Details

sample78.0ms

Algorithm

intervals

Results

14.0ms	40×	body	2560	valid
13.0ms	183×	body	80	valid
11.0ms	35×	body	1280	valid
5.0ms	79×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	2×	body	320	valid

simplify91.0ms

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: 35.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite135.0ms

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:

62.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
38.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
58.0ms	(- (* b b) (* (* 4.0 a) c))
122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2115
1	450
0	167

prune646.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.7b

localize31.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
3.6b	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
7.8b	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
24.2b	(sqrt (fma (* a c) (- 4.0) (* b b)))

rewrite170.0ms

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:

18.0ms	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
83.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
1.0ms	(sqrt (fma (* a c) (- 4.0) (* b b)))

series821.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))
265.0ms	(/ (/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b))))) (* 2.0 a))
286.0ms	(/ (+ 0 (* (* 4.0 c) a)) (- (- b) (sqrt (fma (* a c) (- 4.0) (* b b)))))
128.0ms	(sqrt (fma (* a c) (- 4.0) (* b b)))

simplify1.8s

Counts

242 → 242

Iterations

Iter	Nodes
done	5000
2	4024
1	778
0	319

prune964.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma b b (* (- a) (* 4.0 c)))
1.6b	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
11.6b	(/ (* (* 4.0 c) a) a)
24.2b	(sqrt (fma b b (* (- a) (* 4.0 c))))

rewrite57.0ms

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)))
16.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
33.0ms	(/ (* (* 4.0 c) a) a)
3.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma b b (* (- a) (* 4.0 c)))
111.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
11.0ms	(/ (* (* 4.0 c) a) a)
106.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

simplify1.2s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	2590
1	505
0	212

prune453.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 c) (- (- b) (sqrt (fma b b (* (- a) (* 4.0 c))))))
0.3b	(fma b b (* (- a) (* 4.0 c)))
1.6b	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
24.2b	(sqrt (fma b b (* (- a) (* 4.0 c))))

rewrite45.0ms

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`
10×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`associate-/r*` `neg-mul-1` `times-frac`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `associate-/r/` `flip--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 148

Calls

4 calls:

22.0ms	(/ (* 4.0 c) (- (- b) (sqrt (fma b b (* (- a) (* 4.0 c))))))
0.0ms	(fma b b (* (- a) (* 4.0 c)))
15.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
1.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (* 4.0 c) (- (- b) (sqrt (fma b b (* (- a) (* 4.0 c))))))
56.0ms	(fma b b (* (- a) (* 4.0 c)))
92.0ms	(- (- b) (sqrt (fma b b (* (- a) (* 4.0 c)))))
86.0ms	(sqrt (fma b b (* (- a) (* 4.0 c))))

simplify748.0ms

Counts

160 → 160

Iterations

Iter	Nodes
done	5001
2	2050
1	497
0	213

prune424.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

regimes247.0ms

Accuracy

93.1% (1.7b remaining)

Error of 7.0b against oracle of 5.3b and baseline of 29.6b

bsearch204.0ms

Steps

Iters	Range	Point
9	2.1340360609407003e+79	6.102484722804822e+84	1.7219779856274558e+83
6	-9.106238092000907e-243	-2.101224228167501e-243	-3.157831273622664e-243
5	-4.0529501114613944e+21	-1.3554105129294137e+21	-3.9950858563514354e+21

Iters

Range

Point

2.1340360609407003e+79

6.102484722804822e+84

1.7219779856274558e+83

-9.106238092000907e-243

-2.101224228167501e-243

-3.157831273622664e-243

-4.0529501114613944e+21

-1.3554105129294137e+21

-3.9950858563514354e+21

simplify15.0ms

Iterations

Iter	Nodes
done	66
3	66
2	59
1	55
0	43

end0.0ms

sample2.5s

Algorithm

intervals

Results

549.0ms	2886×	body	80	nan
411.0ms	1094×	body	2560	valid
403.0ms	448×	body	640	valid
375.0ms	5779×	body	80	valid
289.0ms	931×	body	1280	valid
66.0ms	93×	body	5120	valid
32.0ms	226×	body	320	valid
12.0ms	125×	body	160	valid