Details

sample52.0ms

Algorithm

intervals

Results

12.0ms	159×	body	160	valid
9.0ms	554×	pre	80	true
8.0ms	298×	body	80	nan
3.0ms	97×	body	80	valid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
29.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite113.0ms

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:

8.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(* (* 3.0 a) c)
64.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(* (* 3.0 a) c)
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.2s

Counts

105 → 105

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	167	1559
1	440	1478
2	1681	1247
done	5000	1234

prune222.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`prod-exp` `associate-/r*` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down` `associate-/r/`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 165

Calls

4 calls:

15.0ms	(* 3.0 (* a c))
16.0ms	(* (* 3.0 a) c)
56.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
85.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series371.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* 3.0 (* a c))
20.0ms	(* (* 3.0 a) c)
180.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
151.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify1.8s

Counts

177 → 177

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	251	4838
1	622	4351
2	2617	3972
done	5000	3970

prune411.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
83×	`times-frac`
72×	`add-sqr-sqrt`
68×	`add-cbrt-cube`
57×	`*-un-lft-identity`
49×	`associate-r`
41×	`div-exp` `prod-exp`
35×	`add-cube-cbrt`
25×	`cbrt-unprod`
22×	`cbrt-undiv`
16×	`pow1`
15×	`associate-l`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/`
7×	`pow-prod-down` `associate-/r*`
6×	`div-inv` `unswap-sqr`
5×	`rec-exp` `distribute-rgt-neg-in` `1-exp` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l*`

Counts

4 → 181

Calls

4 calls:

16.0ms	(* (* 3.0 a) c)
17.0ms	(* (* 3.0 a) c)
51.0ms	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
134.0ms	(* (/ 1 3.0) (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series570.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
20.0ms	(* (* 3.0 a) c)
378.0ms	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
153.0ms	(* (/ 1 3.0) (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

simplify1.5s

Counts

193 → 193

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	290	4842
1	869	4488
2	3794	3662
done	5001	3660

prune416.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
0.3b	(* (* 3.0 a) c)
0.4b	(* (* c (/ (* a 3.0) 3.0)) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

309×	`times-frac`
222×	`add-sqr-sqrt` `*-un-lft-identity`
138×	`add-cube-cbrt`
108×	`add-exp-log`
88×	`associate-r`
68×	`add-cbrt-cube`
43×	`prod-exp`
42×	`distribute-lft-out--` `difference-of-squares`
40×	`div-exp`
27×	`cbrt-unprod` `associate-/l*`
21×	`cbrt-undiv` `distribute-rgt-neg-in` `sqrt-prod`
14×	`pow1` `associate-/r/`
9×	`div-inv`
8×	`flip3--` `flip--`
6×	`pow-prod-down` `add-log-exp`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r/` `associate-/r`
2×	`associate-l` `*-commutative`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `associate-*l/` `clear-num` `associate-/l/`

Counts

4 → 299

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
65.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
16.0ms	(* (* 3.0 a) c)
124.0ms	(* (* c (/ (* a 3.0) 3.0)) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series374.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 3.0 a) c))
122.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
20.0ms	(* (* 3.0 a) c)
183.0ms	(* (* c (/ (* a 3.0) 3.0)) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

simplify2.1s

Counts

311 → 311

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	430	8868
1	1203	7983
2	4129	6495
done	5000	6494

prune554.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes131.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	17	19
done	17	19

end0.0ms

sample1.3s

Algorithm

intervals

Results

276.0ms	16543×	pre	80	true
269.0ms	4488×	body	160	valid
248.0ms	8543×	body	80	nan
108.0ms	3512×	body	80	valid