Details

sample121.0ms

Algorithm

intervals

Results

28.0ms	28×	body	1280	valid
19.0ms	35×	body	2560	valid
16.0ms	188×	body	80	valid
7.0ms	85×	body	80	nan
4.0ms	14×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	5×	body	5120	valid
1.0ms	4×	body	160	valid

simplify334.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	79
2	43
1	25
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite244.0ms

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:

182.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(- (* b b) (* (* 4.0 a) c))
31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series670.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(- (* b b) (* (* 4.0 a) c))
173.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
160.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1452
1	445
0	171

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

208.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
18.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series705.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
84.0ms	(- (* b b) (* (* 4.0 a) c))
156.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
157.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.7s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	1956
1	522
0	198

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 c) a))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
21.2b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 110

Calls

4 calls:

154.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) (* 2.0 a))
13.0ms	(- (* b b) (* (* 4.0 c) a))
101.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
18.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) (* 2.0 a))
77.0ms	(- (* b b) (* (* 4.0 c) a))
166.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
125.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify3.1s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1661
1	525
0	199

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.7b

localize80.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
1.6b	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
21.2b	(sqrt (- (* b b) (* (* 4.0 c) a)))
21.2b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 120

Calls

4 calls:

87.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
72.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
22.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))
24.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
156.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
113.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))
134.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify5.0s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
3	2850
2	773
1	295
0	115

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.7b

regimes624.0ms

Accuracy

89.2% (3.2b remaining)

Error of 8.5b against oracle of 5.4b and baseline of 34.7b

bsearch230.0ms

Steps

Iters	Range	Point
7	3.170449429657488e+21	2.218413533118306e+23	1.2320326028736612e+23
6	1.5727591416233446e-143	1.789606490082599e-142	2.1777947371956335e-143
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-1.2705286994550075e+152

Iters

Range

Point

3.170449429657488e+21

2.218413533118306e+23

1.2320326028736612e+23

1.5727591416233446e-143

1.789606490082599e-142

2.1777947371956335e-143

-1.3198903247987554e+155

-1.1250773400730914e+152

-1.2705286994550075e+152

simplify16.0ms

Iterations

Iter	Nodes
done	47
1	47
0	39

end0.0ms

sample2.8s

Algorithm

intervals

Results

785.0ms	5804×	body	80	valid
634.0ms	932×	body	1280	valid
606.0ms	1083×	body	2560	valid
153.0ms	2988×	body	80	nan
102.0ms	489×	body	640	valid
72.0ms	107×	body	5120	valid
37.0ms	247×	body	320	valid
12.0ms	121×	body	160	valid