Details

sample230.0ms

Algorithm

intervals

Results

25.0ms	116×	body	320	valid
19.0ms	252×	body	80	nan
17.0ms	508×	pre	80	true
15.0ms	100×	body	160	valid
6.0ms	21×	body	640	valid
2.0ms	19×	body	80	valid

simplify204.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
60.0ms	(- (* b b) (* (* 4.0 a) c))
140.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
137.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts

82 → 82

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	154	1565
1	401	1461
2	1342	1245
done	5001	1233

prune325.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite346.0ms

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-exp-log` `add-cbrt-cube`
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×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

16.0ms	(- (* b b) (* (* 4.0 a) c))
48.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
121.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series753.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b b) (* (* 4.0 a) c))
140.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
249.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
297.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.6s

Counts

163 → 163

Iterations

Useful iterations: 2 (661.0ms)

Iter	Nodes	Cost
0	247	5048
1	612	4510
2	2499	4166
done	5000	4166

prune692.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

338×	`times-frac`
267×	`add-sqr-sqrt`
256×	`*-un-lft-identity`
151×	`add-cube-cbrt`
107×	`add-exp-log`
85×	`associate-r`
65×	`add-cbrt-cube`
52×	`distribute-lft-out--` `difference-of-squares`
47×	`div-exp`
35×	`prod-exp`
30×	`associate-/l*`
26×	`distribute-rgt-neg-in` `sqrt-prod`
25×	`cbrt-undiv`
21×	`cbrt-unprod`
16×	`associate-/r/`
11×	`div-inv`
10×	`associate-/r*`
9×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`pow1` `associate-l`
6×	`rec-exp` `1-exp`
4×	`unswap-sqr`
2×	`frac-2neg` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `pow-flip` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 335

Calls

4 calls:

43.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
57.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
91.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
196.0ms	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series638.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
164.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
211.0ms	(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify2.3s

Counts

347 → 347

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	432	10281
1	1197	9280
2	3923	8279
done	5001	8279

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))))) (* 2.0 a))
0.3b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3)))))
0.5b	(cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))
0.7b	(pow (- (pow b 2) (* 4.0 (* a c))) 3)

rewrite477.0ms

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` `flip3--` `flip--`
4×	`cube-div` `div-inv` `add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-mult` `cbrt-div` `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 → 209

Calls

4 calls:

216.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))))) (* 2.0 a))
198.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3)))))
20.0ms	(cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))
31.0ms	(pow (- (pow b 2) (* 4.0 (* a c))) 3)

series748.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))))) (* 2.0 a))
314.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3)))))
60.0ms	(cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))
135.0ms	(pow (- (pow b 2) (* 4.0 (* a c))) 3)

simplify2.0s

Counts

221 → 221

Iterations

Useful iterations: 2 (835.0ms)

Iter	Nodes	Cost
0	340	7876
1	808	6400
2	3258	6014
done	5000	6014

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes147.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	25
1	26	25
done	26	25

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.2s	16302×	pre	80	true
941.0ms	3635×	body	320	valid
811.0ms	8302×	body	80	nan
594.0ms	2951×	body	160	valid
581.0ms	513×	body	640	valid
65.0ms	901×	body	80	valid