid
23.0ms	182×	body	80	valid
22.0ms	35×	body	1280	valid
12.0ms	91×	body	80	nan
7.0ms	15×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify156.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* -4 a) c (* b b))
0.1b	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.0b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
24.0b	(sqrt (fma (* -4 a) c (* b b)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`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`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
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` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma (* -4 a) c (* b b))
44.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
13.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma (* -4 a) c (* b b))
153.0ms	(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
107.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
112.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.6s

Counts

179 → 179

Iterations

Iter	Nodes
3	3080
2	1153
1	497
0	222

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
0.2b	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
1.0b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
24.0b	(sqrt (fma (* -4 a) c (* b b)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
186×	`times-frac`
130×	`add-cube-cbrt`
60×	`prod-diff`
50×	`sqrt-prod`
38×	`distribute-rgt-neg-in`
34×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
10×	`fma-neg`
8×	`div-exp` `add-log-exp`
7×	`neg-mul-1`
6×	`pow1` `flip3--` `div-inv` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `diff-log` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 290

Calls

4 calls:

25.0ms	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
25.0ms	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
14.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(/ a (- (- b) (sqrt (fma (* -4 a) c (* b b)))))
157.0ms	(/ 1 (/ a (- (- b) (sqrt (fma (* -4 a) c (* b b))))))
93.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
120.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify2.5s

Counts

302 → 302

Iterations

Iter	Nodes
3	5077
2	1881
1	785
0	340

prune4.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma c (* -4 a) (* b b))
0.1b	(/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) a)
1.0b	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
24.0b	(sqrt (fma c (* -4 a) (* b b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`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`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
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` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

0.0ms	(fma c (* -4 a) (* b b))
21.0ms	(/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) a)
11.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma c (* -4 a) (* b b))
114.0ms	(/ (- (- b) (sqrt (fma c (* -4 a) (* b b)))) a)
111.0ms	(- (- b) (sqrt (fma c (* -4 a) (* b b))))
96.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.7s

Counts

179 → 179

Iterations

Iter	Nodes
3	3033
2	1148
1	499
0	223

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (* -2 (/ c b)) 2)
0.0b	(* -2 (/ c b))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`times-frac` `associate-r`
12×	`*-un-lft-identity` `add-cube-cbrt`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-l*`
2×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l` `associate-/l/`

Counts

2 → 62

Calls

2 calls:

20.0ms	(/ (* -2 (/ c b)) 2)
22.0ms	(* -2 (/ c b))

series66.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (* -2 (/ c b)) 2)
32.0ms	(* -2 (/ c b))

simplify1.1s

Counts

68 → 68

Iterations

Iter	Nodes
3	2614
2	769
1	275
0	112

prune510.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.7b

regimes737.0ms

Accuracy

81.7% (6.2b remaining)

Error of 12.1b against oracle of 5.9b and baseline of 39.6b

bsearch326.0ms

Steps

Iters	Range		Point
6	2.332248586404817e+54	2.734436825826664e+55	2.6656023684116586e+55
5	6.064264318896163e-122	1.6648703498210103e-121	1.5983000936606613e-121
8	-7.174637898164774e-44	-1.9059117916534993e-48	-8.544460916074322e-48

simplify51.0ms

Iterations

Iter	Nodes
4	69
3	69
2	67
1	61
0	46

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.1s	5890×	body	80	valid
975.0ms	1042×	body	2560	valid
796.0ms	935×	body	1280	valid
528.0ms	203×	body	320	valid
475.0ms	2913×	body	80	nan
259.0ms	476×	body	640	valid
113.0ms	109×	body	5120	valid
29.0ms	107×	body	160	valid