Details

sample242.0ms

Algorithm

intervals

Results

65.0ms	96×	body	160	valid
26.0ms	109×	body	320	valid
19.0ms	256×	body	80	nan
17.0ms	512×	pre	80	true
4.0ms	17×	body	640	valid
2.0ms	34×	body	80	valid

simplify138.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite180.0ms

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:

19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
57.0ms	(- (* b b) (* (* 4.0 a) c))
182.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
146.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2113
1	452
0	167

prune586.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma c (* 4.0 (- a)) (pow b 2))
0.1b	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.3b	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))
0.3b	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
60×	`prod-diff`
41×	`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/`
4×	`expm1-log1p-u` `pow1` `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` `sub-neg` `flip3-+` `neg-log` `flip-+` `fma-udef`

Counts

4 → 225

Calls

4 calls:

0.0ms	(fma c (* 4.0 (- a)) (pow b 2))
16.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
57.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))
54.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))

series642.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma c (* 4.0 (- a)) (pow b 2))
105.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
233.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))
231.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))

simplify1.9s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4041
1	781
0	322

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))) a)
0.1b	(fma 4.0 (- (* a c)) (* b b))
0.1b	(+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))
0.4b	(/ (* a c) (/ (* (- (+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))) a) 4.0))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-cbrt-cube` `add-exp-log`
19×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`times-frac` `add-cube-cbrt`
12×	`associate-l`
10×	`cbrt-undiv` `div-exp`
7×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`fma-def` `associate-r` `div-inv` `distribute-lft-out`
2×	`flip3-+` `associate-*l/` `flip-+` `distribute-neg-frac`
1×	`distribute-lft-neg-out` `+-commutative` `clear-num` `neg-mul-1` `sum-log` `frac-2neg` `pow-prod-down` `associate-/r/` `-commutative` `fma-udef` `associate-/l` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

80.0ms	(* (- (+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))) a)
0.0ms	(fma 4.0 (- (* a c)) (* b b))
11.0ms	(+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))
21.0ms	(/ (* a c) (/ (* (- (+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))) a) 4.0))

series579.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (- (+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))) a)
97.0ms	(fma 4.0 (- (* a c)) (* b b))
143.0ms	(+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))
189.0ms	(/ (* a c) (/ (* (- (+ b (sqrt (fma 4.0 (- (* a c)) (* b b))))) a) 4.0))

simplify2.1s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	3729
1	580
0	201

prune764.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

504×	`times-frac`
331×	`*-un-lft-identity`
245×	`add-sqr-sqrt` `add-cube-cbrt`
130×	`associate-l`
84×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
43×	`distribute-lft-out`
42×	`associate-/l*`
30×	`add-cbrt-cube` `add-exp-log`
21×	`neg-mul-1`
14×	`associate-/r/` `distribute-neg-frac`
9×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
8×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `fma-def` `pow-prod-down`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-r` `associate-l/` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 371

Calls

4 calls:

0.0ms	(fma 4.0 (* c (- a)) (* b b))
6.0ms	(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
70.0ms	(/ (/ a (- (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))) a)
162.0ms	(* (/ (/ a (- (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))) a) (* c 4.0))

series728.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(fma 4.0 (* c (- a)) (* b b))
118.0ms	(+ b (sqrt (fma 4.0 (* c (- a)) (* b b))))
265.0ms	(/ (/ a (- (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))) a)
228.0ms	(* (/ (/ a (- (+ b (sqrt (fma 4.0 (* c (- a)) (* b b)))))) a) (* c 4.0))

simplify800.0ms

Counts

383 → 383

Iterations

Iter	Nodes
done	5000
1	1625
0	512

prune3.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes245.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	33
3	33
2	32
1	27
0	20

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.2s	8233×	body	80	nan
1.1s	3662×	body	320	valid
661.0ms	16233×	pre	80	true
561.0ms	2940×	body	160	valid
138.0ms	471×	body	640	valid
66.0ms	927×	body	80	valid