Details

sample59.0ms

Algorithm

intervals

Results

13.0ms	314×	body	80	nan
10.0ms	150×	body	160	valid
10.0ms	570×	pre	80	true
4.0ms	106×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9
done	121	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5002	735
done	5002	735

prune255.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`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-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 231

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
194.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify148.0ms

Counts

243 → 243

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	832	5100
1	3967	3830
2	5001	3828
done	5001	3828

prune552.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
0.3b	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
0.3b	(* (* a c) (fma b b (* (* 4.0 a) c)))
0.7b	(pow (* (* 4.0 a) c) 3)

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `times-frac`
36×	`difference-of-squares`
34×	`add-cube-cbrt`
21×	`sqr-pow`
19×	`add-exp-log` `add-cbrt-cube`
15×	`pow1`
13×	`associate-/l*`
12×	`distribute-lft-out--`
11×	`associate-/r*`
9×	`unpow-prod-down`
8×	`sqrt-prod`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-r` `pow-exp` `rem-cube-cbrt`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `associate-/r/` `flip--` `fma-udef` `div-inv`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `distribute-lft-in` `flip3-+` `unpow3` `div-sub` `cube-prod` `associate-l` `*-commutative` `flip-+`

Counts

4 → 162

Calls

4 calls:

133.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
51.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
17.0ms	(* (* a c) (fma b b (* (* 4.0 a) c)))
16.0ms	(pow (* (* 4.0 a) c) 3)

series548.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
137.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
65.0ms	(* (* a c) (fma b b (* (* 4.0 a) c)))
59.0ms	(pow (* (* 4.0 a) c) 3)

simplify143.0ms

Counts

174 → 174

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	753	3354
1	3724	3127
2	5001	3123
done	5001	3123

prune797.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (* 64.0 (* (pow a 3) (pow c 3)))) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
0.3b	(* (pow a 3) (pow c 3))
0.3b	(/ (- (pow b 6) (* 64.0 (* (pow a 3) (pow c 3)))) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
0.3b	(* (* a c) (fma b b (* (* 4.0 a) c)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
37×	`times-frac`
32×	`add-cube-cbrt`
25×	`add-exp-log`
16×	`unswap-sqr`
15×	`associate-r` `add-cbrt-cube`
14×	`unpow-prod-down` `cube-prod`
13×	`associate-l`
12×	`prod-exp` `difference-of-squares`
11×	`associate-/r*`
10×	`sqr-pow`
9×	`pow1`
8×	`sqrt-prod` `distribute-lft-out--`
6×	`pow-to-exp` `pow-exp` `associate-/l*`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `cube-mult` `flip3--` `frac-2neg` `unpow3` `div-exp` `clear-num` `associate-/r/` `*-commutative` `flip--` `fma-udef` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `div-sub` `flip-+`

Counts

4 → 168

Calls

4 calls:

86.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (* 64.0 (* (pow a 3) (pow c 3)))) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
20.0ms	(* (pow a 3) (pow c 3))
37.0ms	(/ (- (pow b 6) (* 64.0 (* (pow a 3) (pow c 3)))) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
17.0ms	(* (* a c) (fma b b (* (* 4.0 a) c)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (* 64.0 (* (pow a 3) (pow c 3)))) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4))))))
61.0ms	(* (pow a 3) (pow c 3))
138.0ms	(/ (- (pow b 6) (* 64.0 (* (pow a 3) (pow c 3)))) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
62.0ms	(* (* a c) (fma b b (* (* 4.0 a) c)))

simplify154.0ms

Counts

180 → 180

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	728	2939
1	4240	2703
2	5001	2702
done	5001	2702

prune824.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes165.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	43	23
2	43	23
done	43	23

end0.0ms

sample1.5s

Algorithm

intervals

Results

306.0ms	4423×	body	160	valid
283.0ms	16584×	pre	80	true
280.0ms	8584×	body	80	nan
122.0ms	3577×	body	80	valid