Details

sample50.0ms

Algorithm

intervals

Results

11.0ms	487×	pre	80	true
11.0ms	163×	body	160	valid
7.0ms	231×	body	80	nan
3.0ms	35×	body	320	valid
2.0ms	58×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
40.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite30.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(* (* 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))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(* (* 3.0 a) c)
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

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

prune174.0ms

Filtered

85 candidates to 59 candidates (69.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

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))

rewrite73.0ms

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:

5.0ms	(* (* 3.0 a) c)
26.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
5.0ms	(* 3.0 (* a c))
31.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series324.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
161.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms	(* 3.0 (* a c))
125.0ms	(/ (/ (+ (- (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

171 → 171

Iterations

Useful iterations: 2 (87.0ms)

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

prune428.0ms

Filtered

171 candidates to 106 candidates (62.0%)

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

rewrite72.0ms

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×	`associate-r` `pow-prod-down` `associate-/r/`
4×	`div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `flip--` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 159

Calls

4 calls:

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

series325.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* 3.0 a) c)
18.0ms	(* (* 3.0 a) c)
161.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
123.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify102.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	627	3101
1	3139	2568
2	5001	2534

prune389.0ms

Filtered

171 candidates to 103 candidates (60.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
238×	`add-sqr-sqrt`
227×	`*-un-lft-identity`
142×	`add-cube-cbrt`
117×	`add-exp-log`
86×	`associate-r`
77×	`add-cbrt-cube`
48×	`div-exp`
42×	`distribute-lft-out--` `difference-of-squares`
41×	`prod-exp`
28×	`associate-/l*`
27×	`cbrt-undiv` `cbrt-unprod`
21×	`distribute-rgt-neg-in` `sqrt-prod`
14×	`associate-/r/`
11×	`pow1` `div-inv`
10×	`associate-l`
7×	`flip3--` `flip--`
6×	`associate-/r*`
5×	`rec-exp` `1-exp`
4×	`pow-prod-down` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `associate-l/` `associate-/l/`

Counts

4 → 309

Calls

4 calls:

6.0ms	(/ (* 3.0 (* a c)) 3.0)
18.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
5.0ms	(* 3.0 (* a c))
37.0ms	(* (/ (* 3.0 (* a c)) 3.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series311.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (* 3.0 (* a c)) 3.0)
118.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
19.0ms	(* 3.0 (* a c))
151.0ms	(* (/ (* 3.0 (* a c)) 3.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

simplify64.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1256	4905
1	5001	4302

prune639.0ms

Filtered

321 candidates to 168 candidates (52.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes142.0ms

Accuracy

0% (0.4b 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	20	16
1	20	16

end0.0ms

sample1.4s

Algorithm

intervals

Results

317.0ms	4901×	body	160	valid
297.0ms	16403×	pre	80	true
256.0ms	8403×	body	80	nan
135.0ms	1396×	body	320	valid
55.0ms	1703×	body	80	valid