Details

sample61.0ms

Algorithm

intervals

Results

11.0ms	110×	body	320	valid
10.0ms	569×	pre	80	true
10.0ms	313×	body	80	nan
7.0ms	96×	body	160	valid
2.0ms	12×	body	640	valid
1.0ms	38×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5002	674

prune190.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
145.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
182.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify120.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5003	2388

prune418.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.4b	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.5b	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-sqr-sqrt` `times-frac`
118×	`pow1`
92×	`*-un-lft-identity`
66×	`pow-prod-down`
56×	`add-exp-log` `add-cbrt-cube`
52×	`add-cube-cbrt`
42×	`difference-of-squares`
39×	`associate-/l*`
29×	`prod-exp` `cbrt-unprod`
20×	`sqrt-prod` `distribute-lft-out--`
12×	`associate-/r*`
10×	`distribute-rgt-neg-in`
9×	`pow-sqr` `pow-prod-up`
8×	`cbrt-undiv` `div-exp` `associate-/r/`
5×	`div-inv` `associate-/l/`
4×	`unpow-prod-down` `flip3--` `flip--` `add-log-exp` `sqr-pow`
3×	`frac-2neg` `pow-plus` `clear-num`
2×	`flip3-+` `flip-+`
1×	`pow2` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 235

Calls

4 calls:

114.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
75.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
22.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
30.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
226.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
92.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
35.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	993	5284
1	5002	4705

prune703.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 4.0 (/ 2.0 (* a c)))
0.3b	(/ 2.0 (* a c))
0.3b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.4b	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

389×	`times-frac`
281×	`add-sqr-sqrt`
255×	`*-un-lft-identity`
169×	`add-cube-cbrt`
117×	`add-exp-log`
85×	`associate-r`
77×	`add-cbrt-cube`
62×	`div-exp`
42×	`distribute-lft-out--` `difference-of-squares`
37×	`cbrt-undiv`
33×	`associate-/l*`
27×	`prod-exp`
26×	`associate-l`
21×	`distribute-rgt-neg-in` `sqrt-prod`
19×	`div-inv`
17×	`cbrt-unprod`
16×	`associate-/r/`
11×	`associate-/r*`
8×	`unswap-sqr`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 360

Calls

4 calls:

5.0ms	(/ 4.0 (/ 2.0 (* a c)))
5.0ms	(/ 2.0 (* a c))
37.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
109.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series315.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 4.0 (/ 2.0 (* a c)))
21.0ms	(/ 2.0 (* a c))
118.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
152.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify82.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1474	5495
1	5002	4888

prune862.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.4b 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	31	21
1	34	21
2	34	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

373.0ms	3582×	body	320	valid
290.0ms	16147×	pre	80	true
260.0ms	8147×	body	80	nan
200.0ms	2971×	body	160	valid
65.0ms	466×	body	640	valid
33.0ms	981×	body	80	valid