Details

sample46.0ms

Algorithm

intervals

Results

9.0ms	536×	pre	80	true
9.0ms	144×	body	160	valid
8.0ms	280×	body	80	nan
4.0ms	112×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
29.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite55.0ms

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:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series251.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
44.0ms	(- (* b b) (* (* 3.0 a) c))
108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (47.0ms)

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

prune188.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite352.0ms

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))
160.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms	(* 3.0 (* a c))
177.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series354.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
163.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms	(* 3.0 (* a c))
129.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify115.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (84.0ms)

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

prune452.0ms

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)))

rewrite110.0ms

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))
22.0ms	(/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
46.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (- (* 3.0 a)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
46.0ms	(- (* b b) (* (* 3.0 a) c))
176.0ms	(/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
146.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (- (* 3.0 a)))

simplify122.0ms

Algorithm

egg-herbie

Counts

472 → 472

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1526	10150
1	5001	9892

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize15.0ms

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

rewrite841.0ms

Algorithm

rewrite-expression-head

Rules

13631×	`times-frac`
5692×	`add-sqr-sqrt` `*-un-lft-identity`
3952×	`add-cube-cbrt`
1588×	`distribute-rgt-neg-in`
1153×	`distribute-lft-neg-in` `neg-mul-1`
870×	`distribute-lft-out--` `difference-of-squares`
435×	`sqrt-prod`
338×	`div-inv`
315×	`associate-/r/`
194×	`associate-/r*`
146×	`flip3--` `flip--`
44×	`add-exp-log`
35×	`add-cbrt-cube`
28×	`associate-/l*`
27×	`div-exp`
18×	`cbrt-undiv`
9×	`pow1`
6×	`add-log-exp`
3×	`1-exp` `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 → 4134

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
27.0ms	(/ (- (* 3.0 a)) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
127.0ms	(/ (/ (- (* 3.0 a)) 1) (/ (- (* 3.0 a)) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
47.0ms	(- (* b b) (* (* 3.0 a) c))
156.0ms	(/ (- (* 3.0 a)) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
150.0ms	(/ (/ (- (* 3.0 a)) 1) (/ (- (* 3.0 a)) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))

simplify1.2s

Algorithm

egg-herbie

Counts

4146 → 4146

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5292	128692

prune12.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes163.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	33	22
1	45	21
2	45	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

290.0ms	16511×	pre	80	true
287.0ms	4451×	body	160	valid
256.0ms	8511×	body	80	nan
117.0ms	3549×	body	80	valid