Details

sample93.0ms

Algorithm

intervals

Results

27.0ms	253×	body	80	nan
15.0ms	143×	body	160	valid
13.0ms	509×	pre	80	true
6.0ms	113×	body	80	valid

simplify159.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

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:

18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(- (* b b) (* (* 4.0 a) c))
57.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
166.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms	(- (* b b) (* (* 4.0 a) c))
125.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1484	1361
done	5000	1347

prune468.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(- (* 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)))))

rewrite252.0ms

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:

38.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
107.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
84.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms	(- (* b b) (* (* 4.0 a) c))
222.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
303.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.8s

Counts

243 → 243

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	338	10026
1	802	7598
2	3039	6483
done	5001	6397

prune840.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3))))) (* 2.0 a))
0.3b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3)))))
0.5b	(cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3))
0.7b	(pow (fma b b (* (* 4.0 a) (- c))) 3)

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
138×	`times-frac`
96×	`*-un-lft-identity`
60×	`difference-of-squares`
56×	`add-cube-cbrt`
52×	`cbrt-prod`
50×	`sqrt-prod`
42×	`associate-/l*`
20×	`distribute-lft-out--`
19×	`add-exp-log` `add-cbrt-cube`
16×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*` `sqr-pow`
10×	`distribute-rgt-neg-in`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `flip3--` `flip--` `associate-/l/`
2×	`cube-mult` `frac-2neg` `unpow3` `prod-exp` `clear-num` `cbrt-unprod`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `pow-exp` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 213

Calls

4 calls:

114.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3))))) (* 2.0 a))
85.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3)))))
2.0ms	(cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3))
3.0ms	(pow (fma b b (* (* 4.0 a) (- c))) 3)

series748.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3))))) (* 2.0 a))
315.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3)))))
86.0ms	(cbrt (pow (fma b b (* (* 4.0 a) (- c))) 3))
146.0ms	(pow (fma b b (* (* 4.0 a) (- c))) 3)

simplify1.7s

Counts

225 → 225

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	333	7874
1	761	6439
2	2929	6026
done	5001	6024

prune931.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 2)) (cbrt (fma b b (* (* 4.0 a) (- c)))))
0.5b	(cbrt (fma b b (* (* 4.0 a) (- c))))
0.5b	(pow (fma b b (* (* 4.0 a) (- c))) 2)
0.6b	(cbrt (pow (fma b b (* (* 4.0 a) (- c))) 2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
30×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`unpow-prod-down` `associate-l`
10×	`unswap-sqr`
7×	`pow1` `add-exp-log`
6×	`associate-r` `unpow2`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-prod-down`
1×	`pow-to-exp` `pow-pow` `pow3` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

31.0ms	(* (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 2)) (cbrt (fma b b (* (* 4.0 a) (- c)))))
1.0ms	(cbrt (fma b b (* (* 4.0 a) (- c))))
5.0ms	(pow (fma b b (* (* 4.0 a) (- c))) 2)
4.0ms	(cbrt (pow (fma b b (* (* 4.0 a) (- c))) 2))

series546.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (cbrt (pow (fma b b (* (* 4.0 a) (- c))) 2)) (cbrt (fma b b (* (* 4.0 a) (- c)))))
162.0ms	(cbrt (fma b b (* (* 4.0 a) (- c))))
91.0ms	(pow (fma b b (* (* 4.0 a) (- c))) 2)
193.0ms	(cbrt (pow (fma b b (* (* 4.0 a) (- c))) 2))

simplify1.9s

Counts

105 → 105

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	159	2307
1	328	2146
2	780	2003
3	2286	1974
done	5000	1898

prune657.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes317.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify24.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	32	54
1	42	52
2	48	52
3	54	52
done	54	52

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.3s	4499×	body	160	valid
1.1s	8644×	body	80	nan
708.0ms	16644×	pre	80	true
274.0ms	3501×	body	80	valid