Details

sample86.0ms

Algorithm

intervals

Results

16.0ms	186×	body	80	valid
15.0ms	29×	body	2560	valid
10.0ms	24×	body	1280	valid
8.0ms	102×	body	80	nan
4.0ms	14×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	128
5	128
4	119
3	86
2	46
1	25
0	14

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

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` `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 → 90

Calls

4 calls:

68.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2115
1	450
0	167

prune653.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize54.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
3.5b	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
10.9b	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
22.9b	(sqrt (fma (* a c) (- 4.0) (* b b)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `div-inv` `flip--`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `diff-log` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 230

Calls

4 calls:

32.0ms	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
65.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
72.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
4.0ms	(sqrt (fma (* a c) (- 4.0) (* b b)))

series845.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
297.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
320.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
110.0ms	(sqrt (fma (* a c) (- 4.0) (* b b)))

simplify1.8s

Counts

242 → 242

Iterations

Iter	Nodes
done	5000
2	4024
1	778
0	319

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma b b (* (- a) (* 4.0 c)))
2.0b	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
15.8b	(/ (* (* 4.0 c) a) a)
22.9b	(sqrt (fma b b (* (- a) (* 4.0 c))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `times-frac` `div-exp` `prod-exp` `cbrt-unprod`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `div-inv` `flip--` `associate-/l*`

Counts

4 → 140

Calls

4 calls:

0.0ms	(fma b b (* (- a) (* 4.0 c)))
27.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
15.0ms	(/ (* (* 4.0 c) a) a)
1.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma b b (* (- a) (* 4.0 c)))
120.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
17.0ms	(/ (* (* 4.0 c) a) a)
125.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

simplify1.4s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	2590
1	505
0	212

prune684.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (* 4.0 c) 1) (- (- b) (sqrt (fma b b (* (- a) (* 4.0 c))))))
0.8b	(fma b b (* (- a) (* 4.0 c)))
2.0b	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
22.9b	(sqrt (fma b b (* (- a) (* 4.0 c))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

33.0ms	(/ (* (* 4.0 c) 1) (- (- b) (sqrt (fma b b (* (- a) (* 4.0 c))))))
0.0ms	(fma b b (* (- a) (* 4.0 c)))
26.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
2.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ (* (* 4.0 c) 1) (- (- b) (sqrt (fma b b (* (- a) (* 4.0 c))))))
60.0ms	(fma b b (* (- a) (* 4.0 c)))
115.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
131.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

simplify1.7s

Counts

164 → 164

Iterations

Iter	Nodes
done	5001
2	3133
1	568
0	229

prune768.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes346.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.8b

bsearch314.0ms

Steps

Iters	Range	Point
7	1.9371672431899034e+133	5.16149553175908e+134	3.9872679706944845e+133
10	-4.750525065312607e-249	-1.830196375340447e-262	-4.8285684223134326e-262
9	-3.792961868720521e+75	-7.261872368850313e+67	-3.5695008721667037e+75

Iters

Range

Point

1.9371672431899034e+133

5.16149553175908e+134

3.9872679706944845e+133

-4.750525065312607e-249

-1.830196375340447e-262

-4.8285684223134326e-262

-3.792961868720521e+75

-7.261872368850313e+67

-3.5695008721667037e+75

simplify20.0ms

Iterations

Iter	Nodes
done	76
4	76
3	74
2	62
1	54
0	42

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.0s	1054×	body	2560	valid
730.0ms	2946×	body	80	nan
715.0ms	5961×	body	80	valid
540.0ms	877×	body	1280	valid
138.0ms	455×	body	640	valid
63.0ms	97×	body	5120	valid
52.0ms	214×	body	320	valid
17.0ms	111×	body	160	valid