Details

sample100.0ms

Algorithm

intervals

Results

24.0ms	123×	body	320	valid
23.0ms	511×	pre	80	true
18.0ms	255×	body	80	nan
11.0ms	87×	body	160	valid
4.0ms	13×	body	640	valid
2.0ms	33×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.9b

localize10.0ms

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)
27.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite57.0ms

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:

2.0ms	(- (* b b) (* (* 3.0 a) c))
35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(* (* 3.0 a) c)
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms	(* (* 3.0 a) c)
16.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (46.0ms)

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

prune561.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite364.0ms

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--` `div-sub` `flip--` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 159

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
164.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms	(* 3.0 (* a c))
180.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series83.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
42.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(* 3.0 (* a c))
33.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify109.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	684	3100
1	3307	2567
2	5001	2533

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite445.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
102×	`*-un-lft-identity`
87×	`times-frac`
60×	`sqrt-prod`
50×	`add-cube-cbrt`
49×	`associate-r`
37×	`add-exp-log` `add-cbrt-cube`
26×	`distribute-lft-out--` `difference-of-squares`
13×	`distribute-rgt-neg-in`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
10×	`cbrt-undiv` `div-exp`
8×	`associate-/r*`
7×	`associate-l` `associate-/l*`
4×	`pow-prod-down` `associate-/r/` `add-log-exp`
3×	`div-inv` `associate-/l/` `unswap-sqr`
2×	`flip3--` `frac-2neg` `sqrt-div` `associate-r/` `clear-num` `-commutative` `flip--`
1×	`flip3-+` `flip-+`

Counts

4 → 184

Calls

4 calls:

6.0ms	(* 3.0 (* a c))
133.0ms	(/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
222.0ms	(* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
76.0ms	(/ (* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

series211.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 3.0 (* a c))
51.0ms	(/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
81.0ms	(* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
75.0ms	(/ (* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

simplify116.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	716	4188
1	3731	3569
2	5001	3275

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize13.0ms

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

624×	`times-frac`
364×	`add-sqr-sqrt` `*-un-lft-identity`
168×	`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`
21×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r/`
14×	`pow1`
13×	`associate-/r*`
9×	`div-inv`
8×	`flip3--` `flip--`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`div-sub` `distribute-frac-neg`
2×	`neg-sub0` `frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 466

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
8.0ms	(* (* 3.0 a) c)
22.0ms	(/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
47.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (- (* 3.0 a)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
4.0ms	(* (* 3.0 a) c)
53.0ms	(/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
45.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (- (* 3.0 a)))

simplify109.0ms

Algorithm

egg-herbie

Counts

478 → 478

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1469	10133
1	5002	9864

prune3.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes353.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	14
1	32	14
2	32	14

end0.0ms

sample2.9s

Algorithm

intervals

Results

744.0ms	16130×	pre	80	true
721.0ms	3611×	body	320	valid
522.0ms	8130×	body	80	nan
393.0ms	2981×	body	160	valid
132.0ms	501×	body	640	valid
59.0ms	907×	body	80	valid