Details

sample546.0ms

Algorithm

intervals

Results

453.0ms	521×	pre	80	true
21.0ms	108×	body	320	valid
17.0ms	265×	body	80	nan
14.0ms	108×	body	160	valid
3.0ms	13×	body	640	valid
2.0ms	27×	body	80	valid

simplify140.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	76	16
4	96	16
5	104	16
done	104	16

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
28.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
45.0ms	(* (* 3.0 a) c)
45.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* b b) (* (* 3.0 a) c))
146.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
34.0ms	(* (* 3.0 a) c)
99.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify2.3s

Counts

85 → 85

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	154	1437
1	437	1361
2	2551	1143
done	5002	1133

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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 (- (pow b 2) (* 3.0 (* a c))))))
0.4b	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (* 3.0 a))

rewrite368.0ms

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×	`associate-r` `associate-l` `div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 157

Calls

4 calls:

31.0ms	(* (* 3.0 a) c)
16.0ms	(* 3.0 (* a c))
137.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
170.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (* 3.0 a))

series618.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 3.0 a) c)
30.0ms	(* 3.0 (* a c))
309.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
247.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (* 3.0 a))

simplify3.3s

Counts

169 → 169

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	243	4718
1	652	4242
2	4422	3884
done	5001	3880

prune756.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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 (- (pow b 2) (* 3.0 (* a c))))))
0.3b	(* (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (/ 1 (* 3.0 a)))

rewrite497.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
61×	`add-exp-log`
59×	`*-un-lft-identity`
46×	`times-frac`
37×	`add-cbrt-cube`
31×	`add-cube-cbrt` `associate-l`
26×	`prod-exp`
16×	`pow1` `div-exp`
14×	`cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
11×	`associate-r`
8×	`cbrt-undiv`
7×	`distribute-rgt-neg-in` `pow-prod-down` `associate-/r*` `sqrt-prod`
4×	`rec-exp` `1-exp` `associate-/r/` `add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `associate-l/` `clear-num` `un-div-inv` `flip-+`

Counts

4 → 152

Calls

4 calls:

34.0ms	(* (* 3.0 a) c)
32.0ms	(* 3.0 (* a c))
118.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
298.0ms	(* (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (/ 1 (* 3.0 a)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* 3.0 a) c)
41.0ms	(* 3.0 (* a c))
292.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
219.0ms	(* (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c)))))) (/ 1 (* 3.0 a)))

simplify540.0ms

Counts

164 → 164

Iterations

Useful iterations: done (531.0ms)

Iter	Nodes	Cost
0	249	4308
1	745	3808
done	5000	3318

prune735.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* (* a c) 3.0) (* 3.0 a)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
0.3b	(* (* a c) 3.0)
0.3b	(* 3.0 (* a c))
0.3b	(/ (* (* a c) 3.0) (* 3.0 a))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log` `add-cbrt-cube`
44×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac`
24×	`prod-exp` `cbrt-unprod`
20×	`add-cube-cbrt`
19×	`cbrt-undiv` `div-exp`
14×	`pow1`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`div-inv`
8×	`associate-/r*`
6×	`distribute-rgt-neg-in` `pow-prod-down` `sqrt-prod` `associate-/l*`
4×	`associate-r` `associate-l` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/` `*-commutative`
1×	`flip3--` `flip--` `associate-/l/`

Counts

4 → 135

Calls

4 calls:

130.0ms	(/ (/ (* (* a c) 3.0) (* 3.0 a)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
36.0ms	(* (* a c) 3.0)
41.0ms	(* 3.0 (* a c))
23.0ms	(/ (* (* a c) 3.0) (* 3.0 a))

series296.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (/ (* (* a c) 3.0) (* 3.0 a)) (- (- b) (sqrt (- (pow b 2) (* 3.0 (* a c))))))
21.0ms	(* (* a c) 3.0)
33.0ms	(* 3.0 (* a c))
27.0ms	(/ (* (* a c) 3.0) (* 3.0 a))

simplify3.3s

Counts

147 → 147

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	201	3550
1	596	3453
2	4854	2771
done	5001	2771

prune602.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes172.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	19
1	23	17
2	24	17
done	24	17

end1.0ms

sample4.9s

Algorithm

intervals

Results

1.2s	16302×	pre	80	true
1.0s	3545×	body	320	valid
1.0s	8302×	body	80	nan
478.0ms	3015×	body	160	valid
231.0ms	487×	body	640	valid
69.0ms	953×	body	80	valid