Details

sample85.0ms

Algorithm

intervals

Results

22.0ms	246×	body	80	nan
19.0ms	136×	body	160	valid
18.0ms	502×	pre	80	true
10.0ms	120×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
27.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite62.0ms

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:

7.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
49.0ms	(- (* b b) (* (* 3.0 a) c))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	419	716
1	1930	613
2	5002	608

prune187.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* 3.0 (* a c))
0.3b	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
79×	`add-sqr-sqrt` `*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
23×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
10×	`distribute-rgt-neg-in` `sqrt-prod`
9×	`pow1`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`flip3--` `flip--` `div-inv`
3×	`div-sub` `associate-l` `pow-prod-down` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `clear-num`
1×	`sub-neg` `flip3-+` `diff-log` `associate-r` `*-commutative` `flip-+`

Counts

4 → 153

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(* 3.0 (* a c))
180.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
198.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series366.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
25.0ms	(* 3.0 (* a c))
165.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
131.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify110.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	701	3126
1	3188	2612
2	5003	2569

prune441.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

624×	`times-frac`
363×	`add-sqr-sqrt` `*-un-lft-identity`
167×	`add-cube-cbrt`
155×	`distribute-rgt-neg-in`
106×	`distribute-lft-neg-in` `neg-mul-1`
98×	`distribute-lft-out--` `difference-of-squares`
54×	`associate-/l*`
49×	`sqrt-prod`
16×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
13×	`associate-/r*`
9×	`pow1` `flip3--` `flip--` `div-inv`
6×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `distribute-frac-neg` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`neg-sub0` `frac-2neg` `clear-num`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 460

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
24.0ms	(/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
52.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (- (* 3.0 a)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
50.0ms	(- (* b b) (* (* 3.0 a) c))
185.0ms	(/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
150.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (- (* 3.0 a)))

simplify111.0ms

Algorithm

egg-herbie

Counts

472 → 472

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1526	10150
1	5001	9892

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

432×	`times-frac`
303×	`add-sqr-sqrt`
301×	`*-un-lft-identity`
137×	`add-cube-cbrt`
129×	`distribute-rgt-neg-in`
88×	`distribute-lft-neg-in`
86×	`associate-/l*`
82×	`distribute-lft-out--` `difference-of-squares`
80×	`associate-r`
41×	`sqrt-prod`
36×	`add-exp-log` `add-cbrt-cube`
30×	`neg-mul-1`
13×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r*` `associate-/r/`
6×	`pow1` `associate-l` `div-inv` `add-log-exp`
5×	`flip3--` `distribute-frac-neg` `flip--`
3×	`div-sub`
2×	`neg-sub0` `frac-2neg` `clear-num`
1×	`distribute-lft-neg-out` `sub-neg` `diff-log` `associate-r/` `pow-prod-down` `-commutative` `distribute-rgt-neg-out` `associate-/l/` `unswap-sqr`

Counts

4 → 398

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
27.0ms	(/ (- c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
97.0ms	(* (- (* 3.0 a)) (/ (/ (- c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a)))
54.0ms	(/ (/ (- c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series619.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* (* 3.0 a) c))
180.0ms	(/ (- c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
150.0ms	(* (- (* 3.0 a)) (/ (/ (- c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a)))
239.0ms	(/ (/ (- c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify81.0ms

Algorithm

egg-herbie

Counts

410 → 410

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1221	6285
1	5001	5929

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes147.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	27	14
1	35	14
2	47	12
3	58	12
4	73	12
5	95	12
6	118	12
7	118	12

end0.0ms

sample2.6s

Algorithm

intervals

Results

674.0ms	8613×	body	80	nan
642.0ms	4531×	body	160	valid
623.0ms	16613×	pre	80	true
289.0ms	3469×	body	80	valid