Details

sample73.0ms

Algorithm

intervals

Results

17.0ms	37×	body	2560	valid
14.0ms	191×	body	80	valid
11.0ms	30×	body	1280	valid
7.0ms	103×	body	80	nan
5.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
0.4b	(- (* b b) (* (* 3 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.3b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

85.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
11.0ms	(- (* b b) (* (* 3 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
63.0ms	(- (* b b) (* (* 3 a) c))
107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
82.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1430
1	442
0	170

prune530.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (fma b b (* c (* -3 a))))) (* 3 a))
0.5b	(fma b b (* c (* -3 a)))
1.6b	(+ (- b) (sqrt (fma b b (* c (* -3 a)))))
21.3b	(sqrt (fma b b (* c (* -3 a))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

43.0ms	(/ (+ (- b) (sqrt (fma b b (* c (* -3 a))))) (* 3 a))
0.0ms	(fma b b (* c (* -3 a)))
13.0ms	(+ (- b) (sqrt (fma b b (* c (* -3 a)))))
2.0ms	(sqrt (fma b b (* c (* -3 a))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (fma b b (* c (* -3 a))))) (* 3 a))
52.0ms	(fma b b (* c (* -3 a)))
93.0ms	(+ (- b) (sqrt (fma b b (* c (* -3 a)))))
81.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify2.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
3	4179
2	1112
1	367
0	149

prune378.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3 a))
0.4b	(- (* b b) (* (* 3 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.3b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sum-log` `flip3--` `sqrt-div` `1-exp` `pow-flip` `flip--` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `associate-+l-` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 94

Calls

4 calls:

21.0ms	(/ 1 (* 3 a))
18.0ms	(- (* b b) (* (* 3 a) c))
42.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1 (* 3 a))
69.0ms	(- (* b b) (* (* 3 a) c))
122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
110.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	4257
2	1121
1	380
0	155

prune532.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (* -3 a))
0.5b	(fma b b (* c (* -3 a)))
1.6b	(- (sqrt (fma b b (* c (* -3 a)))) b)
21.3b	(sqrt (fma b b (* c (* -3 a))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-r` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

27.0ms	(* c (* -3 a))
0.0ms	(fma b b (* c (* -3 a)))
18.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
2.0ms	(sqrt (fma b b (* c (* -3 a))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* c (* -3 a))
73.0ms	(fma b b (* c (* -3 a)))
105.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
84.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify2.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	2931
2	835
1	320
0	144

prune375.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

regimes489.0ms

Accuracy

87.7% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 32.0b

bsearch279.0ms

Steps

Iters	Range	Point
11	2.0729826645785407e+19	5.016256902410509e+38	1.6715468005080632e+36
6	5.248607558045132e-171	4.537764770085819e-170	1.4458951003956485e-170
8	-1.8800110361077525e+106	-1.0719713592587512e+102	-5.657184583194415e+105

Iters

Range

Point

2.0729826645785407e+19

5.016256902410509e+38

1.6715468005080632e+36

5.248607558045132e-171

4.537764770085819e-170

1.4458951003956485e-170

-1.8800110361077525e+106

-1.0719713592587512e+102

-5.657184583194415e+105

simplify10.0ms

Iterations

Iter	Nodes
done	46
1	46
0	39

end0.0ms

sample2.7s

Algorithm

intervals

Results

918.0ms	5915×	body	80	valid
550.0ms	1068×	body	2560	valid
312.0ms	837×	body	1280	valid
265.0ms	3076×	body	80	nan
122.0ms	463×	body	640	valid
119.0ms	123×	body	5120	valid
46.0ms	240×	body	320	valid
46.0ms	124×	body	160	valid