Details

sample50.0ms

Algorithm

intervals

Results

10.0ms	510×	pre	80	true
9.0ms	134×	body	160	valid
8.0ms	254×	body	80	nan
7.0ms	122×	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: 27.0b

localize11.0ms

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))
26.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite29.0ms

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:

5.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
45.0ms	(- (* b b) (* (* 3.0 a) c))
112.0ms	(/ (+ (- 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

prune182.0ms

Pruning

7 alts after pruning (7 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	(/ (+ (- (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))

rewrite70.0ms

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))
25.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
5.0ms	(* 3.0 (* a c))
28.0ms	(/ (/ (+ (- (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:

50.0ms	(- (* b b) (* (* 3.0 a) c))
169.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.0ms	(* 3.0 (* a c))
127.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify107.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (82.0ms)

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

prune447.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(* (* 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))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

438×	`times-frac`
272×	`add-sqr-sqrt` `*-un-lft-identity`
226×	`distribute-rgt-neg-in`
188×	`distribute-lft-neg-in`
120×	`add-cube-cbrt` `associate-/l*`
76×	`distribute-lft-out--` `difference-of-squares`
74×	`neg-mul-1`
38×	`sqrt-prod`
28×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
14×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `pow-prod-down` `associate-/r/` `distribute-neg-frac`
4×	`div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `distribute-frac-neg` `flip--`
2×	`neg-sub0` `frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 434

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
5.0ms	(* (* 3.0 a) c)
14.0ms	(/ (- (* (* 3.0 a) c)) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
32.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

series393.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
20.0ms	(* (* 3.0 a) c)
195.0ms	(/ (- (* (* 3.0 a) c)) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
158.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

simplify94.0ms

Algorithm

egg-herbie

Counts

446 → 446

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1182	7821
1	5001	7548

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.4b	(/ (/ (* 3.0 a) 1) (/ (* 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)))))))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

5387×	`times-frac`
2047×	`add-sqr-sqrt` `*-un-lft-identity`
1440×	`distribute-rgt-neg-in`
1247×	`add-cube-cbrt`
1240×	`distribute-lft-neg-in`
400×	`distribute-lft-out--` `difference-of-squares`
377×	`associate-/r*`
280×	`neg-mul-1`
212×	`div-inv`
200×	`sqrt-prod`
131×	`add-exp-log`
90×	`add-cbrt-cube`
81×	`div-exp`
49×	`cbrt-undiv`
30×	`associate-/r/`
25×	`prod-exp`
20×	`distribute-neg-frac`
16×	`cbrt-unprod`
11×	`flip3--` `flip--`
10×	`1-exp`
9×	`pow1`
8×	`associate-/l*`
6×	`add-log-exp`
3×	`associate-r` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 2009

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(/ (/ (* 3.0 a) 1) (/ (* 3.0 a) (/ (- c) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))))
38.0ms	(/ (* 3.0 a) (/ (- c) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
47.0ms	(- (* b b) (* (* 3.0 a) c))
155.0ms	(/ (/ (* 3.0 a) 1) (/ (* 3.0 a) (/ (- c) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))))
155.0ms	(/ (* 3.0 a) (/ (- c) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))

simplify439.0ms

Algorithm

egg-herbie

Counts

2021 → 2021

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	47357

prune4.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes174.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	10
1	24	10
2	24	10

end0.0ms

sample1.4s

Algorithm

intervals

Results

316.0ms	16495×	pre	80	true
303.0ms	4435×	body	160	valid
279.0ms	8495×	body	80	nan
123.0ms	3565×	body	80	valid