Details

sample52.0ms

Algorithm

intervals

Results

12.0ms	123×	body	320	valid
9.0ms	511×	pre	80	true
8.0ms	255×	body	80	nan
6.0ms	87×	body	160	valid
2.0ms	13×	body	640	valid
1.0ms	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.9b

localize13.0ms

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))))

rewrite54.0ms

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))
33.0ms	(/ (+ (- 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))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
23.0ms	(* (* 3.0 a) c)
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

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

prune179.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

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))

rewrite356.0ms

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)
160.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
5.0ms	(* 3.0 (* a c))
179.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series333.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
164.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms	(* 3.0 (* a c))
130.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify112.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (88.0ms)

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

prune439.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize27.0ms

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))

rewrite434.0ms

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:

7.0ms	(* 3.0 (* a c))
129.0ms	(/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
215.0ms	(* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
74.0ms	(/ (* (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))

series1.2s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* 3.0 (* a c))
297.0ms	(/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
434.0ms	(* (sqrt (* (* 3.0 a) c)) (/ (sqrt (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
405.0ms	(/ (* (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))

simplify119.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (88.0ms)

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

prune505.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 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) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(/ (* 1 (/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
37×	`add-cbrt-cube`
34×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`times-frac`
19×	`prod-exp`
18×	`add-cube-cbrt`
15×	`div-exp`
14×	`pow1`
13×	`cbrt-unprod`
9×	`cbrt-undiv`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
6×	`associate-r` `pow-prod-down`
4×	`distribute-rgt-neg-in` `1-exp` `sqrt-prod` `associate-/l*` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `associate-l` `clear-num` `associate-/r/` `*-commutative` `div-inv`
1×	`flip3--` `flip3-+` `associate-*r/` `flip--` `flip-+`

Counts

4 → 113

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
6.0ms	(* (* 3.0 a) c)
35.0ms	(/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.0ms	(/ (* 1 (/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

series372.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
20.0ms	(* (* 3.0 a) c)
178.0ms	(/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
150.0ms	(/ (* 1 (/ (+ (* (* 3.0 a) c) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

simplify104.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	543	1620
1	3295	1308
2	5001	1292

prune248.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes111.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	14
1	26	14
2	26	14

end0.0ms

sample1.5s

Algorithm

intervals

Results

346.0ms	3611×	body	320	valid
287.0ms	16130×	pre	80	true
254.0ms	8130×	body	80	nan
189.0ms	2981×	body	160	valid
65.0ms	501×	body	640	valid
29.0ms	907×	body	80	valid