Details

sample118.0ms

Algorithm

intervals

Results

24.0ms	144×	body	160	valid
20.0ms	255×	body	80	nan
19.0ms	511×	pre	80	true
9.0ms	112×	body	80	valid

simplify161.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
28.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `add-log-exp`
9×	`pow1`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 93

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
9.0ms	(- (* b b) (* (* 3.0 a) c))
86.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
49.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* 3.0 a) c)
66.0ms	(- (* b b) (* (* 3.0 a) c))
177.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
124.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.8s

Counts

105 → 105

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	167	1559
1	440	1478
2	1676	1247
done	5001	1234

prune388.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.3b	(- (* b b) (* (* 3.0 a) c))
0.4b	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
0.4b	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite287.0ms

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:

42.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms	(- (* b b) (* (* 3.0 a) c))
112.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
102.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series704.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
61.0ms	(- (* b b) (* (* 3.0 a) c))
231.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
269.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify2.1s

Counts

243 → 243

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	337	10026
1	798	7598
2	3007	6483
done	5001	6397

prune936.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.3b	(* 3.0 (* a c))
0.4b	(* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(/ (* 3.0 a) (* 3.0 (* a c)))

rewrite598.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-exp-log`
120×	`prod-diff`
97×	`add-cbrt-cube`
91×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
85×	`add-cube-cbrt`
76×	`prod-exp`
62×	`distribute-rgt-in` `distribute-lft-in`
61×	`sqrt-prod`
46×	`div-exp`
44×	`cbrt-unprod`
37×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
26×	`cbrt-undiv`
14×	`pow1`
12×	`neg-mul-1`
8×	`rec-exp` `1-exp` `associate-r` `associate-l`
5×	`times-frac` `pow-prod-down` `associate-/r/`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-r/` `flip--` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`div-inv`
2×	`sub-neg` `pow-flip` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`inv-pow` `unswap-sqr`

Counts

4 → 273

Calls

4 calls:

227.0ms	(/ 1 (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.0ms	(* 3.0 (* a c))
277.0ms	(* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
56.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(/ 1 (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
37.0ms	(* 3.0 (* a c))
139.0ms	(* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
16.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))

simplify3.5s

Counts

285 → 285

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	413	16095
1	1074	11356
2	4383	7155
done	5000	7154

prune604.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ c 1))
0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ 1 (+ (* (/ 1 c) (- b)) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ c 1))))
0.3b	(* (/ 1 c) (- b))

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

395×	`times-frac`
222×	`*-un-lft-identity`
220×	`add-sqr-sqrt`
213×	`add-cube-cbrt`
91×	`distribute-rgt-neg-in`
87×	`distribute-lft-neg-in`
84×	`sqrt-prod`
28×	`div-inv`
24×	`add-exp-log`
19×	`associate-/l*`
18×	`associate-/r*`
16×	`add-cbrt-cube`
15×	`neg-mul-1`
13×	`associate-l`
10×	`associate-r`
9×	`div-exp`
8×	`distribute-lft-out`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`1-exp` `unswap-sqr`
2×	`rec-exp` `flip3--` `frac-2neg` `sqrt-div` `associate-*l/` `clear-num` `flip--` `cbrt-unprod` `associate-/l/` `distribute-neg-frac`
1×	`neg-sub0` `sub-neg` `pow-flip` `flip3-+` `fma-neg` `diff-log` `div-sub` `distribute-frac-neg` `prod-diff` `pow-prod-down` `frac-add` `*-commutative` `distribute-rgt-neg-out` `flip-+` `inv-pow`

Counts

4 → 364

Calls

4 calls:

78.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ c 1))
20.0ms	(- (* b b) (* (* 3.0 a) c))
231.0ms	(/ 1 (+ (* (/ 1 c) (- b)) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ c 1))))
54.0ms	(* (/ 1 c) (- b))

series513.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ c 1))
49.0ms	(- (* b b) (* (* 3.0 a) c))
275.0ms	(/ 1 (+ (* (/ 1 c) (- b)) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ c 1))))
23.0ms	(* (/ 1 c) (- b))

simplify1.9s

Counts

376 → 376

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	567	10232
1	1318	7990
2	2771	7716
done	5000	7713

prune806.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes254.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	27	44
1	36	42
2	44	41
3	48	41
done	48	41

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	8506×	body	80	nan
729.0ms	4451×	body	160	valid
678.0ms	16506×	pre	80	true
280.0ms	3549×	body	80	valid