Details

sample95.0ms

Algorithm

intervals

Results

18.0ms	162×	body	160	valid
15.0ms	272×	body	80	nan
14.0ms	528×	pre	80	true
8.0ms	46×	body	320	valid
3.0ms	48×	body	80	valid

simplify114.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	111
5	111
4	102
3	78
2	44
1	24
0	14

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(- (* b b) (* (* 4.0 a) c))
94.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms	(- (* b b) (* (* 4.0 a) c))
127.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify759.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1908
1	419
0	154

prune503.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`clear-num` `sub-neg` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

25.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
99.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series540.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms	(- (* b b) (* (* 4.0 a) c))
218.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
179.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify1.7s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	3819
1	657
0	247

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
90×	`*-un-lft-identity`
56×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
27×	`add-cbrt-cube` `add-exp-log`
17×	`distribute-lft-out`
15×	`associate-/r*` `div-inv`
10×	`cbrt-undiv` `div-exp`
8×	`neg-mul-1` `associate-/l*` `add-log-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-/r/` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/`

Counts

4 → 171

Calls

4 calls:

17.0ms	(/ (* (* c a) 4.0) a)
68.0ms	(/ (/ (* (* c a) 4.0) a) (- (+ b (sqrt (- (* b b) (* (* c a) 4.0))))))
12.0ms	(+ b (sqrt (- (* b b) (* (* c a) 4.0))))
6.0ms	(- (* b b) (* (* c a) 4.0))

series394.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (* (* c a) 4.0) a)
225.0ms	(/ (/ (* (* c a) 4.0) a) (- (+ b (sqrt (- (* b b) (* (* c a) 4.0))))))
92.0ms	(+ b (sqrt (- (* b b) (* (* c a) 4.0))))
66.0ms	(- (* b b) (* (* c a) 4.0))

simplify441.0ms

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
1	834
0	295

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (/ (- (* (pow b 3) b) (* (* c c) (* (* a 4.0) (* a 4.0)))) (+ (* (* c 4.0) a) (pow b 2)))))
0.3b	(* (pow b 3) b)
0.4b	(* (* c c) (* (* a 4.0) (* a 4.0)))
0.5b	(/ (- (* (pow b 3) b) (* (* c c) (* (* a 4.0) (* a 4.0)))) (+ (* (* c 4.0) a) (pow b 2)))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
62×	`pow-prod-down`
52×	`add-exp-log`
49×	`add-cbrt-cube`
34×	`prod-exp`
32×	`cbrt-unprod`
23×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`pow-prod-up`
13×	`associate-l`
11×	`pow-plus`
9×	`times-frac`
8×	`pow-sqr`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `cube-prod` `associate-r`
3×	`associate-/r` `associate-/l`
2×	`pow2` `flip3-+` `associate-/r/` `*-commutative` `flip-+` `sqr-pow` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `unpow3` `div-sub` `div-exp` `pow-exp` `div-inv` `flip--` `distribute-lft-out`

Counts

4 → 135

Calls

4 calls:

117.0ms	(+ b (sqrt (/ (- (* (pow b 3) b) (* (* c c) (* (* a 4.0) (* a 4.0)))) (+ (* (* c 4.0) a) (pow b 2)))))
14.0ms	(* (pow b 3) b)
94.0ms	(* (* c c) (* (* a 4.0) (* a 4.0)))
57.0ms	(/ (- (* (pow b 3) b) (* (* c c) (* (* a 4.0) (* a 4.0)))) (+ (* (* c 4.0) a) (pow b 2)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(+ b (sqrt (/ (- (* (pow b 3) b) (* (* c c) (* (* a 4.0) (* a 4.0)))) (+ (* (* c 4.0) a) (pow b 2)))))
44.0ms	(* (pow b 3) b)
44.0ms	(* (* c c) (* (* a 4.0) (* a 4.0)))
124.0ms	(/ (- (* (pow b 3) b) (* (* c c) (* (* a 4.0) (* a 4.0)))) (+ (* (* c 4.0) a) (pow b 2)))

simplify2.3s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	4708
1	669
0	219

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes335.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	45
2	45
1	44
0	29

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.3s	4827×	body	160	valid
1.3s	8517×	body	80	nan
761.0ms	16517×	pre	80	true
300.0ms	1361×	body	320	valid
135.0ms	1812×	body	80	valid